srAnsTmAL mamas or Amean :1 ‘ ; cosr Accoumemms r; , U i » ; ~, . _ ‘. Thesis: for the {agree 015%). D. memcm S‘i’A‘e’E UNIVERSITY .. . ' ROGER ALIAN ROEMMCH - 7 1975 '. ' This is to certify that the thesis entitled "A Statistical Analysis of Alternative Cost Accounting Methods" presented by Roger Roemmich has been accepted towards fulfillment of the requirements for Ph.D. , Business Administration degree 1]] 0-7639 | l I costs to action. estimate mEthods methOds ABSTRACT STATISTICAL ANALYSIS OF ALTERNATIVE COST ACCOUNTING METHODS BY Roger Allan Roemmich Decision makers require accurate estimates of future costs to allow them to choose between alternative courses of action. The discipline to which they turn for these cost estimates is cost accounting. Cost accounting literature suggests four alternative methods for estimating future costs. These alternative methods are: 1. Direct costing (using the account classifica- tion approach). 2. Full costing. 3. Simple linear regression or mixed costing. 4. Multiple regression. This study attempts to evaluate these four alterna- tive methods of cost estimation in terms of the predictive accuracy of cost projections. Three different measures of Predictive accuracy are employed in this study. These measures are average relative error, average absolute rela- tive error, and average squared relative error. *3 very 13!? annual cc 1972 for indirect The secon has provi the peric generate the cost 1972-191 diction: 0f the finding °°ntrik The data examined in this study are provided by two very large banks. One bank with 83 branches has provided annual cost and statistical information for the period 1963— 1972 for ten branches, which were randomly selected, and indirect cost data for the overall bank for the same period. The second bank providing data has 46 branches. This bank has provided annual cost and statistical information for the period 1970-1973 for each of the 46 branches. Based upon the data provided, predictions are generated under each of the alternative costing models for the costs of the last two years (1971-1972 for Bank A and 1972-1973 for Bank B) for each of the branches. These pre- dictions are then evaluated for predictive accuracy in terms of the three types of error measures. One of the dangers of employing each of the methods concerns the underlying assumptions of the methods. Viola- tions of these assumptions limit the generalization of findings and result in inaccurate estimates of marginal contribution of cost factors. The two methods for which this danger is greatest are simple linear regression and multiple regression. Accordingly, these models are tested for vio- lations of the following assumptions: 1. A linear relationship exists between cost and output. 2. Disturbance terms are not serially correlated. 3. The variance of the disturbance term is constant and not a function of the level of the dependent or independent variables. for predi sendent \ for the . terms of statiStj model f is Show Little c05t1n< to all mation This m model outPEr indire 4. The disturbances are normally distributed. 5. The explanatory variables are not highly corre- lated. This condition is called multicolli- nearity. Multicollinearity in particular is an extremely severe problem in cost estimation studies though less severe for predictive purposes. Tests are made for the ten inde- pendent variables employed in the multiple regression models for the existence, pattern, and location of multicollinearity. The four alternative prediction models are ranked in terms of their predictive accuracy, and T-tests are made to statistically compare the alternative costing models. This study finds multiple regression to be the best model for use in cost estimation. Simple linear regression is shown to be better than direct costing and full costing. JLittle difference is observed between direct costing and full costing for predicting future costs. Because sufficient information may not always exist to allow firms to use regression by branches for cost esti- rnation, a pooled multiple regression model was also employed. Innis model did not perform as well as the mutliple regression uuxdel using regression by individual branches, but it did outperform all other models. Both of the banks examined in this study account for branches as profit centers. This approach implies that indirect costs are controllable at the branch level and that such costs can be attributed to individual branches. It is the find; analysis camot be] vidual b: the finding in this study based upon a multiple regression analysis of indirect cost behavior that indirect costs cannot be identified with either output measures or indi- vidual branches. it Depart: STATISTICAL ANALYSIS OF ALTERNATIVE COST ACCOUNTING METHODS BY Roger Allan Roemmich A THESIS Submitted to .Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Accounting and Financial Administration 1975 DEDICATED TO Marilyn, Kerri, and My Parents ii without 1: members, tate Uni appreciat Daniel Cc and encou PlEtiOn c COthEe final pro T' of this d; her stead: ACKNOWLEDGMENTS This dissertation could never have been completed without the assistance, counsel, and guidance of faculty members, friends, and fellow graduate students at Michigan State University. To my dissertation committee I express my sincere appreciation. Professor Harold Sollenberger, Professor Daniel Collins, and Professor David Verway not only directed and encouraged me, but conscientiously expedited the com- pletion of the dissertation. The many consultations with my committee members immeasurably improved the quality of the final product. To my wife, Marilyn,I pay tribute. The completion of this dissertation would not have been possible without her steadfast support through crisis after crisis. iii 0;":ch L... .u.\ ””9. \l- 5 Hr.“ uhuub . :‘D TABLE OF CONTENTS CHAPTER PAGE I. DEFINING THE PROBLEM . . . . . . . . . . . 1 II. STUDY OF ALTERNATIVE COSTING METHODS . . . 23 III. TEST OF THE MODELS . . . . . . . . . . . . 72 IV. COMPARING THE ALTERNATIVE COSTING MODELS . 116 V. LIMITATIONS AND EXTENSIONS OF THIS RESEARCH . . . . . . . . . . . . . . . . 138 SELECTED BIBLIOGRAPHY . . . . . . . . . . . . . . . . 144 iv 10. ll. 12. 13. Me “ Du CC 85. C:I Ba Ba Ra Ba Te ti Te. ti' TABLE 10. 11. 12. 13. LIST OF TABLES Correlation of Cost Categories with Output measures 0 O O O O O O O I O O O O O O O O 0 Regression Equations--Bank A . . . . . . . . Regression Equations--Bank B . . . . . . . . Multiple Regression for Total Indirect Costs for Bank A for the Period 1963-1972 . . . . Tbtal Cost Equation--Bank A . . . . . . . . Total Cost Equation--Bank B . . . . . . . . Durbin-Watson Test for Serial Correlation . Comparison of Residuals for Cost Estimates-- Bank A O O O O O O O O O C O O I O O O O I 0 Comparison of Residuals for Cost Estimates-- Bank B O O O O O O O O O O O O O O O O O O O Ranking of Alternative Costing Models—- Bank A O O O O O O O O I O O O O O O O O O O Ranking of Alternative Costing Models-- Bank B O I O O O O O O O O O O O O O O O O 0 Test of Mean Differences--Relevant Sta- tistical Comparisons for Bank A . . . . . . Test of Mean Differences--Relevant Sta- tistical Comparisons for Bank B . . . . . . PAGE 54 94 96 98 101 104 107 126 128 130 131 132 135 Tel FIGURE 1. LIST OF FIGURES Test for Homogeneity of Variance—-Bank A-- Simple Linear Regression by Branches . . Test for Homogeneity of Variance-~Bank A-- Multiple Regression by Branches . . . . Test for Homogeneity of Variance--Bank B-- Multiple Regression Pooled . . . . . . . Test for Homogeneity of Variance--Bank A-- Multiple Regression Pooled . . . . . . . Test for Homogeneity of Variance-~Bank A-- Simple Linear Regression Pooled . . . . vi PAGE 110 111 112 113 114 J» C (I) (H Ba. Di: EXHIBIT 1. LIST OF EXHIBITS PAGE Bank A, Branch III--Residential (Suburban) Profit Contribution Report . . . . . . . . 16 Bank B, Branch X, Statement of Income for the Years Indicated . . . . . . . . . . . 19 Current Deve10pment of Bank Cost Accounting. 31 Bank A--83 Branches--Annual Data . . . . . . 55 Bank A--83 Branches . . . . . . . . . . . . 56 Bank B--46 Branches--Annual Observations for Period 1970-1973 . . . . . . . . . . . 66 Distribution of Standardized Residuals vii 31 is that : mance eve E This est: the costs in order p diSCOVEry- Canters_ I Thus, a f is the at W; butable C(l It is a Sin: reall: Or to r This 5 capabJ -‘ COSt E F CHAPTER I DEFINING THE PROBLEM A major requirement of management information systems is that cost information be provided for budgeting, perfor— mance evaluation and cost control. Budgeting requires the estimation of future costs. This estimation requires that, "The cost accountant discover the costs attributable to 'particular parts' of the business in order to guide management in its decisions."1 Performance evaluation and cost control require the discovery of costs attributable to actions of responsibility centers. A responsibility center is defined as the lowest level within an organization at which costs can be controlled. Thus, a fundamental requirement of responsibility accounting is the ability to attribute costs to segments of the business. While noting the complexity of determining such attri- butable costs, Clark observed: It is possible, however, to use statistics in studying a single business, in trying to find out how its costs really vary in response to changes in volume of output or to changes in other characteristics of the business. This sort of study is not highly developed, but it is capable of becoming a valuable aid and supplement to cost accounting. Clark's n noted: More subs: relev out b road, most S the theor Shillingl mining "a S tative po‘ I avera: , ~I entire tiOn 5 Ma attelnpts ai tie attrih by Jonatha lished in first form Harris ex; led by the traditiona 2 In 1963 Shillinglaw attempted to clarify and expand Clark's notion by defining attributable cost. Shillinglaw noted: More than forty years' discussion has produced fairly substantial agreement as to what kinds of costs are relevant to short-run decisions. The route pointed out by J. M. Clark has since become a well-traveled road, and has led to near-unanimity of treatment in most textbooks in elementary and cost accounting.2 Shillinglaw observed that Clark's work has provided the theoretical framework for cost allocation schemes. Shillinglaw hoped to provide a general framework for deter— mining ”attributable costs" for quantitative policy decisions. Shillinglaw defined "attributable costs" for quanti- tative policy decisions as: The cost per unit that could be avoided, on the average, if a product or function were discontinued entirely without changing the supporting organiza- tion structure.3 Management accounting literature contains many attempts at presenting theoretical schemes for discovering the attributable costs. One such discussion was an article by Jonathan N. Harris, "What Did We Earn Last Month,” pub- lished in the NACA Bulletin in 1936. This represented the first formal discussion of direct costing in this country. Harris expressed the viewpoint that managers were being mis- led by the financial statements developed for them on the traditional "absorption costing" basis. This article sparked many OthE full cost v A costing a of Accour cations g A ma: study maril prof: decis T a direct cc cal suppc the 1.158 O and costs to be wia T) where all product c can be ti T direct co the study . Velum pFOdUQ 3 many others which gave arguments pro and con for direct and full costing. In 1960 as a result of the controversy between direct costing and full costing advocates, the National Association of Accountants published Research Report #37, Current Appli— cations 2; Direct Costing. The NAA noted that: A majority of the companies participating in this study have designed their direct costing plans pri- marily to supply costs and income margin data for profit planning and for making current operating decisions. In this report, the NAA discussed full costing, direct costing, and mixed costing in terms of their theoreti- cal support and actual usage. Mixed costing, which involved the use of simple linear regression between an output measure and costs, was described as sophisticated but was not found to be widely used. The NAA study defined full costing as an approach where all costs of operation and administration are considered product costs and are allocated to the product to which they can be tied most closely. This report noted the following typical definition of direct cost as supplied by one of the firms participating in the study: Direct costs are those costs which vary directly with volume (raw materials, direct labor, and direct sup- plies) plus certain costs which vary closely with pro- duction and can be allocated to a product or group of products on a reasonable accurate basis. This defini- tion was chosen because it fills our need for clearcut cost maki cribed t costs fr particip 4 costs in analyzing results of Operations and ig making short-run dealsions on product pric1ng. Earlier NAA Research Reports #16, 17, and 18 des- cribed three techniques for separating direct or product costs from period costs. Practice reported by companies participating in Research Report #37 is summarized below: 1. Assignment of costs to direct or period cate- gories by inspection of the charts of accounts. 2. Statistical analysis of costs, using techniques such as scatter charts and mathematical methods for determining variable cost rates and amounts of fixed costs. (Note: While these methods have been often described in accounting litera— ture, they were seldom used by companies partici- pating in the study.) 3. Industrial engineering studies to predict how costs are expected to vary with volume.6 It has been noted that statistical analysis of costs in practice has lagged behind descriptions suggesting its applicability. For example, Clark, NAA Research Reports #16, 17, and 18, and Beyer's, Profitability Accounting for Planning and Control,7 all suggest a need to examine the role such techniques can play in determination of relevant costs for various short-term policy decisions. for disc Inarticu regressi until re. calculat; computer: multiple multiple realistiq than one C regressic literatu‘ 51°“ Anal developed COst and consumer ing estir: outstancli Cent Of member Cr 0 analysis Nagata am lat ethec 5 In 1966 Benston suggested another possible approach for discovering the costs proportionately attributable to 'particular parts" of the business.8 This approach is multiple regression. As Benston notes, multiple regression was not feasible until recently because of the complexity and sheer number of calculations required. However, increasing availability of computers with their capacity for calculations now makes multiple regression practical. Benston further notes that multiple regression is attractive to managers because it is realistic in recognizing that costs are a function of more than one factor. One of the first efforts which applied multiple regression analysis to cost behavior patterns in accounting literature was Eugene E. Comiskey's, "Cost Control by Regres- sion Analysis." The cost behavior model used by Comiskey was developed from the results of multiple regression analysis of cost and other operating data of branch offices of a major consumer finance chain. Comiskey was interested in predict- ing estimated direct branch Operating costs per account outstanding. Comiskey was successful in explaining 73 per cent of the variance in observed direct unit cost for the 83 member cross section he examined.9 Other efforts which have applied multiple regression analysis to cost behavior patterns include those of Ernest A. Nagata and John B. Gayle. Nagata's objective was to formu- late the direct (non-allocated) loan branch expenses as a 6 function of the operating characteristics of the loan branch. Operating characteristics included the size of the branch, the size of loans, and the mix of loan types. Nagata was able to explain 91 per cent of the variance in direct loan branch expenses for the 45 branches he examined.10 Gayle used multiple regression techniques based on a research study to help estimate the cost and time necessary to develop computer programs. He was able to explain 78 per . . 1 cent of the variance in costs. 1 The Research Question Four alternative methods for determining the level of future costs have now been suggested. The major thrust of tfluis research is to examine these models to determine which technique is most apprOpriate for estimating future cost levels for cost control, performance evaluation, budgeting, cost allocation, and pricing. In addition to estimating or predicting future cost levels, an effort is made to assess the ability of simple linear regression and multiple regression to determine the marginal contribution of individual factors to costs. This approacm.recognizes that some individuals interpret regression coefficients in this manner. Specification tests are included in Chapter III which report on the advisability of interpre- ting regression coefficients as the costs attributable to a Specific factor. The four methods examined are: .7 1. Direct costing (using an Account-Classification system), 2. Full costing, 3. Simple linear regression or mixed costing, and 4. Multiple regression. Since budgeting, performance evaluation, and cost control all require the estimation of future costs, the models are ranked and evaluated in terms of their ability to predict future costs. The choice of this criterion for ranking and evaluation is consistent with the desire of decision makers to make decisions based upon the most likely outcome of a course of action with implicit recognition of the risk of inaccurate projections. Beaver, Kennelly and Voss have provided an intuitive justification for using predictive ability criteria as a means of evaluating accounting alternatives: Because prediction is an inherent part of the decision process, knowledge of the predictive ability of alternative measures is a prerequisite to the use of the decision-making criterion. At the same time, it permits tentative conclusions regarding alterna- tive measurements, subject to subsequent confirmation when the decision models eventually become specified. The use of predictive ability as a purposive criterion is more than merely consistent with accounting's decision-making orientation. It can provide a body of research that will bring accounting closer to its goal of evaluation in terms of a decision-making criterion.1 While the emphasis in this research is primarily upon the assessment of the benefits of alternative information models for budgeting and predicting future costs, the cost incurre choosin bility 1 cm con ‘ senti .— f“ () f a b F respons; are mad. appears through OI "eyek may be E Careful more the relatioI of altel with dii the marg suggest to 3110., 0f Short 8 incurrent relationships that emerge can also be used for choosing cost allocation strategies for use in responsi- bility accounting systems (performance evaluation) and for the control function. Performance evaluation requires identification of costs attributable to "particular parts" of a business in order to allocate costs to profit or responsibility centers. In practice many cost allocations are made on the basis of a single output measure which appears to have a direct relationship with the level of cost incurrence. This direct relationship may have been observed through scatter diagrams or charts, statistical techniques, or "eyeballing." While relating costs to an individual output measure may be appealing from a practical standpoint, Benston is careful to point out that cost is typically a function of more than one variable. Thus, this research explores the relationship between individual cost categories and a number of alternative output measures and exogeneous variables.13 In addition, individual cost categories are associated with different levels of business activity in order to assess the marginal contribution of potential cost determinants and suggest schemes for allocation of indirect costs in addition to allowing for predictions about the impact upon cost levels of short-run policy decisions. Data Sources and Sample The data sources for this study are two large banks which develop cost and contribution data for branches as profit centers on an annual basis. Bank A has provided cost and statistical information for 10 years for 10 of its 83 branches, and Bank B has provided cost and statistical information for all of its 46 branches for four years. In addition, Bank A provided aggregate indirect cost data for ten years. Exhibits 1 and 2, respectively, are examples of the type of data provided by Bank A and Bank B. These two banks were chosen for this study because they develop statistical information in greater detail for segments or branches than other banks considered for inclusion. Banks are used in this study because they develop detailed information about costs and revenues for internal decision making purposes and for use in external forecasts provided to regulatory agencies. Such information is pre- sented in a contribution format to demonstrate the contribu- tion of existing branches to costs and revenues. Existing branches then serve as experience for the projection of expected revenues and costs for new branches. Bank Cost Data John R. Walker recently explored the development and current state of bank cost accounting. He observed that "Historically bank accounting records have been maintained 10 primarily to fulfill external requirements rather than to 14 Accordingly, he concluded provide management information." that conventional bank accounting is of limited usefulness for "cost purposes" and internal decision making. Walker advances several reasons which help to explain the late development of bank cost accounting and the increased emphasis in this area in recent years. Among the reasons are : 1. Banks are unique in that they pay for their raw material (deposits) largely by rendering services. These services include protection of the custom- er's funds, making transfers to others upon the customer's order, collection of checks deposited, record keeping, and as many other services as bankers can devise. Failure to recognize the opportunity cost of providing these services has resulted in a lack of emphasis upon the cost of services. 2. Despite an increasing emphasis on services, interest on loans and investments still repre- sents the major source of income for banks. Thus, as long as total net operating earnings have been satisfactory, there has been a tendency on the part of the management of many banks to consider service activities as unimportant and not to be particularly concerned about their 11 profitability. However, decreasing profit margins have increased management's awareness of the potential income generated by services and the need for much more detailed and precise cost information. Corporate treasurers have become increasingly concerned about the cost of maintaining excess cash balances. There is a growing desire on the part of corporate customers to pay for bank services by means of cash fees or with the lowest possible demand deposit balances. In order to price services it is necessary for banks to know their costs. Another product of shrinking profit margins has been the development of new services as sources of income. Included among these services are the rapid growth of computer services, credit cards, freight payment plans, various types of remit- tance banking, and a host of other new services. All of these new services represent uncharted waters for bankers, and a sound knowledge of costs is vital if the rocks are to be avoided. Another reason for the need for better cost accounting information is for use in projections required by regulatory agencies in making appli- cation for new branches. 12 6. A final and obvious reason for the emphasis upon improvement of bank cost accounting is the tre- mendously improved capacities and capabilities provided by the computer for cost analysis.15 Walker notes five related situations in which bank management must make significant decisions and points out that the relevant cost data for these decisions will be quite different. These situations are: . The decision to introduce a new service. The decision whether or not to automate a service. The initial price on a new service. :5 u N H O . Price concession, if any, to be offered to a large volume customer. 5. The decision to discontinue a service.16 Unfortunately, development of an information system capable of providing cost accounting inputs for decisions has been considered time consuming, complex and too costly by individual banks. In addition, Walker feels that "many banks lack personnel with the necessary background and training to undertake a program such as this.” In an effort to enable smaller banks to use cost finding programs, the Federal Reserve Functional Cost Analy- sis Program was developed by the Federal Reserve Bank of New York in.the 19503. In 1968, over 1,000 banks participated in the Program. This program, and others like it, use functional II “I 13 income analysis to develop unit costs for various types of transactions. Some potential problems which may result from the use of functional income analysis are: 1. The data used are from a prior period. Cost data used for pricing purposes should reflect current cost levels plus any near-term increases expected. 2. Item costs represent costs from a particular mix of deposits, loans and other activities, and a particular volume of transactions that prevailed during the period covered by the analysis. 3. The composition of the final cost figure is so obscured by allocations that it is very difficult to determine the make-up of a given unit cost figure. This research effort will attempt to minimize the limitations of functional income analysis by including the prevailing price index, the number of employees per branch, and the age of branches as variables to be considered with output measures in the cost analysis. Research Outline Chapter I has discussed the need to discover the attributable costs for actions or ”particular parts" of a 14 business. The four alternative costing methods suggested in the management accounting literature have been listed. A short history of bank cost accounting systems has been included to give the reader a feel for some of the peculi- arities of the chosen empirical data source. In addition, Exhibits 1 and 2 are provided to show the reader the exact form of the data provided by Bank A and Bank B. In Chapter II the four costing methods are discussed in detail, including the advantages, disadvantages and imple- mentation of each. Included in the discussion are the three error measures employed for comparison. The way of implement- ing each method is detailed in an exhibit of this chapter. Chapter III examines the problems of model specifica- tion, the limitations resulting from violations of assumptions and describes the model tests employed in this research. The results of model tests are reported and the significance of these findings is discussed. Chapter IV reports the results of comparisons between the alternative costing models, results of indirect cost regression and regression for individual cost categories. Chapter V includes the discussion of the limitations of this study, the potential extentions of this study and brings forth some hypotheses for further testing. Summary In summary, the major aim of this research is to examine alternative information models for the determination 15 of attributable or relevant costs for quantitative policy decisions and cost allocations. Alternative models to be examined are: . Direct costing, . Full costing, . Simple linear regression or mixed costing, and owaH . Multiple regression. In an effort to discover attributable costs for "par- ticular parts" of a business, individual cost categories are related to output measures, the number of profit centers in existence, the consumer price index for the period, the age of profit centers, and the number of employees in a branch. The results of relating cost categories to exogeneous variables as well as to output measures should improve pre- dictions and provide better estimates of the marginal contri- bution of various factors to cost incurrence. 16 EXHIBIT 1 BankiA, Branch III--Residential (SUBURBAN) Profit Contribution Report 1972 1971 Income Earnings on Average Deposits $ 1,004,820 $ 881,897 Service Charges and Fees on Deposits Accounts 35,724 36,837 Other 5,047 4,880 1,045,591 923,614 Expenses Cost of Funds Interest on Deposits 589,729 494,546 F.D.I.C. 7,007 4,658 Intangible Tax 9,187 7,571 Examinations 924 588 606,847 507,363 Direct Salaries 87,874 79,189 Fringe Benefits 17,369 16,814 Advertising and Public Relations 3,493 4,352 Employment Service - - Furniture and Equipment 4,445 4,488 Losses 355 266 Occupancy 68,238 69,671 Office Supplies 5,852 6,192 Postage 3,854 3,905 Securities and Safekeeping-Fees Waived 431 391 Telephone and Telegraph 2,553 2,450 Travel and Entertainment 266 350 Other 2,341 1,921 197,071 189,989 Indirect Auditing 3,209 2,161 Bank Vaults 310 416 Branch Office Administration 3,315 3,013 Branch Unassigned 20,167 17,244 Computer and E.D.P. 10,560 10,281 Distribution 8,734 7,828 Employee Training 3,883 3,662 Security - - Other* 14,070 12,352 64,248 56,957 17 EXHIBIT 1 (continued) Total Expenses Less: Charges to Depts.** 1972 868,166 8,364 Net Expenses 859,802 Contribution to Overhead and Profit General Overhead Net Profit Before Taxes Earnings Rate Cost of Funds Rate Average Number of Staff PROFIT CONTRIBUTION REPORT SUPPLEMENTAL DATA 185,789 5,209 180.580 6.12 3.23 10.60 1972 *Other Indirect Expenses Bank Transport 1,639 Bond and Coupon 583 Collection 199 Commercial Business Development 1,684 Credit 1,396 Customer Securities 679 Operations 987 Personnel 1,268 Purchasing 1,565 Other 4,070 Total 14,070 **Expenses Charged to Departments Bank Mortgage 1,331 Commercial Loan 175 Master Charge 298 Time Credit 6,560 Other - Total 8,364 Averagg Deposits (in thousands) Business 4,405 Check III 796 Special Checking 403 Other 497 Total Demand 6,101 1971 754,309 8,840 745,469 178,145 4 785 mirage 6.30 3.18 10.00 1971 1,462 535 123 1,593 1,438 298 993 1,324 1,494 3,092 12,352 1,145 155 324 7,216 8,840 3,623 688 401 571 5,283 18 EXHIBIT 1 (continued) 1972 1971 Savings 5,914 4,997 Time Deposits 4,352 4,178 Certificates of Deposit 689 282 Savings Certificates 1,757 1,236 Other - - Total Savings and Time 12,712 10,695 Total Deposits 18,813 15,978 Average Number of Accounts Business 408 392 Check III 662 616 Special Checking 1,320 1,282 Savings 2,990 2,867 Time Deposits 459 460 Certificates of Deposits 12 6 Savings Certificates 195 133 Master Charge 210 119 19 EXHIBIT 2 Bank B, Branch X Statement of Income for the Years Indicated Operating Income Interest on fees on loans Service charges on deposit accounts Other service charges and fees Other income Pool income TOTAL OPERATING INCOME Operating Expense Salaries and wages Employee benefits Interest on deposits Occupancy expense Furniture and equipment expense Provision for loan losses Other operating expenses Service department expense TOTAL OPERATING EXPENSE Income before taxes Applicable income taxes NET INCOME Interest on Deposits Savings Certificates of deposit Savings thrift certificates Time open accounts TOTAL 1973 $ 7,868 1,384 5,082 1,244 M 608,620 75,533 13,164 216,795 14,878 2,640 -0- 16,668 53,239 392,917 215,703 103,487 $112,21Q $174,182 $216,795 1972 $ 5,632 1,699 4,224 463 5.12.152; 531,611 67,350 10,816 200,157 13,771 2,394 -0- 16,696 48,766 2.5.2.219 171,661 82,093 $ 89,568 $160,379 -0- * 39,778 -0- $200,157 *Note: This figure is on a cash basis, while 1973 was changed to the accrual basis. The comparable figure for 1972 was $-O-. 20 EXHIBIT 2 (continued) 1973 1972 OccupancyiExpense Building maintenance $ 3,357 $ 2,925 Rental of offices 7,200 7,200 Repairs, insurance & taxes 1,623 1,037 water, fuel & light 2,150 2,060 Maintenance contracts —0- —0- Capital funds charge -0- -O- Depreciation-bank premises 548 549 TOTAL $ 14,878 $ 13,771 In the case of "Rental" branches, the eXpenses for maintenance, rents paid, repairs, and insurance are directly allocate. Owned (leased and sub-leased) branches and the departments therein are subject to a "Capital Funds Charge" based on square footage occupied. This charge includes rent, utilities, maintenance, insurance, etc. Furniture and Equipment Expense Depreciation furn. & equip. $ 906 Main. contracts furn. & equip. 985 Rental equipment 392 Repairs furniture & equipment 357 TOTAL $ 2,640 Other OperatingLExpenses Armored car $ 1,266 Bank commissioners examination 121 Blanket bond 413 Convention and dinners 611 F.D.I.C. insurance 3,309 Guard Services -0- Miscellaneous charge-offs 1,898 Postage 512 Printing & supplies-general stock 2,145 Telephone & telegraph 5,509 Tellers difference 143 *Other 741 TOTAL $ 16,668 995 915 292 192 2,394 1,110 221 303 683 3,125 -0- 1,030 589 1,868 5,685 616 1,466 $ 16,696 EXHIBIT 2 (continued) Service Department Expense* General administration Central file Computer oper; systems & prog. Personnel Proof Audit Central savings Runners Bookkeeping credit Commercial loan accounting Other TOTAL 21 1973 $ 12,367 2,452 6,556 2,511 26,457 1,357 8,654 2,703 (16,308 1,522 4,967 $ 53,239 1972 $ 12,856 1,923 4,650 1,987 24,809 760 8,484 2,814 (16,402) 2,814 4,071 $ 48,766 *This category represents your allocated share of expense of the depart- ments listed above. Statistical Information 1973 1972 Average Deposits Number Amount Number Amount Time deposits: Savings 3,327 $4,349,000 3,821 $4,132,000 Certif. of deposit ~O- -O- -O- -0- Savings thrift certif. 337 792,000 334 758,000 Time open 321 30,000 -0- -0— TOTAL 3,985 $5,171,000 4,155 $4,890,000 Demand deposits 3,451 3,762,000 3,579 3,565,000 TOTAL DEPOSITS 7,436 $8,233,009 7,734 $8,455,000 Average Commercial Loans 29 $ 81,000 37 $ 86,000 Deposit Loaned to Pool $8,135,000 $7,688,000 Officers and Employees 9 8 10. 11. 12. 13. 14. 15. 22 CHAPTER I--FOOTNOTES John Maurice Clark, Studies in Economics of Overhead Costs (Chicago: University of Chicago Press, 1932), p. 36. Gordon Shillinglaw, "The Concept of Attributable Cost," Journal g§_AccountingResearch V. 1 (Spring 1963), p. 73. Ibid., p. 80. National Association of Accountants, Current Application 9: Direct Costing (New York: National Association of Accountants, 1961), p. 14. Ibid., p. 11. Ibid., p. 17. Robert Beyer, Profitability Accounting for Planning and Control (New York: The Ronald—PressEompany, 1963), PP. 47-38. George T. Benston, "Multiple Regression Analysis of Cost Behavior," Accounting Review V. 41 (October 1966), PP. 658-659. Eugene B. Comiskey, "Cost Control by Regression Analysis," Accounting Review V. 41 (April 1966), pp. 235-238. Ernest A. Nagata, "The Cost Structure of Consumer Finance Small-Loan Operations," The Journal of Finance V. XXVIII (December 1973), pp. 1327- 1337. John B. Gayle, "Multiple Regression Techniques for Esti- mating Computer Programming Costs," Journal of Systems Management V. 22 (February 1971), pp. 13-16._ William H. Beaver, J. W. Kennelly and W. H. Voss, "Pre- dictive Ability as a Criterion for the Avaluation of Accounting Data," Accountinngeview V. 43 (October 1968), pp. 679-680. George T. Benston, "Multiple Regression Analysis of Cost Behavior," Accounting Review V. 41 (October 1966): P. 658. John Rex Walker, Bank Costs for Decision Making (Boston: Bankers Publishing Company, 1970), P. 35. Ibid., PP. 25-28. CHAPTER II STUDY OF ALTERNATIVE COSTING METHODS Decisions to expand or change the mix of operations require that the decision maker be able to predict within certain confidence limits the revenues and costs associated with such decisions. The major aim of this research is to consider the problem of determining the appropriate costing models for short-term policy decisions. An important factor in determining the appropriate costing model is the environ- ment within which a firm's accounting system develops. In this chapter I examine the accounting system environment, discuss peculiarities of the bank cost accounting system environment, discuss alternative costing methods and select error measures for evaluating alternative costing methods. The Accounting System Environment The accounting system is intertwined with operating management. Accounting records are kept not only because they are needed to tally performance for later appraisal and for income determination, but also because business operations would be a hopeless tangle without the paperwork that is so often regarded with disdain. The preceding quotation from Cost Accounting: A Managerial Emphasis by Charles T. Horngren is important in 23 24 that it notes several purposes for which accounting records are kept. External Uses One major reason for maintaining accounting records is to provide a basis for external users such as creditors, investors or potential investors, and regulatory agencies to be able to evaluate a company's financial position, its recent performance in terms of income generation, and the source of its ownership interests. Cost Responsibility and Control Another major reason for maintaining accounting records is to provide accounting statements for all levels of management designed primarily for use as a tool of opera- ting management for controlling operations and costs. Responsibility for controlling costs is assigned to super- visory areas which have direct control over cost incurrence and costs are accumulated by levels of responsibility within the organization. This system of accumulating costs by supervisory areas which have direct control over cost incur- rence is often labelled responsibility accountipg. Respon- sibility accounting is an internal performance evaluation technique whereby accumulated costs of a supervisory level are compared with budgeted costs for that segment. In an address before the Cleveland Treasurer's Club, Cleveland, Ohio, on December 19, 1951, John A. Higgins of Arthur Andersen & Co. noted that a responsibility accounting 25 system . . . emphasizes information that is useful to the operating management and de-emphasizes the account- ing and bookkeeping aspects that clutter up so many of our accounting and financial statements today.2 Higgins implied that there are incongruencies which arise from the use of information developed for external purposes by operating management for internal functions of planning and control. These incongruencies arise because external users are primarily interested in the current position and recent performance of a business while operating management is interested in identifying efficient and ineffi- cient areas of operation within a company. Planning Another reason for maintaining accounting information is to provide past cost data for such planning activities as budgeting, product or service mix decisions, and decisions to expand or contract operations. The information needed for such planning activities differs from the information normally provided by responsibility accounting systems in the level at which costs are aggregated. For planning purposes it is desirable to determine the marginal contribution of individual factors to cost incurrences. For responsibility accounting purposes costs are associated with supervisory levels which have control over them with attention focused upon rate variances which are caused by differences between the rate at which inputs are purchased and a budgeted or 26 standard input rate and efficiency variance which measure the difference caused by using more or less inputs than budgeted to produce one unit of good output. The need for identifying the marginal contribution of individual factors to cost incurrence means that the data required for planning purposes is necessarily more detailed and less aggregated than that required for responsibility accounting purposes. The four costing models or methods (full costing, direct costing, simple linear regression, and multiple linear regression) considered in this study are chosen from the approaches suggested in Horngren3 for approximating cost functions. The National Association of Accountants in 1960, Separating and Using Costs as Fixed and Variable, and again in 1961, Current Application gthirect Costing, provided dis- cussion of three methods of analyzing cost variability or behavior. The NAA provided discussion of direct costing, full costing, and simple linear regression or mixed costing. Their research indicated that most firms were using some form of direct costing. Those firms not using direct costing were generally found to be using full costing. The 1961 direct costing study listed three ways in which direct costing was employed by companies participating in the study. These practices were: 1. Assignment of costs to direct or period cate- gories by inspection of the charts of accounts. artiCle ' . The latte soPhis tic Assoc1ati AnalYSis . nized the many faCt. COSting' quate for for Each 1 1 provides 9 E __ 1 27 2. Statistical analysis of costs, using techniques such as scatter charts and mathematical methods for determining variable cost rates and amounts of fixed costs. While these methods have been often described in accounting literature, they are seldom used by companies participating in the study. 3. Industrial engineering studies to predict how costs are expected to vary with volume. The field study showed that industrial engineers often make or participate in such studies.4 The suggestion that statistical analysis of costs is not widely used in practice is consistent with the 1960 NAA article, Separating and Using Costs as Fixed and Variable. The latter article described simple linear regression as sophisticated but not widely used. In 1966 George J. Benston won the American Accounting Association's Manuscript Contest with "Multiple Regression Analysis of Cost Behavior." In this article Benston recog- nized the problem of measuring the costs caused by each of many factors Operating simultaneously. Benston found full costing, direct costing, and simple linear regression inade- quate for the purpose of determining the incremental costs for each factor. Benston suggested that multiple regression provides a more complete specification of the functional 28 relationship between costs and their causes because the causes can be considered simultaneously under this approach.5 For further discussion of these four alternative costing models one might examine Benston's "Multiple Regres- 6 sion Analysis of Cost Behavior“ or chapter three of Cost Accountipgé-Accounting Data for Management's Decisions by 7 Nicholas Dopuch, Jacob G. Birnberg and Joel Demski. Bank Cost Accounting Environment As noted by John R. Walker in Bank Costs for Decision Making, the historic function of banks, and still the princi- pal function, is the accepting of deposits and the lending and investing of the resulting funds.8 A strong demand for funds combined with higher long- term and short-term interest rates has resulted in a substan- tial increase in the rate of return on loans and investments in recent years. This increase in operating revenue has been more than offset by increases in operating expenses resulting in shrinking profit margins. Fortunately for many banks, this lower profit margin has been earned on a considerably larger base such that total earnings have continued to increase.9 Nevertheless, this trend toward smaller profit margins requires much better knowledge of costs than has existed in the past. Another source of potential revenue being explored by banks is providing new services to cus- tomers . Walker suggests, 29 A commercial bank can be viewed as a simple model in which the inputs are the various classifications of cost and the outputs are the costs of the various services rendered. Using this approach, Walker's cost inputs are personnel costs, equipment costs, occupancy costs, supplies, promo- tional costs, institutional costs, interest, and cost of capital. Walker's cost outputs are lending services, deposit services, trust services, custodial services, com- puter services, and lock box and other services.10 walker has taken the first step toward developing better cost accounting data in banks, the identification of types of cost inputs, and the identification of the types of services provided by banks. Unfortunately, it is very diffi- cult to identify direct relationships between cost inputs and service outputs. The identification of the functional rela- tionship between cost inputs and service outputs is crucial for use in pricing decisions, decisions as to the mix of services to be provided, the evaluation of the performance of managers, budgeting of future costs, and cost allocations. The objective in this research study is to examine four basic accounting models which have been suggested for use in determining this functional relationship and to evalu- ate each of these models in terms of its ability to predict input costs giygg the outputs for that period. In this manner by examining the predictive errors for each model, we can assess the ability of the model to approximate the rela- tionship between cost inputs and service outputs. 30 Historically, bank cost accounting information has been developed for purposes of cost control rather than for purposes of cost planning. Therefore, a thorough under- standing of the functional relationship between costs and output has not been required. Cost planning activities require information which can be used in identifying this functional relationship. Exhibit 3 depicts the accounting system environment for banks, including the identification of users of accounting information and the type of data required by the users. As noted by Walker, little effort has been made to date to provide special information for cost planning activities. The information used in cost planning has been data developed for external reporting purposes or for use in performance evaluation (responsibility accounting reports). The approach used in this dissertation is to use data developed for evaluation of the overall performance of individual branches (responsibility accounting reports) to identify the functional relationship between service outputs and cost inputs. This effort is an attempt to evaluate alter- native models for approximating the relationship and to pro- vide insight into the types of data which might be develOped for purposes of better cost planning and cost control. One problem in using the costs developed for perfor- mance evaluation is that many joint costs and indirect costs have been allocated to branches. To the extent possible, an effort has been made in this study to explore functional relationships for these indirect costs and to draw some 31 mcofium possumaaom mum muasmmm .Q mastoe mo cowma>ou pom unwsom ma coaumauomcw 3oz .o mastoa mo unmadoao>mv pow cmcfiamxo mum muse luso tam muons“ cowaumn mofiocmwo nuoofimcoo umoo .m manmcowumaou Hmcowuocam .m huouoaswom .m axons owuma mummuouom ca cowuwumtfim tam madame Icoo wcammouo mowocmwm cownuoov Isa wcfi>aooou usb xuOumaswmu mo muootoud no Housman“ :« mxcmn umoa :« mucoawuwavmu mmofi>umm kn commaaasoum muoxma on: you pogo cocoao>mt sauoom .¢ unmoouom .< coaumauomaw Hmoauoumam .< cosmuuwn .d IHo>ow mama exams Hanan tam mumwtoauoucw cw pouaumaabm mummmcma vmdoao>ov hauoom .m mum muasmom .m Hmovw>fivou .m muuooou mxcmn wumucoo muwawpam:0dmmu coaumuu mcaucsooom omuma huo> cw chHum ma tmumaaanuum aoau Imacfiatm %u«HHn vodoao>ou Ham: .4 lumoamcoo once .4 umauomaw Hmowuouowm .< scum .< IancOQmom mcoau mmauamwm Impotamcou umou .o huoumaswom .o mmfiocmwm mucosa to» uswom mo mmaom .m lawmaasm one muasmom .m muouatouo .m muouno>=w weapon scan ouquco now down wcwucsooom voumasasoom cow» Icmuoa was muuoaou vodoao>ov Hams .< mo mmaam .< Imauomna Hmowuoumwm .< nuoumm>sH .< amououxm usoanoao>oo muouoom vmuwdoum ow coquma cowumauomaH coaumauouaH acouuso mo owmum wcfiswmuumcoo auoon wcwuooooo< 30m wcwucsooud wowussoou4 mo muons no make waauasouo¢ umoo soon mo ucoadoao>oa acouuao m HHmHmNm 32 tentative concluSions about the advisability of profit center accounting in banks. These conclusions are noted in Chapter V. Full Costing Under the full costing theory or approach to cost incurrence, all costs are assumed to attach or associate with a product. This approach requires that all costs be classi- fied or allocated to individual products in order that the total costs or effort associated with the production of an output be matched with the revenues or output of that process. The classification of costs with individual products under the full costing approach is normally based upon the subjective judgment of the accounting record keeper. The accounting record keeper is also required to allocate cer- tain "joint costs" between individual products. A joint cost is one which can be identified as resulting from the effort to produce a combination of products. It cannot, how- ever, be identified with the production of an individual product. Thus, the accountant is required to subjectively allocate such a cost between individual products. The full costing approach is useful for purposes of external reporting because all costs are associated with the effort to produce individual products. This identification ‘with individual products facilitates a matching of the reve- nues resulting from the effort of producing a product and the cost of producing the product. Where a product is not yet 33 sold the ”full cost" of the product is carried in the inven- tories reported for that product. Full costing or absorption coating is the method recommended by "generally accepted accounting principles" for approximating cost relationships in determination of income producing efforts for Income State- ment preparation and for determination of the inventories for preparation of the Statement of Financial Position or Balance Sheet. Another advantage of the use of full cost for cost estimation is that subjective classifications of costs and allocation of costs can be made where previous experience with particular products is limited and where the available data is very sketchy. In addition, the out-of-pocket costs of using a method such as full costing which relies so heavily on subjective classifications and allocations are very low; although one should recognize there are potential opportunity costs lost when full costing is used, and it is less accurate than a more sophisticated cost estimation technique. Although the primary advantages of full costing are related to the external reporting function and to the low cost of implementation there are those who advocate its use for such planning activities as pricing final products. These advocates maintain that by basing final product prices upon full costs it can be determined whether the market determined prices are sufficient to justify further produc- tion of the product. 34 Among the disadvantages of full costing are: l. The use of subjective classificationszof costs and subjective allocations rather than objective criteria for cost assignments. 2. Proponents of direct costing contend that certain costs cannot be associated with the production of individual products and that these costs should be treated as costs of the period in which they are incurred. 3. The only relevant factors for any decision-making purposes are the future costs of an action com- pared with the future benefits of that action. The full-costing technique would include costs committed and incurred in the past when such costs are attached to the final product. 4. Full costing aggregates costs for a product while the requirements of planning activities are such that the marginal effect of many factors operating simultaneously must be known. The data provided by the two banks in this study are [reaponsibility accounting reports for each of the branches. For purposes of generating predictions as to the level of Costs in future periods, the full costs of the year immedi- ateely preceding the year for which a prediction is required 35 are divided by an output measure to find the average full cost per unit of output. This average is then multipled by the actual output in the next period to get a prediction of the level of costs in that period. One problem of imple- menting this full costing approach to get predictions of costs in future years is the choice of a single output mea- sure for each bank. The choice requires an estimation of the strength of the relationship between output measures and total costs. The choice of an output measure for each bank was made upon the highest correlation or strongest relation- ship between an output measure and total costs. By choosing the output measure which has the highest correlation with total costs the ratio of explained variance to total variance is minimized and the dispersion of residual terms is smallest. On this basis the output measure chosen for develop- ing predictions under full costing was "earned on average deposits" for Bank A and "demand deposits" (number of accounts) for Bank B. Table 1 illustrates the data upon 'which these output measures were chosen. Direct Costing The direct costing or account classification approach requires the subjective separation of costs into variable and fixed costs. A cost category is classified as fixed if the level of the cost does not seem to change as a function of idle level of output, and a cost category is treated as 36 variable if it appears to change directly with changes in output. Under this approach the total costs are predicted by totalling the cost categories classified as fixed and adding the predicted variable costs which are equal to the estimated variable costs per unit multiplied by the actual number of units of output. Application of direct costing methodology assumes that the cost data possess certain characteristics. The utility of the cost predictions generated by this method is dependent upon the degree of satisfaction of these conditions. One assumption of the direct costing approach is that the level of output remains at a level where the existing capacity will be sufficient for production of outputs. This assumption states that fixed costs do not change within a "relevant range" of activity. Beyond the "relevant range" the existing physical facilities become inadequate and an addition to those facilities and therefore to fixed costs would be necessary. Another important assumption employed in using the direct costing approach is that there is a linear relation— ship between a variable cost and the measure of output. To the extent that a variable cost increases by approximately the same amount for each unit increase in output, this con- dition is met. If however a variable cost tends to increase or decrease at a different rate per unit of output for dif— ferent levels of output, then this assumption is violated and predictions of future cost levels will be less accurate. 37 Since we use past cost data to estimate a variable cost per unit of output, it is important that the relation- ship between the variable costs and the output measure not change greatly in future periods. For example, if the cost category is staff salaries and the output measure is the number of hours worked,the last few years' staff salaries may have averaged about $5 for each hour worked. Yet there may be reason to suspect that staff salaries are going to increase $7 or $8 per hours worked in the future. Then use of $5 per hour variable costs in the direct costing format will result in an underestimation of staff salaries for future periods. Thus, it is important for direct costing applications that the average variable cost per unit of activity in the past be representative of what can be expected in the future or that an inflationary adjustment be made in using this method. In the present study it is possible that direct costing might have performed better had such an adjustment been made in the direct cost method. Perhaps the most crucial requirement for the applica- tion of direct costing is to identify a single activity measure which can be shown to have a strong association with the level of a cost category. Although most cost categories can be shown to be a function of more than one activity or factor, it is often possible to choose one output measure which will provide relatively accurate predictions of future cost levels. An example of this approach is the use by manufacturing companies of direct labor cost, direct labor 38 hours or machine hours to predict or allocate overhead cost. Because it was necessary to identify a single activity or output measure for use in predicting future costs under the direct costing approach in this study, total costs were compared with ten potential activity measures in each of the banks. On the basis of the strongest fit with variable cost behavior as measured by correlation and con- firmed by visual-fit graphing, the output measure as illus- trated in Table l chosen for Bank A is Earnings on Average Deposits and for Bank B the activity measure is Demand Deposits (number of accounts). A complete outline of the procedure used to generate individual cost predictions is included in Exhibit 5 at the end of this chapter. Individual cost categories in each bank are classi- fied as fixed or variable on the basis of the strength of their relationship with the activity measure for that bank. This relationship is summarized by the correlation computed between a cost category and the output measure. Thus, the classification scheme classifies a cost as fixed or variable depending upon its correlation with the output measure. To insure that the predictive performance of direct costing relative to other costing models is not unduly biased by the particular scheme used to identify fixed and variable costs, four different classification rules are employed in this study. For example in one classification in Bank A, costs 1 revenu tion 0 scheme of cla for d: ,1 schemn manne A \Or] 39 costs which have a correlation of .60 or greater with revenues are considered variable, and those with a correla- tion of less than .60 are considered fixed. The other three schemes use correlations of .70, .80, and .90 for purposes of classification. Thus, there were four different sets of predictions for direct costing, one for each of the classification schemes. These predictions are generated in the following manner 3 1. Each cost is correlated with the output or volume measure. 2. On the basis of this correlation, a cost is classified as fixed or variable. (Repeat four times using correlations of .60, .70, .80, and .90 for classification.) 3. Predictions of total costs for a branch are generated by multiplying the actual output times the variable costs per unit of output and adding the fixed costs of the branch in the previous year. 4. The three error measures are then developed for each of the four sets of predictions. As noted in Table l in the case of Bank A the lowest correlation of a cost category with earnings on average 4O deposits is .78675. When .60 and .70 are used for classi- fying costs as variable or fixed, all costs are classified as variable. Thus, the predicted costs are simply the actual dollars of earnings on average deposits times the variable cost per dollar of earnings on average deposits. However, when .80 is used for classification purposes, other direct expenses are classified as fixed; and when .90 is used, other direct expenses, occupancy costs, and office supplies are classified as fixed. In Bank B at the .60 level, occupancy costs and furni- ture costs are classified as fixed; at the .70 level, interest on deposits and other operating expenses are also classified as fixed; at .80, salaries are added to the fixed costs; and at .90, all costs are classified as fixed. The primary advantages of direct costing for use in prediction of future costs are ease of application, low cost of application, use of a minimum amount of data for prepa- ration of estimates allowing estimates to be made where experience in a branch or in offering a service is minimal, and for use in pricing a service where excess capacity exists and the market for the service allows the bank to recover Variable costs plus a margin but not to recover full costs. Many of the advantages of direct costing are also advantages of full costing. These advantages are those of 1&NM cost and ease of application. Direct costing advocates cOntend that direct costing is far superior to full costing for estimating future costs because within that range where 41 excess capacity exists the incremental costs of an action or strategy will be only those costs of a variable nature. Further direct costing advocates contend that managers often make erroneous decisions when future cost projections are based upon full costing techniques. They demonstrate that full costing projections fail to recognize a decrease in fixed costs per unit resulting from greater utilization of existing facilities. The direct costing approach has the advantage of recognizing the difference in behavior between variable costs and fixed costs. Among the disadvantages of direct costing perhaps the most important is the requirement that costs be related to a single output measure. Clearly most costs are a func- tion of a number of factors and to predict or make decisions based upon a single factor may ignore crucial considerations which result in serious errors of estimation or prediction. Other disadvantages of direct costing relate to need for assuming a linear relationship between variable costs and an output measure. For example, given the high short- term interest rate which exists at present, the cost of carrying excess funds and supplies is such that it may be desirable to estimate these costs by means of a curved line which shows the cost of carrying additional units increasing at an increasing rate. For further discussion of full and direct costing see NAA Research Reports Nos. 23, 24, and 37. 42 Simple Linear Regression The mixed costing or simple linear regression approach recognizes that most costs have an element of fixed behavior and an element of variable behavior. For instance, in the two banks in this study salaries showed a fixed element which might be identified with remuneration of officers and directors and a variable element which would seem to be asso- ciated with lower level staff. Simple linear regression uses least squares regression techniques to fit a prediction line or equation to the data with the y-intercept being treated as the fixed component and the slope of the line treated as the variable cost per unit of output or the vari- able cost component. The advantages of simple linear regression include breaking individual cost categories down into fixed and variable components. Both full costing, which treats all costs as variable, and direct costing, which classifies a cost category as fixed or variable, recognize a single dimension or factor for explaining the behavior or prediction of a cost category. Simple linear regression estimates or Predicts a cost based upon a combination of its elements and its variable relationship with the independent variable or factor. Intuitively and pragmatically simple linear regres- Sion appeals to decision makers as a tool for estimating relationships and making predictions because inclusion of bOth fixed and variable components for explaining cost 43 behavior allows for a more complete specification of cost- causing factors. The fact that the variable component is based upon only one cost is probably the major disadvan— tage of simple linear regression. Benston noted in a dis- cussion of the available methods for estimating or predict- ing future costs that . . . supervisors tend to disregard data that they believe are 'unrealistic,‘ such as those based on the simplification that costs incurred are a func- tion of units of output only. Therefore, multiple regression analysis should prove more acceptable to supervisors than procedures that require gross simplifications of reality. Benston further noted that while simple linear regression utilizes only a single output measure and no other factors to estimate cost relationships, in the past it has been defended on the reasonable grounds that multiple regres- sion was too difficult computationally and therefore too costly to be economically feasible. These arguments no longer seem to be valid with the widespread availability of computer time at a low cost. While full costing and direct costing have the advantages of being useable in instances where multiple regression is not practical due to limited past data or experience with a service or branch, simple linear regres- sion also has the disadvantage of requiring a number of past Observations in order to provide meaningful predictions. Ideally the prediction of cost categories would be baSed.upon experience or observations within individual 44 branches because the combination of factors which cause costs to be incurred tend to be unique to a single branch. By basing cost predictions or cost estimations upon the experience of individual branches, the marginal contribution of individual factors to costs are estimated for that branch. Since the experience in any one branch is not necessarily appropriate for predicting the costs of new branches it may be desirable to estimate relationships between cost factors and costs for an average branch. This average branch equation is also useful for comparing indi- vidual branches to standards based upon an average branch or perhaps an ideal branch. Thus, in addition to generating a simple linear regression equation for each branch of each bank, data for all the branches of Bank A were pooled into the computation of a simple linear regression equation for Bank A. Exhibits 1 and 2 illustrate the type of data provided by the banks in this study. Exhibits 4, 5, and 6 show the frequency of this data, the number of branches for which it was available, and the use made of this data. This equation is a summary or average relationship for the branches in Bank A. This pooled regression model has the disadvantage of being based upon all branches and is therefore less accurate for predicting costs in any indi- Vidual branch. The advantage of the pooled equation is that it can be used for predicting the experience of new branches and can be compared with the equations for individual 45 branches to show the marginal contribution to costs in a branch as compared to an average branch. In Bank B the statistical information available included many potential factors which could be important in cost incurrence. However, the information was available for only four years, 1970-1973: thus, the mechanical or informa- tional requirements for regression by individual branches were not met. As a result, the only simple regression model generated for Bank B is one based upon the pooled experience of all the 46 branches. The simple linear equation therefore is based upon the experience of an average branch. Multiple Regression George Benston argued persuasively that managers and foremen are often reluctant to use cost predictions based upon simple linear regression, full costing, or direct costing because each of these methods assumes that costs can 12 The increasing avail- be associated with a single factor. ability of computer time at a reasonably low price has made the computations required by multiple regression practical and has virtually eliminated the cost difference which used to exist between using multiple regression and using the other techniques for cost estimation. The principle advantage of using multiple regression for cost estimation or cost prediction is the advantage of being able to simultaneously consider the individual con- tribution of many factors acting together and to estimate 46 the combined effect of these factors upon the level of cost incurrence. Now that the cost differential between multiple regression and other cost estimation techniques is minimal, the major drawback of multiple regression is that it is based upon a number of fairly restrictive assumptions whose vio- lations may severely limit the applicability of the computed regression equation. In Chapter III the assumptions of multiple regression will be discussed, the tests employed in this research for violations of the assumptions will be examined, and the implications of violations will be assessed. The most accurate predictions using multiple regres- sion techniques are based upon observations within individual branches. One set of equations was deve10ped for each branch in Bank A for use in predicting costs of that branch. In Bank B the number of observations (years) was only four so that regression by individual branches was not possible due to the technical requirements of multiple regression. For an explanation of data usage see Exhibit 4. Since each inde- pendent variable requires one degree of freedom and the total degrees of freedom available when only four observa- tions exist is three, there were not sufficient degrees of freedom to examine potential cost-causing factors. In order to provide an estimate of the effect of cost-causing factors in an average branch of Bank A and in an average branch of Bank B, the branches of Bank A.were pooled to generate a multiple regression equation and the branches 47 of Bank B were pooled to generate a multiple regression equation. These equations, based upon the pooled branches of that bank, are useful for predicting the experience of new branches and for providing a standard against which to evaluate the performance of individual branches. Earlier in this chapter, three different purposes or types of accounting information were discussed. Those types of accounting information were: 1. Reports prepared for external purposes. 2. Responsibility accounting reports deveIOped for internal performance evaluation. 3. Information developed for inclusion in decision models designed to predict future costs or bene— fits. The information provided by the two banks examined in this study is responsibility accounting data developed for the measurement of the performance of individual branches and branch managers. An example of the data provided in these reports is provided in Exhibits 1 and 2 of Chapter I. Although the expressed purpose for developing this data was for internal performance evaluation, the informa- tion included in these reports comprises part of the necessary input information for inclusion in decision models designed to predict future costs. It is for the latter purpose that the information is used in this study. 48 Banks do not have a single output. The output of banks may take the form of dollars of time deposits, dollars of demand deposits, dollars of outstanding loans (either short- or long-term), dollars of credit card borrowings, or many other types of output. To give recognition to each of these types of potential output, certain of these output measures are included in the ten independent variables employed in the multiple regression models for Banks A and B. It is important that considerable care be exercised in the selection of independent variables for a regression model. Failure to include significant explanatory factors can result in a systematic bias to predictions made using the model. In the present study ten independent variables are used in the final set of independent variables used for generating models. Any of these ten variables which are not significant at an alpha level of .10 are discarded before selection of the final prediction equation. Output measures included in the independent variable set for Bank A are Earnings on Average Deposits, Savings Deposits (dollars), Time Deposits (dollars), Certificates of Deposit (dollars), and Savings Certificates (dollars). For Bank B output measures included in the independent variable set are Savings Deposits (dollars), Certificates of Deposit (dollars), Savings Thrift Certificates (dollars), Demand Deposits (dollars), and Average Commercial Loans (dollars). 49 Because there is some evidence and concern in the banking profession that costs are a function of the number of accounts rather than dollar measures of output, the fol- lowing independent variables were included in the independent variable set for Banks A and B, respectively. For Bank A these variables are Personal Checking Accounts, Savings Certificates (number of accounts), and Savings Deposits (number of accounts). For Bank B these variables are Savings Deposits (number of accounts), Savings Thrift Cer- tificates (number of accounts), and Demand Deposits (number of accounts). During the time period involved in this study there was considerable flux in the price of goods and commodities due to inflation. Therefore, in order to estimate the effect of changes in the price level upon costs, the Consumer Price Index is included in the independent variable set for both Banks A and B. In Bank A the branches ranged in age from seventy years to five years. Since many organizations note that older branches tend to have higher salary costs and lower plant or facilities costs the relationship between a branch's age and costs is important. In order to assess the impact of the age of a branch on the level of various cost categories, the age of branches is included as an independent variable for Bank A. In Bank B as a result of visual inspection there appears to be a very strong relationship between the number 50 of officers and directors and the level of certain cost categories. Thus, the number of officers and directors is included in the independent variable set of Bank B. This study is constrained by the data currently available. As noted earlier in this chapter the data used is developed for control purposes for responsibility account- ing reports. If a bank were to study its ability to predict future costs much further consideration could be given to the selection of variables, cost of collecting the data and the benefits likely to accrue to a bank from more accurate cost predictions. Error Measures The comparison of the four approaches suggested in the literature (direct costing, full costing, simple linear regression, and multiple regression) is made in terms of their ability to predict cost levels for existing bank branches. Two reasons for using predictive ability as a criterion for comparing the four costing approaches are that it is objec- tive and that accurate predictions are necessary to enable decision makers to choose intelligently between alternative courses of action. A prediction has been generated for each period for each branch under the four costing models. This prediction is then compared with the actual cost for that period to determine the residual or error. The four models are com- pared on the basis of the following error measures: 51 (1) Average relative error; (2) Average absolute value of relative error; and (3) Average squared relative error.13 For a detailed description of the manner in which predictions are generated and accuracy of predictions measured, see Exhibits 5 and 6. Average Relative Error An important measure of the adequacy of an alterna- tive costing method for estimating costs is the relative or percentage error of the prediction of future costs. The average relative error provides a means for estimating how material or significant the risk is if‘decisions are based upon the predicted costs. The average relative error provides a measure of bias in the predictor. The sign of this error indicates whether the method tends to over- or under-predict future costs. Average relative error is determined by dividing the error or residual in each case by the actual observed cost. The result is the relative error for that case. Average relative error is determined by summing the relative errors and dividing by the number of observations, (N). Average _ 1_§ Predicted Cost - Actual Cost Relative Error - N 1 Actual 53st One potential danger of using average relative error as a means of assessing the adequacy of alternative costing models is that offsetting errors may result in a very low 52 average relative measure when a number of errors exist but in opposite directions, thus minimizing their effect. Average Absolute Value of Relative Error Average absolute value of relative error is an impor- tant measure of the accuracy in predictions ignoring the direction of errors. Ignoring the direction of errors means that an error of $100 is treated the same whether the pre- dicted cost is greater than the actual cost or the actual cost is greater than the predicted cost. Decision makers should be interested in the average absolute value of relative error as a measure of the size of errors resulting from a prediction model. The size of pre- diction errors can be an important consideration in the assessment of risk. g [Predicted Costa: Actual Costl Average Absolute = 1 Actual Cost Relative Error N . 1 1 Average Squared Relative Error Another problem which cannot be ignored in assessing the adequacy of alternative information models is the impact of large estimation errors. Firms expect some variance from projections and tend to reject projects where the marginal contribution is so small that it may be eliminated by a small error in projection. Large errors, however, tend to result in large losses and often discontinuation of a segment of a business. It is desirable therefore to include an error 53 measure which gives large errors more weight than a number of small errors which sum to the same amount. The average squared relative error is used to give large errors addi- tional weight. Average Squared = 1 g (Predicted Cost - Actual Cost)2 Relative Error Ni=1 Actual Cost Summary This chapter has briefly illustrated the cost account- ing system environment for banks. The need for knowledge of future costs and a linking of those costs with different types of bank output has been noted. Four alternative costing models (full costing, direct costing, simple linear regression or mixed costing and multiple regression) are selected from those discussed in the accounting literature. For each of the alternative costing models the manner in which the model is implemented in this study is disclosed in Exhibits 4, 5, and 6. The criteria for evaluating and com- paring these alternative models are average relative error, average absolute value of relative error and average squared relative error. The rationale for selecting these error measures is discussed in terms of utility, bias and potential costs and benefits. 54 TABLE 1 Correlation of Cost Categories with Output Measures Bank A Correlation of Output Measures with Total Cost Earnings on Average Deposits (dollars) . . Time Deposits (dollars) . . . . . . . . . . Personal Accounts (number of accounts) . . Savings Deposits (dollars) . . . . . . . . Savings Certificates (number of accounts) Savings Deposits (number of accounts) . Savings Certificates (dollars) . . . . . . Certificates of Deposit (dollars) . . . . . . . . . . . . . . .98152 . . . . . . . . . . .92031 . . . . . . . . . . .85739 . . . . . . . . . . .82404 . . . . . . . . . .75873 . . . . . . . . . . .70035 . . . . . . . . . . .60204 . . . . . . . . . . .24239 Correlation of Cost Category with Earnings on Average Deposits Interest . . . . . . . . . . . . . . . . . Indirect Expenses . . . . . . . . . . . . Fringe Benefits . . . . . . . . . . . . . Salaries . . . . . . . . . . . . . . . . Occupancy . . . . . . . . . . . . . . . . Office Supplies . . . . . . . . . . . . . Other Direct Expenses . . . . . . . . . . Bank B Correlation of Output Measures . . . . . . . . . . .96341 . . . . . . . . . . .96333 . . . . . . . . . . .96086 . . . . . . . . . . .94125 . . . . . . . . . . .89208 . . . . . . . . . . .87359 . . . . . . . . . . .78675 with Total Cost Demand Deposits (number of accounts) . . . Savings Thrift Certificates (dollars) . . Savings Deposits (dollars) . . . . . . . . Certificates of Deposit (dollars) . . . . . . . . . . . . . . .68940 . . . . . . . . . . .68376 . . . . . . . . . . .66959 . . . . . . . . . . .62429 Savings Thrift Certificates (number of accounts) . . . . . . . .61433 Savings Deposits (number of accounts) . . . . . . . . . . . . .59492 Correlation of Cost Category with Demand Deposits Service Department Expense . . . . . . . . Employee Benefits . . . . . . . . . . . . Salaries . . . . . . . . . . . . . . . . . Other Expenses . . . . . . . . . . . . . . Interest . . . . . . . . . . . . . . . . . Furniture . . . . . . . . . . . . . . . Occupancy . . . . . . . . . . . . . . . . Provision for Losses . . . . . . . . . . . . . . . . . . . . . .82801 . . . . . . . . . . .81467 . . . . . . . . . . .77500 . . . . . . . . . . .68917 . . . . . . . . . . .67798 . . . . . . . . . . .47966 . . . . . . . . . . .46243 . . . . . . . . . . .30062 55 EXHIBIT 4 Bank A--83 Branches--Annua1 Data Data Provided for 10 Branches for Period 1963-72 Data Used To: 1. develop full costing predictions for each individual branch for 1971 and 1972 (20 predictions); develop direct costing predictions for each individual branch for 1971 and 1972 (20 predictions); develop simple linear regression predictions for each individual branch for 1961 and 1972 (20 predictions); develop multiple regression predictions for each individual branch for 1971 and 1972 (20 predictions); pool the experience of the 10 branches from 1963-70 (80 observations) to develop predictions for individual branches for 1971 and 1972 (20 predictions) for simple linear regression and multiple regression. Bank B--46 Branches--Annual Data Data Provided for 46 Branches for Period 1970—73 Data Used To: 1. 2. develop full costing predictions for each individual branch for 1972 and 1973 (92 predictions); develop direct costing predictions for each individual branch for 1972 and 1973 (92 predictions); pool the experience of the 46 branches from 1970-71 (92 observations) to develop predictions for individual branches for 1972 and 1973 (92 predictions) for simple linear regression and multiple regression. 56 EXHIBIT 5 Bank A—-83 Branches 10 Branches Randomly Selected Total Observations 83 Branch 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1 x x x x x x x x x x 2 x x x x x x x x x x 3 x x x x x x x x x x 4 x x x x x x 5 x x x x x 6 x x x x x x x x x x 7 x x x x x x x x x x 8 x x x x x x x x x x 9 x x x x x x x 10 x x x x x x Branch 4 opened 1967 Branch 5 opened 1968 Branch 9 Opened 1966 Branch lOopened 1967 A description of the method of applying each alterna- tive costing method follows. After a prediction of total costs has been develOped three common steps are: 1. Each prediction is compared with the actual cost for that period to determine the residual or error in that prediction. 2. For the 10 branches of Bank A, the Average Rela- tive Error, Average Absolute Relative Error and Average Squared Relative Error are determined. 57 EXHIBIT 5 (continued) 3. The error measures determined are compared with alternative costing models in a test of "Mean Differences" to statistically evaluate the predictive ability of each. Full Costing 1. Total costs for years 1963-1970 are correlated with 10 potential output measures and graphed against each R output measure. On this basis "Earnings on Average Deposits" is chosen as the output measure for prediction of future costs. fl 2. For each branch a prediction of total costs is required for the years 1971 and 1972. To generate the pre- diction for a branch in 1971, the 1970 "Total Costs" are divided by "Earnings on Average Deposits" to find an average cost per dollar of "Earnings on Average Deposits." The form of the predicting equation is: 1970 average cost 1971 "Earnings per dollar of "BAD" on Average Deposits" . The 1972 prediction is made by determining the 1971 average cost per dollar of "Earnings on Average Deposits" and multi- plying by the 1972 "Earnings on Average Deposits." Thus, a total of 20 predictions are generated. 58 EXHIBIT 5 (continued) Direct Costing (.60, .70, .80, and .90)* 1. Total costs for years 1963-1970 are correlated with 10 potential output measures and graphed against each output measures. On this basis "Earnings on Average Deposits" is chosen as the output measure for prediction of future costs in individual branches. 2. Each cost category (interest, salaries, fringe benefits, occupancy costs, office supplies, other direct expenses, and indirect expenses) is correlated with "Earnings on Average Deposits" and classified as fixed or variable. 3. For each branch a prediction equation is formed based upon the classification of cost categories. This equation is of the form: Fixed Costs + (Variable Costs,/$ of EAD)(EAD) where EAD = "Earnings on Average Deposits" VC are computed based on previous year, and EAD is based on actual value of independent variable in current year. *To allow for the possibility that the results of direct costing predictions are biased by the correlation scheme used for classifying costs as fixed or variable, four different sets of direct costing predictions are generated. These are based upon classifying costs with a correlation of less than .60, .70, .80, or .90 as fixed. Those costs with higher correlations are classified as variable. S9 4. For each branch a prediction of total costs is generated for the years 1971 and 1972. Thus, a total of 20 predictions are generated. Simple Linear Regression (Individual Branches) 1. Total costs for years 1963-1970 are correlated with 10 potential output measures and graphed against each output measure. On this basis "Earnings on Average Deposits" is chosen as the output measure for prediction of future costs in individual branches. 2. Each cost category (interest, salaries, fringe benefits, occupancy costs, office supplies, other direct expenses, and indirect expenses) is regressed with “Earnings on Average Deposits" and divided into its fixed component and a variable component. 3. For each branch a prediction equation is formed based upon the regression of cost categories. This equation is of the form: fixed costs + (variable costs per dollar of "Earnings on Average Deposits") (total dollars of "Earnings on Average Deposits"). 4. For each branch a prediction of total costs is generated for the years 1971 and 1972. Thus, a total of 20 predictions are generated. 60 Simple Ligear Regression (Cross-Sectional or Pooled) l. The observations of all 10 branches are pooled into one set of data. Since the time period used for develop- ing prediction equations is 1963-1970, there are 64 observa- tions. 2. Total costs for years 1963-1970 are correlated with 10 potential output measures and graphed against each output measure. On this basis "Earnings on Average Deposits" is chosen as the output measure for prediction of future costs in individual branches. The basis for this choice is illus- trated in Table l. 3. Each cost category (interest, salaries, fringe benefits, occupancy costs, office supplies, other direct expenses, and indirect expenses) is regressed with "Earnings on Average Deposits" and divided into its fixed component and a variable component. 4. From the pooled observations, a prediction equa- tion is formed based upon the regression of cost categories. This equation represents an average branch and is of the form: fixed costs " (variable costs per dollar of "Earnings on Average Deposits") (total dollars of "Earnings on Average Deposits"). 5. For each branch a prediction of total costs is generated for the years 1971 and 1972. Thus, a total of 20 predictions are generated. 61 Multiple Linear Regression TRegressiOn by Branches--Revised) 1. Cost information used for generating predicting equations is from the period 1963-1970 for 1971 predictions and 1963-1971 for 1972 predictions. Thus a separate set Of prediction equations are developed for 1971 and a new set revised tO include 1971 experience are developed for 1972. F3 Because the degrees Of freedom are not sufficient to . examine all ten independent variables at once an ad hoc procedure is used where several runs are made with different combinations Of variables and the four independent variables found to be least significant are discarded (8 years - l = 7 degrees Of freedom). Thus, for each branch total costs are regressed against six Of ten possible independent variables Operating simultaneously. Independent variables considered are "Earnings on Average Deposits (dollars)," "Saving Deposits (dollars)," "Time Deposits (dollars)," "Certificates Of DePosit (dollars)," "Saving Certificates (dollars)," "Per- sonal Accounts (number of accounts)," "Savings Certificates (number Of accounts)," "Savings Deposits (number of accounts)," "Consumer Price Index (U.S.)," and "Age of Branch (years)." 2. For each branch a prediction equation is formed based uPon the regression Of cost categories. This is Of the form: Constant + (regression coefficient Of X1) (value Of X1 in 1971) + (regression coefficient Of X2) (value Of X2 in 1971) + . . (regression coefficient of Xn) (value of Xn in 1971), 62 3. For each branch a prediction Of total costs is generated for the years 1971 and 1972. Thus, a total Of 20 predictions are generated. The three Multiple Linear Regression models which follow all combine the experience of all 10 branches in developing predictive equations. The rationale for this Fa "pooling" Of branches results from frequent technical prob- lems Of insufficient Observations to perform multiple regres- sion by branches and a desire to compare the marginal con- tribution Of cost factors in an average branch with the marginal contribution Of that factor in a specific branch. Those methods described as revised have one predictive equa- tion develOped for 1971 based upon 1963-1970 experience and another predictive equation developed for 1972 based upon 1963-1971. Multiple Linear Reggession (Pooled--Revised) l. The Observations Of all 10 branches are pooled into one set Of data. Since the time period used for develop- ing prediction equations is 1963-1970, there are 64 Observa- tions. Independent variables are considered simultaneously in multiple regression. Independent variables considered are ”Earnings on Average Deposits (dollars)," "Saving Deposits (dollars)," "Time Deposits (dollars),” "Certificates Of Deposit (dollars)," "Saving Certificates (dollars)," "Person- nel Accounts (number of accounts), "Savings Certificates 63 (number of accounts),“ "Savings Deposits (number Of accounts)," "Consumer Price Index (U.S.)," and "Age Of Branch (years)." 2. From the pooled Observations a prediction equa- tion is formed based upon the regression Of total costs. This equation represents an average branch and is Of the form: Constant + (regression coefficient of XI) (value of X1 in 1971) + (regression coefficient Of Xn) (value Of Xn in 1971). 3. Predictions for 1972 are generated by revising the time period to 1963-1971 to generate new equations for predicting costs. In this manner the equation used for pre- diction is based upon the most recent Observations. 4. For each branch a prediction Of total costs is generated for the years 1971 and 1972. Thus, a total Of 20 predictions are generated. Multiple Linear Regression (Pooled--Not Revised) 1. The Observations Of all 10 branches are pooled into one set Of data. Since the time period used for develop- ing prediction equations is 1963-1970, there are 64 Observa- tions. Independent variables are considered simultaneously in multiple regression. Independent variables considered are ”Earnings on Average Deposits (dollars)," "Saving Deposits (dollars)," "Time Deposits (dollars)," "Certificates Of Deposit (dollars)," "Saving Certificates (dollars)," "Person- nel Accounts (number Of accounts)," "Savings Certificates 64 (number Of accounts)," "Savings Deposits (number Of accounts)," "Consumer Price Index (U.S.)," and "Age Of Branch (years)." 2. From the pooled Observations a prediction equa- tion is formed based upon the regression Of total costs. This equation represents an average branch and is Of the form: Constant + (regression coefficient Of Xn) (value Of Xn F1 in 1971). 3. Predictions for 1972 are generated by using ‘ regression coefficients for the period 1963—1970 multiplied b by 1972 independent variable values. 4. For each branch a prediction Of total costs is generated for the years 1971 and 1972. Thus, a total Of 20 predictions are generated. Multiple Linear Regression (Sum Of Cost Categories) 1. In this method the predicted total costs are the sum Of the predicted cost categories. As shown in Table 2 Of Chapter III an equation Of the form y = a + blx1 + bzx2 + b3x3 + . . . bnxn is develOped for each cost category. The predicted Total Costs result from the following equation: TC = INT + SAL + FB + OCC + OFF SUPP + ODE + IE where TC INT SAL FB OCC OFF SUPP ODE IE the time period tO 1963 - 1971 to generate new equations for predicting costs. diction is based upon the most recent Observations. generated for the years 1971 and 1972. 2. 3. 65 Total Costs Predicted Predicted Interest Costs Predicted Salaries Predicted Fringe Benefits Predicted Occupancy Costs Predicted Office Supplies Predicted Other Direct Expenses Predicted Indirect Expenses Predictions for 1972 are generated by revising For each branch a prediction Of total costs is predictions are generated. In this manner the equation used for pre- Thus, a total Of 20 66 EXHIBIT 6 Bank B--46 Branches Annual Observations for Period 1970-1973 Total Observations 184 A description Of the method Of applying each alterna- tive costing method follows. After a prediction of total F} costs has been develOped three common steps are: 1. Each prediction is compared with the actual cost b for that period to determine the residual or error in that prediction. 2. For the 46 branches Of Bank B the average rela- tive error, average absolute relative error, and average squared relative error are determined. 3. The error measures determined are compared with alternative costing models in a test Of "Mean Differences" to statistically compare the predictive ability Of each. Full Costing 1. Total costs for years 1970-1973 are correlated with 10 potential output measures and graphed against each output measure. On this basis ”Demand Deposits" is chosen as the output measure for prediction Of future costs. See Table l for evidence as to the choice Of output measures. 2. For each branch a prediction of total costs is required for the years 1972 and 1973. To generate the 67 prediction for a branch in 1972, and 1971 "Total Costs" are divided by "Demand Deposits" to find an average cost per dollar Of "Demand Deposits." The form Of the predicting equation is: (1971 average cost per dollar Of "DD") (1972 "Demand Deposits). The 1973 prediction is made by deter- mining the 1972 average cost per dollar Of "Demand Deposits" and multiplying by the 1973 "Demand Deposits." Thus, a total Of 92 predictions are generated. Direct Costing (.60, .70, .80, and .90)* 1. Total costs for years 1970-1973 are correlated with 10 potential output measures and graphed against each output measure. On this basis, "Demand Deposits” is chosen as the output measure for prediction Of future costs in indi- vidual branches. 2. Each cost category (salaries, employee benefits, interest on deposits, occupancy costs, furniture, provision for loan losses, other Operating expenses, service depart- ment expense, and total Operating expense) is correlated with "Demand Deposits" and classified as fixed or variable. 3. For each branch a prediction equation is formed based upon the classification Of cost categories. This * TO allow for the possibility that the results Of direct costing predictions are biased by the correlation scheme used for classifying costs as fixed or variable, four different sets Of direct costing predictions are generated. These are based upon classifying costs with a correlation Of less than .60, .70, .80, or .90 as fixed. Those costs with higher correlations are classified as variable. 68 equation is Of the form: fixed costs + (variable costs per dollar of "Demand Deposits") (total dollars Of "Demand Deposits"). 4. For each branch a prediction Of total costs is generated for the years 1972 and 1973. Thus, a total Of 92 predictions are generated. Simple Linear Regression (Pooled--Revised) l. The Observations Of all 46 branches are pooled into one set Of data. Since the time period used for develOp- ing prediction equations is 1970-1971, there are 92 Observa- tions. 2. Total costs for years 1970-1971 are correlated with ten potential output measures and graphed against each output measure. On this basis "Demand Deposits" is chosen as the output measure for prediction Of future costs in indi- vidual branches. 3. Each cost category (interest On deposits, sala- ries, employee benefits, occupancy costs, furniture, other Operating expenses, provision for loan losses, and service department expenses) is regressed with "Demand Deposits" and divided into its fixed component and a variable component. 4. From the pooled Observations, a prediction equa- tion is formed based upon the regression of cost categories. 69 This equation represents an average branch and is Of the form: fixed costs + (variable costs per dollar Of "Demand Deposits") (total dollars Of "Demand Deposits"). 5. For eachbranch a prediction Of total costs is generated for the years 1972 and 1973. Thus, a total Of 92 predictions are generated. ', [-F‘I'I ’ v,- Multiple Linear Regression TPOOled--Revised7_ 1. The Observations Of all 46 branches are pooled t,‘ into one set Of data. Since the time period used for developing prediction equations is 1970-1971, there are 92 Observations. 2. Ten independent variables are considered simul- taneously in the multiple regression model for Bank B. These independent variables are Savings Deposits (number), Savings Deposits (dollars), Certificates Of Deposit (dollars), Savings Thrift Certificates (number), Savings Thrift Certifi- cates (dollars), Demand Deposits (number), Demand Deposits (dollars), Consumer Price Index, Number Of Officers and Directors, and Average Commercial Loans (dollars). 3. From the pooled Observations, a prediction equation is formed based upon the regression Of total costs. This equation represents an average branch and is Of the form: Constant + (regression coefficient of X1) (value of X1 in 1972) + (regression coefficient of x2) (value of X2 70 in 1972) + . . . (regression coefficient Of Xn) (value Of xn in 1972). 4. Predictions for 1973 are generated by revising the time period to 1970-1972 to generate new equations for predicting costs. In this manner, the equation used for pre- diction is based upon the most recent Observations. F} I 5. For each branch a prediction Of total costs is generated for the years 1972 and 1973. Thus, a total of 92 predictions are generated . u 71 CHAPTER II--FOOTNOTES Charles T. Horngren, Cost Accounting: A_Managerial Emphasis (Englewood Cliffs, New Jersey: Prentice- Hall, Inc., 1972), p. 666. John A. Higgins, "Responsibility Accounting," Arthur P) Andersen Chronicle, V. 12, NO. 2 (April, 1952), p. l. ' Horngren, pp. 812-23. National Association Of Accountants, Current Applica- . tion Of Direct Costing (New York: National Association v Of Accountants, 1961), pp. 19- 20. George T. Benston, "Multiple Regression Analysis Of Cost Behavior," Accounting Review, V. 41 (October, 1966), PP. 658-659. Ibid., PP. 657-72. Jacob G. Birnberg, Joel Demski, and Nicholas DOpuch, Cost Accountipg--Accounting Data for Management' 5 Decisions (New York: Harcourt-Brace-Jovanovich, Inc., 1974), PP. 50- 81. John R. Walker, Bank Costs for Decision Making_(Boston, Massachusetts: Bankers Publishing Company, 1970), p. 3. Ibid., pp. 3-4. Walker, pp. 15-16. Benston, p. 658. Ibid., p. 658. Joel S. Demski, "Predicting Ability of Alternative Performance Measurement Models," Journal Of Accountipg Research, V. 7 (Spring, l969),p pp 103- W4 CHAPTER III TEST OF THE MODELS The primary concern Of this research is to compare alternative costing models on the basis Of their ability tO estimate costs for recurring decisions. The predictive ability results of alternative costing models can only be compared in a meaningful manner if the models are appropri- ately specified. Model specification is a particularly rele- vant issue with respecttx>the linear regression models used in the present analysis; i.e., do the data used in the regression analysis violate any of the assumptions which underlie this statistical procedure? If so, what is their effect on the error measurements that result? The discussion which follows examines the assumptions Of regression, the degree to which the assumptions are violated in this study, and the impact Of those violations upon the findings Of the study. Linear Relationship The two regression models examined in this research are simple linear regression and multiple regression (some authors would call this model multiple linear regression). Both of these models assume a linear relationship between the 72 73 contributive factors and costs. If the relationship between the contributive factors (the independent variables) and costs (dependent variables) is not linear, the least-squares equation generated in the two regression models will have a large standard error Of estimate. The standard error of the estimate shows how well the equation fits the data. The standard error Of regression coefficients will be greater than they would have been without this misspecification Of the models. In the context in which they are used in this study, the standard error Of regression coefficients are used tO generate confidence intervals around the "true" marginal cost Of a contributive factor. For example, in Bank A the regression coefficient for Earnings on Average Deposits as shown in Table 2 is .3617 and the standard error of coeffi- cients is .0618. This means that if the assumptions dis- cussed later in this chapter about the disturbance terms are not seriously violated there is a 95% probability that the true marginal cost per dollar Of earnings on average deposits is between .2379 and .4855. The standard error Of the estimate is an approxima- tion Of the variance Of the error term and is a function Of the strength Of the relationship between the independent variables and the dependent variable and the form of the equation used for estimation. If the relationship between independent and dependent variables is not strong, then the standard error Of the estimate will be large regardless of 74 the form of the equation. Further, given a strong relation- ship between the independent and dependent variables if the form Of the equation is misspecified the standard error Of the estimate will tend to be large. Therefore, where the standard error Of the estimate is small, evidence exists that the relationship between the independent and dependent ) "1 variables is strong and that the form Of the equation is -W.- "I reasonable for the set Of data upon which it is based. In this study evidence which supports the conclusion that there is a linear relationship between contributive Li factors and costs is available in the form of the standard error of the estimate for Total Costs in Banks A and B, respectively. The standard error of the estimate in Bank A (from Table 2) is $61,725.43 and in Bank B (from Table 3) it is $95,751.55. Since the predicted total costs range to $3,431,162 in Bank A and to $2,465,168 in Bank B, it can be seen that the confidence interval for predictions of the level Of total costs do not exceed ten per cent in either direction from the predicted values. Thus, the assumption Of linearity is deemed reasonable in this study. Technical Reqpirements Technical requirements Of regression analysis for cost analysis as noted by Benston include: A. The time periods should be long enough to allow the bookkeeping procedures to pair output produced in a period with the cost incurred because Of that production. 75 B. The time periods chosen should be short enough to avoid variations in production within the period. Otherwise, the variations that occur during the period will be averaged out, possibly obscuring the true relationship between cost and output. C. The number of time periods (observations) must, as a minimum, be one more observation than there are independent variables to make regression analysis possible. Of course, many more observa- tions must be available before one could have any confidence that the relationship estimated from the sample reflects the "true" underlying relationship. D. All factors that affect cost should be specified and included in the analysis. This is a very important requirement that is often difficult to meet.1 The time periods chosen for analysis in this research are years. Examination of data and interviews with bank officials of approximately a dozen large banks led to the conclusion that use of periods of one year as the unit of analysis allows for the pairing of output with the costs incurred because of that production. Moreover, this cir- cumvents, to a large extent, the problem of the timing of arbitrary but necessary cost incurrences. One measure of whether important factors that affect costs have been excluded or overlooked is given by the coefficient of determination, R2. R2 may be defined as the explained error (the mean squared distance, between the pre- dicted cost and the mean cost, squared) divided by the total error (the mean squared distance, between observed values and the mean, squared). When the coefficient of determina- tion approaches one (1) that means that there has been a 100% 76 reduction in total error brought about by fitting the regression line. As shown in Tables 2 and 3 for Banks A and B, respectively, the coefficient of determination for Bank A is .9940, and for Bank B it is .9347. This would seem to indicate that no factor that affects costs in a significant manner has been omitted from the analysis. Benston noted that the number of time periods as a T] minimum should be one more observation than there are inde- pendent variables to make regression analysis possible. While there are no specific guidelines beyond this as to how U many observations are necessary to make multiple regression and simple linear regression useable for prediction and esti- mation purposes, the equation for the standard error of the estimates is: 2 _ £(-') SE _ n-g where S = standard error of the estimate y = actual observed value of dependent variable predicted value of dependent variable ‘< II n = sample size Note that given a certain degree of variation in a population the standard error of the estimate becomes smaller as sample size increases. Interpreted further this means that when standard errors of the estimate are low for a small size then the predicting method may be inferred to be 77 an accurate predictor of future costs. On the other hand if a method (in this study multiple and simple regression by branches) has a large standard error of the estimate where sample size is small it is difficult to assess the cause of this large error. It would then be possible to increase the number of observations and greatly reduce the standard error of the estimate. In this study there are 12 independent variables for which sufficient information exists in Bank A and 14 such independent variables in Bank B. The ad hoc procedure used in this study is to choose for inclusion those independent variables which are significant at the lowest alpha level. Measurement Errors One potential difficulty which must be faced in the preparation of cost analysis is the potential affect of measurement errors on the dependent variables. Among the problem of cost measurement are: 1. When is a cost incurred? 2. To what extent should joint costs be allocated? 3. Should opportunity costs be recognized when available resources are used at no immediate cost to the firm? For purposes of this research, it has been assumed that the banks are able to satisfactorily determine when costs are incurred. 78 The biggest joint cost problem that banks have con- cerns the allocation of indirect costs of operating a number of branches. Responsibility accounting systems encounter a dilemma when faced with the goal of holding segments of a business accountable for only those costs which they can control and a seemingly contradictory goal of accounting for branches of banks as either cost or profit centers. A regression of indirect bank costs for a ten-year period in Bank A, which is shown in Table 4, indicates that indirect costs for banks are quite indivisible and that allo- cation of such costs is quite arbitrary. As noted in Charles T. Horngren's Cost Accounting: A_Managerial Emphasis, joint cost allocations should not be used for decision making purposes.2 Further discussion of the significance of the regres- sion of indirect costs can be found in Chapter V. The nature of the errors of measurement is important since some kinds will affect the useful- ness of regression analysis more than others will. Errors in the dependent variable, cost, are not fatal since they affect the disturbance term. The predictive value of the equation is lessened, but the estimate of marginal cost is not affected. But where there are errors in measuring output or the other independent variables, the disturbance term u5 will be correlated with the independent vari— ables. The preceding quotation from Benston discusses the implication of errors in the measurement of costs. The independent variables examined in Bank A are listed in Table 79 2, and Table 3 lists the independent variables examined in Bank B. Note that each of the independent variables examined is easily identified and measured in terms of dollars, years, or number of accounts. Thus, it will be assumed in this study that measurement errors are minimal. Multicollinearity The existence of high intercorrelations among the explanatory variables makes it difficult to estimate the separate relationships of each to the dependent variable. Under these conditions, the marginal contribution that indi- vidual factors make to costs become difficult to measure via regression techniques. The main consequences of multicollinearity as noted in John Johnston's Econometric Methods are the following: 1. The precision of estimation falls so that it becomes very difficult, if not impossible, to disen- tangle the relative influences of the various X vari- ables. This 1033 of precision has three aspects: Specific estimates may have very large errors; these errors may be highly correlated, one with another; and the sampling variances of the coefficients will be very large. 2. Investigators are sometimes led to drop vari- ables incorrectly from an analysis because their coefficients are not significantly different from zero, but the true situation may be not that the set of sample data has not enabled us to pick it up. 3. Estimates of coefficients become very sensi- tive to particular sets of sample data, and the addi- tion of a few more observations can sometimes produce dramatic shifts in some of the coefficients.4 80 An important question to answer at this point is "What is the consequence of the existence of multicolli- nearity in a cost study of this type?" A very illuminating answer is given by Carl F. Christ in Econometric Models and Methods. Christ says, Suppose the aim is not to estimate parameters such as the regression coefficients in the regression equations we have been discussing, but is instead to forecast the values of the dependent variable. If the joint distribution of the independent variables stay the same in the forecasting period as it was in the sampling period, high covariances among the esti- mated coefficients are no disadvantage. We may get good forecasts even without being able to discover the separate influences of the independent variables, provided they continue to vary together as in the sample period. But if the sample-period relation- ship among the independent variables is much altered during the forecasting period, then accurate fore- casting demands accurate knowledge of the separate effects of the explanatory variables. Thus, in the present study to the extent that pre- diction of future costs is the primary goal, multicolli- nearity will not be a problem as long as the independent variables continue to vary together as in the sample period. Because independent variables may not continue to vary together as in the sample period and because this study would like to assess the marginal contribution of factors, the tests for multicollinearity suggested by Farrar and Clauber are made. The primary purpose of this study is to assess the utility of alternative costing techniques for predicting future costs given a relatively constant mix of services. 81 As Christ notes, given a constant mix of independent vari- ables which can be expected to vary together as in the sample period, multicollinearity does not seriously affect the results of such comparisons. Cost Estimation Purposes However, prediction of future costs given a particu- F} 1ar mix of services is only a small part of the cost esti- L mation activities of a bank. As noted in the first two chapters of this study, other functions for which cost esti- y mations and cost relationships are necessary include cost b, control, performance evaluation, budgeting, cost allocation, and pricing of new and existing services. With the exception of the pricing of services, multicollinearity between inde— pendent variables is not a serious problem for these activi- ties if the mix of goods and services remains the same. If the multicollinearity can be located and analyzed, the utility of multiple regression techniques for cost estimation, cost planning or budgeting, and the product mix and pricing decisions is increased significantly. Additional information can be gathered to show why independent variables are inter- correlated, variables can be regrouped into a new set of independent variables where the intercorrelation among vari- ables is greatly reduced, and new independent variables can be introduced. Statistically the difficulties that arise from a multicollinear set of data may be summarized as follows: 82 Consequences 1. As interdependence among explanatory variables grows, the correlation matrix approaches singu- larity. A matrix is singular if its determinant is equal to zero. 2. Due to the determinant of the correlation matrix approaching zero, the elements of the inverse matrix explode. This results from division by the determinant of the correlation matrix which is nearly zero. Thus, the results of this division become infinitely large. 3. Variances for the affected variables' regression coefficients accordingly also become infinite.6 Further illumination on the potential impact of these statistical problems caused by multicollinearity is shown in the following statement from Farrar and Glauber: The mathematics, in its brute and tactless way, tells us that explained variance can be allocated completely arbitrarily between linearly dependent members of a completely singular set of variables, and almost arbitrarily between members of an almost singular set. Alternatively, the large variances on regression coefficients produced by multicolli- near independent variables indicate, quite properly, the low quality of resulting parameter estimates. It emphasizes one's inability to distinguish the independent contribution to explained variance of an explanatory variable that exhibits little or no truly independent variation.7 83 Text for Existence and Severity Farrar and Glauber also note, Should it be possible to attach distributional properties under an assumption of parenthal orthog- onality to the determinant IXtXI, or to a convenient transformation of IXtXI, the resulting statistic could provide a useful first measure of the presence and severity of multicollinearity within an indepen- dent variable set.8 Bartlett has developed a transformation of xtx that is distributed approximately as Chi Square with %~n(n-1) degrees of freedom. This transformation is useful for test- ing the presence and severity of multicollinearity within an independent variable set.9 The test statistic for a Chi Square distribution with 45 degrees of freedom (% x 10 independent variables x (10 - l) = 45) with a 95% confidence limit is 30.6368. This means there is a 5% chance that the computed Bartlett Chi- Square Test Statistic could be greater than 30.6368 if multicollinearity did not exist. Since the computed value is 939.7509 for Bank A (Table 5) and 30.6336 for Bank B (Table 6), it seems reasonable to conclude that multicollinearity exists and is very severe in the independent variable set for Bank A and that it exists but is not very severe in Bank B. Although the Bartlett Chi-Square Test provides evi— dence as to existence and severity of multicollinearity, it does not provide evidence which suggests how the independent variable set may be enlarged, regrouped or transformed to minimize the effect of multicollinearity. 84 Tests for Pattern and Location Tests for the pattern and location of multicolli- nearity are summarized in Tables 5 and 6. The location of multicollinearity can be observed by examining the computed F-statistics for interdependence. For example, in Bank A the greatest multicollinearity exists with respect to earnings on average deposits the computed value being 606.4452. Other highly multicollinear independent variables for Bank A are the number of personal accounts, the number of dollars of time deposits, and the number of dollars of savings deposits. The number of savings accounts and savings certificates are shown to be less multicollinear: and the age of branches, the consumer price index, and the number of dollars of certificates of deposit are shown to be much less multicollinear. In the case of Bank B the most multicollinear inde- pendent variables are savings deposits (dollars) and savings thrift certificates. The least multicollinearity is located in certificates of deposit, average commercial loans and the Consumer Price Index. The tables for pattern of interdependence show where the intercorrelation among variables is greatest. The diagonal elements represent inz which gives the coeffici- ent of multiple determination for an independent variable treated as a dependent variable with all other independent variables used to predict values for the variable in question. 85 For example, in Bank A by using all other independent vari- ables to predict earnings on average deposits a coefficient of multiple determination of .9866 is obtained. This high R2 indicates that a very low informational content is possessed by earnings on average deposits because the infor- mation is already embodied by other independent variables in the data set. Low inz indicate that the other independent variables do not reflect the same information as an inde- pendent variable. Thus, the reader is cautioned against inferring that the lower the inz for an independent variable the greater the informational content when used in a regres- sion equation. The informational content of an independent variable in a regression equation is a function of the relationship between the variable and the dependent variable, as well as the extent to which the information is embodied in other variables in the independent variable set. Examination of the partial R's below the diagonal reveals the contribution one independent variable makes to the explanation on another independent variable holding all other independent variables constant. For example, in Bank A the partial R between earnings on average deposits and time deposits is .9015 which combined with a partial T of 17.9283 indicates a very strong linkage between these two independent variables. Another strong linkage in Bank A occurs between earnings on average deposits and the number of personal accounts. 86 In Bank B the linkages between independent variables are not shown to be nearly as strong. The strongest link- age occurs between the number of savings deposit accounts and number of dollars of savings deposits where the partial R is .5801 and the partial T-ratio is 8.3669. The tests for pattern and location of interdependence 1.... among the independent variable set for Bank A suggest that i; earnings on average deposits does not add much information to an estimation of the relationship between the independent variable and cost categories. By excluding this one variable y the intercorrelation among the independent variables would be reduced significantly and the regression coefficients would more closely reflect the marginal contribution of independent variables to costs. Interpretation of Results As noted by Christ, multicollinearity is a serious limitation when one is interested in the true value of regression coefficients. In this study multicollinearity is severe in the independent variable set for Bank A but is not severe in the case of Bank B. This means that for Bank A the parameter estimates or regression coefficients for cost factors are markedly sensitive to changes in model specifi- cation. Since the comparisons of alternative costing models assume no major changes in the mix of services offered by the banks, the estimates of predictions of future costs are not seriously affected. Use of the regression coefficients for 87 purposes of cost planning, pricing or budgeting with a dif- ferent combination of services is dangerous because multi- collinearity rapidly decreases the stability of each inde- pendent variable's contribution to explained variance. The significance of this reduced stability is to enlarge the confidence interval around the marginal contribution, regres- sion coefficient, of each independent variable. r1 Serial Correlation One of the crucial assumptions of linear regression models (simple and multiple) is that of zero covariance for L; the disturbance terms. The significance of zero covariance is that all such disturbances are independent. For cross- sectional data, this means we are assuming that the distur- bance value that is "drawn" for any one unit is uninfluenced by values for other units and in time-series data it means serial independence for the disturbance terms.10 In discussing the implications of serial correlation Benston notes, The consequences of serial correlation of the distur- bances are that l. the standard errors of the regres- sion coefficients will be seriously underestimated, 2. the sampling variances of the coefficients will be very large, and 3. predictions of cost made from the regression equation will be more variable than is ordi- narily expected from least-squares estimators. Table 7 reflects the Durbin-Watson statistics for lboth simple and multiple regression which measure the extent to which serial correlation exists in individual branches of 88 Bank A. Because observations were only available for four years for Bank B, all of the analysis was done on a cross- sectional basis. Because of this the data for Bank B was not tested for serial correlations. In this study the main concern is with positive serial correlation or that error terms are not increasing or decreasing with respect to time. The results of the serial correlation tests made showed that with simple linear regres- sion one of six branches shows positive autocorrelation (Branch 4) and two branches (Branches 3 and 5) are in the inconclusive range. The tests for serial correlation for multiple regres- sion show Branch 4 in the inclusive range, and the other branches are in the range where the null of no autocorrela- tion would not be rejected. One way of eliminating or adjusting for serial corre- lation is to use first differences for costs and independent variables. When using first differences, one is trying to predict the change in a cost rather than the actual level of the cost. As can be seen in Table 7, by using first differ- ences the problem of serial correlation could be minimized (serial correlation is reduced to an acceptable level in Branches 3, 4, and 5). The problem which results from this is a lack of comparability between simple linear regression based upon first differences and the alternative costing models based upon actual costs. Because serial correlation 89 is observed in only Branch 4, its affect is minimal in terms of this study. For multiple regression as noted earlier positive autocorrelation or positive serial correlation is not statis- tically evidenced. Therefore, in drawing conclusions about the alternative models this research will recognize that simple linear regression estimates of (1) standard error of regres- sion coefficients could potentially be seriously underesti- mated for Branch 4, and (2) the sampling variances of the coefficients will be larger than shown and predictions using this technique will be more variable than for the other techniques. Multiple regression estimates of standard errors and variance of the coefficients should not be seriously affected by serial correlations. Constant Variances Another assumption of least squares regression tech- niques is that the variance of the disturbance term is con- stant. One violation which is frequently encountered in business and economic applications is where the variance of the error terms is proportional to the level or size of the independent variables squared. Where heteroscedasticity prevails but the other conditions of the model are met, the estimators obtained by ordinary least squares are still unbiased and consistent but they are no longer minimum vari— ance unbiased estimators. The consequence of heteroscedas- ticity is to increase the standard error of the regression 90 coefficients and thereby the confidence interval around regression coefficients. Naturally, because the standard deviation and variance of regression coefficients is in- creased, so is the standard error of the estimate. One way to increase the accuracy of regression models is to use Bartlett's test for heterogeneity followed by a data transformation to restore homoscedasticity. This increased accuracy is a result of smaller standard errors of regression coefficients and smaller standard errors of the estimate.12 A less SOphisticated approach to detection of hetero- geneity is used in this study. Residuals or error terms are graphed against each independent variable to note whether error terms appear to be proportional to levels of the inde- pendent variables. Since this graphing does not indicate serious heterogeneity, equal variances are assumed in this study. Figures 1 through 5 show a plotting of the level of Total Costs against the residual term. The implication of this assumption is that the pre- dictive ability or accuracy of simple linear regression and multiple regression may be underestimated. A data transfor- mation to restore homogeneity might increase the predictive accuracy of these regression models. Normal Distribution For the statistical tests of the regression coeffi- cients and equations to be strictly valid, the residuals or 91 13 The following error terms must be normally distributed. quotation from Neter and Wasserman's Applied Linear Sta- tistical Models discusses several ways of testing for normality. Small departures from normality do not create any serious problems. Major departures, on the other hand, should be of concern. The normality of the F7 error terms can be studied informally by examining the residuals in a variety of graphic ways. One can construct a histogram of the residuals and see if gross departure from normality are shown by it. Another possibility is to determine whether, say, about 68 per cent of the standardized residuals fall L between -1 and l, or about 90 per cent between -1.64 and +1.64.14 Neter and Wasserman note that graphic analysis of residuals is inherently subjective, but that nevertheless subjective analysis of a variety of interrelated residual plots will frequently reveal difficulties in the model more clearly than particular tests.15 In this study plot of residuals were studied: and failing to note gross departures from normality, the assump- tion has been made that the error terms are normally dis- tributed. Exhibit 7 represents a plotting of residuals from the various regression methods. The implication of the specification tests for the multiple regression model when used for predicting future costs given a relatively constant mix of services is minimal. Multicollinearity is severe in Bank A; but as noted in the quotation from Christ, this is not a serious limitation for predictive models unless the relationship between the 92 independent variables changes in the period for which pre- dictions are made. The tests for positive serial correla- tion show that this is not a problem for the multiple regression models. The assumption of linearity between the independent and dependent variables is shown to be reason- able, and the assumptions of normality and homogeneity are made on the basis of visual fit graphing. ”1% Although the specification tests for multiple regres- sion indicate minimal limitations upon a comparison of pre- dictive ability involving multiple regression, it is neces-- U sary to note that because multicollinearity exists in the independent variable set of Bank A any use of the regression coefficients in the multiple regression equation for purposes of budgeting, cost allocation or pricing services is pre- dicted upon the assumption that the mix of services does not change. If the mix of services changes, such regression coefficients are limited in utility because the standard error of the regression coefficients is greatly underesti- mated. The specification tests for simple linear regression are less clear. Positive serial correlation is shown to exist in Branch 4 of Bank A, and the tests are shown to be inconclusive for Branches 3 and 5 of Bank A. As a conse- quence of this potential serial correlation, there is a danger that the standard error of the estimate for cost pre- dictions of Bank A is underestimated. This means that the confidence interval for cost predictions using the simple 93 linear regression is underestimated. This evidence of possible underestimation of the error terms for serial corre- lation will be noted in comparing alternative costing models in Chapter IV. 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Aounudovv ouuooeov owauo>u so ouswohqu .c mmo~.-H ~m-.asn nous“ oouua guns-coo .n nnsa.~o n-<.w~n I Anuaohv Joanna no and .N cacao soo¢.H~o.e~ neoo.~ «ems.on Auunsouun no non-saw «unsound anaconda .H osccoano. hon-esouo nun-Juan «o a 2:3 ow u «000 «o mason ow u «08 A0053." was”. unannouw uo uovuo adv oudowouu woou Donovan uouuu vuuvsaum souum oeuvcuum downpouwom ~o>u~ an. an oomnawuo> he vonqoanun uooo mucuqsaanuu usuuwuuauum soauuwu¢> no sowuuoaoum me xvoaaauaouv N mance r0 .Aev muumoaov mwcw>am Aav .ouoowuuo mo uoaasz Amv “$.moumum pouwc: .o.ooa I momflv xovcfi vogue uoasmcoo Amv .Amv ouamoaov cameo: Anv .A§v muamodov panama Rev .Amv mouaoumau Iuoo uuausu mwca>mm Amv .Aav mmumoauwuuoo uwuunu mwcw>mm Aqv .Amv uwmooov mo mouoowuwuuoo Amy .Amv nuuuooov nwca>om Amy "coauasuo coammoumou sumo ca cowmnauca you pouovumcoo one: moanouum> ocuvcoeuvcw wcwaoaaou may nouoz mooo. hooo. Annuafioev uuaooaou vacuum .a mooo. “Noe. I Auuuasoov nuauoaov uwca>um .e ~m-.a aco~.n Awuosouou mo wonsscv nuuuoeov panama .n c~om.~ omoc.q I Amocoooou no uoaascv uuuuoeoo oucu>am .e mq-.oow.a owno.ano.o unnumcou .n Hooo. mooo. I Amuaaaovv acooH Huwouuaaou owmuo>< .~ uuuoo mama.moo.oa m-c.mm~ Heum.moo.~ uuouoouav van uuouwuuo mo nonesz .a «Bananas. huaaosouo cmmm.~ao.ma o~om.mo~.m ucuuucoo .e memo.» oomo.ma I Amucaoooo mo Honascv ouumoeov owcw>mm .m nuance»: mqoo. o~oo. AauuHHouo auuaoauv uuaa>am .N no mqom.nmo.am «Hoe. oaoo. Aaumaaovv uwmoeov «0 nouuoumauuuo .H anaesqa. uoououcn womq.aac now~.HoH ucmumcoo .s Nooo. aooo. Amuqaaovv unaccouo unca>om .o mamo.~ moom.o I Amussouoo uo .ocv .uuuo uuuusu uwca>cm .m «coco. Hooo. Amuaaaoov.u«uoaou so nouuoamsuuoo .4 mooo. swoo. Amuuaaovv moumowuwuuou uuaunu umcw>om .n noooo. Nooo. AmuaHHOpv nuauoeov panama .~ uuwuooon hass.som.~ «Mao.am a-~.maa uuouoouou can muuuguuo no yogaaz .H oakomsna. «usages» oe~m.~mn.~ ocma.cmw.a usuuucou .n Nooo. «coo. Aouqaaovv uauodov mo ocuoouunuuou .o awom.~H amma.nn I Amuasooua no .oav .uuoo unsung amas>um .n Nmoo. mode. Aouwaaovv auuaoauuuuoo amass» owaw>nm .e Nooo. mooo. Auuodaouv nuqaoaov engage .n mama. ~mcm.n Amucaooou mo nobssov uuwmoeov oucw>om .~ ~mo~.~nm.m omfim.mn~ m-~.omm.n muouuouwo poo auooawuo mo uuaaoz .a sowusmoo. noauoaum ouwaaumm no mucwfioawuooo mo mucoauamwooo Amocoouwaswqm unouuoum «a noose adv uuaowuawuooo huowOuau uouum vuuucauw uouum pumpcmum scammouwmm Ho>oH oH. um moanauuub an voouoneuu uoou huouocoaoum uouoauuawum sowuwwuu> mo sowuuoeoum Ammo Amonosmum HH< now sumo .uuaow av nunosuun oeIIm scan .n mqn<8 97 s~m~.-~ m-n.-~ I Amussooou we .ocv .uuou uuwusu awcw>om .m Ho-.nfi ~0nn.n~ I Auucsouun «0 nunsscv nowaoeov mwcw>om .c nn~5.¢mn.~ onmo.n~c.na muouoouav can uuooauwo «0 wonssz .n oucoexm Node. once. Auuaaaovv nuanoeov umcq>nm .N ucaunuoeo Hoqm.ams.m¢ oNoo. smoo. Annuaaovv ownedov «0 ouuuouuwuuoo .a n~o~nnoo. Hooch aooa.cau.aa mmon.acn.naI ucuuasoo .Ha oh~q.mm asco.sns noun“ «aqua uqaaacoo .oH mHoo. oooo. Anussooon uo nonaocv uuuuoeov owcu>qm .o mmwm.H hqu.n I Auucsouoo no nonessv nuuooeov season .a nooo. hooo. Amundaono uuuooaov vacuum .a «coo. ~oao. Annouaovv nouuoawuuuoo unaunu awca>om .o naoo. oooo. Aouoaaovv ouaaoeov awcu>am .n moeo.na cmHo.ns I Auucsoouu mo .ocv .uuou uuuunu owaa>um .e Hooo. nooo. Amuodaovv uuaoa Hoaouoaaoo omuuo>< .n oocoexm Hana.~nn ~m¢~.~nn.~ mucuuouwv use auouwuuo uo honest .~ usuauuoeoa nman.~m~.~a mooo. Nwoo. Aouafiaovv uuuoaov uo nouuowwauuoo .H caeooeoo. oua>uom woao.uu HH-.aHI Anuasouuo mo .oov .uuoo uuuunu umaw>nm .m «coo. coco. Anuafiuouo uauoaou no .ouuuauauuuo .a ~o-.nmn.a ooce.ama.n announce .o caao. Hmom.~ Auuasouuo no non-saw ouuooauv uwcw>qm .n cmoo. osoo. Auuoaaovv ouunuwuuuuuo uuuucu unsavom .e ~m-.~ -on.n I Auuosooun uo nunssav nauseous nausea .n duodenum Hooo. coco. Aouufluovv oduoa douche-sou unnumbd .N nauunuomo caen.~ao.o mmmo.nm~ waao.nas.~ cucuuouav vs: uuoouuuo mo uoalsz .H ononoaos. uosuo ~won.msn.n s-n.nw~.n I unauaaoo .o osoo. Hmoo. Aauuadovv uuquoaou .mafi>om .n o~a~.~ o~m~.c I Anussooou no nonessv uuuuoeuv van-on .q conned omm~.nsc ooma.mmo.a ouououuqv vs. ouuuauuo mo son's: .n one; #300. soda. I Aaunuaovv nouuowuuuuoo uuuunu nudw>um .N now omoo.noq.o~ mooo. ouoo. Annouaovv ouuuoeov cannon .H nonnuoaa. souoaboum ooooo. Nooo. Auunaaovv ouuoouuauuoo uuaunu awda>nm .n moooo. Neoo. I Anunaaovv awooaou do nounuauuuuou .o NHoo. o~oo. Aouaaaovv auuooeov cannon .n amna.q oeoo.n~ Ambasoooa uo .ocv .uuoo uuwunu owsa>om .c Nooo. coco. I Aouaaaoov nus-cane awaa>am .n mnmn.mwn oueo.mon.~ unconsou .N mooo.oen.n nwm~.- nnoa.o~o uuouuuuav can uuoouuuo no sonsuz .H oumonnan. ousuwnusm uuqsaunm uo macaquauuooo mo oucoauauuuou Aooauuwuqswqa accuses» mo uovuo say ouddquuuwooo huomounu nouum vuuvcaum scuum vuovcmum scammouwwm Hu>oa ca. us moabuauo> he caduceus» uaou mucuosuaoum ucuuuuusmum ocuuuwun> uo noduuonoum Ammo .Avosswucoov n mdnwm .q smock. mmaqa. Amumflaouv unmoame mo .uumo .m anqmw. Nwmqa. A.muoom mo .oov .aop mwoa>mm .N means. ammom. some“ manna uoasocoo .H HoSNHoma. Augusoom naacm. mowam. A.muoom mo .ocv .ouooo Hmcomuom .m “seam. mohaa. x.muuoa «o .oco .aue mm:s>am .q <\z mmmom. usoumcoo .m vocwwmoc ommeq. Hoqma. Amumaaouv mufimoamv amas>mm .~ awesome «coma. Hoomm. AmumHHopv .dmo .w>m so .oumm .H Nmonmom. nosmum mmmmw. Hwamm. amen“ «aqua uoasmaoo .m omens. namnw. Amumaaopv moumoamwuuoo mmcu>mm .e sheen. oases. “.muuom no .oav .amc awas>mm .m Hoamn. muons. A.muoum mo .ocv .muuoo Hmcomuom .N <\z moans. unmumaoo .H mssmnnaa. uH=u> scam aoamo. Adana. xmvaw manna umssmcoo .a mome. names. A.muuum mo .ocv mufimoamc mwaa>um .o <\z mmmqo. nooumcou .m Nmosa. amama. Amumflflonv muamoamn awas>mm .s mmmom. eONNm. AmuwHHovv moumoamauuoo mmcw>mm .m memam. HHoom. A.muoum mo .oov .muoom Hmoomuom .N mmaao. wqomw. Amucsouum mo .osv .uuoo mwca>mm .H cmmmanma. ufivs< Mann muomMumo pouoaoa Amocmofiwfiswfim uncommuw mo umpuo saw muomaowmmooo huowouoo ”moo and: mspmfium> «H Hm>ma 0H. um muflnmaum> up sandmaaxm umoo oucmaum> mo poofimaaxm zuoumcmaoxm unmowmwswwm cowumwumé coaumamuhou mocmwum> no mo GOfluHOQOHm cowuuoooum Awmv Nmmalmoma powwow mnu Mom < xcmm pom mumoo uoouach annoy you cofimmouwom manauasz a mqmmm .s Nqsmq. Hoqmm. A.muuum mo .oav .uumu amas>mm .m ammo“. mamas. A.muuom no .occ .aou «waspmm .N Hooch. mqqmm. A.muoom mo .ocv .muoum Haaomuoa .H HmAMNAma. cofiusnfiuuufla .mmoooum moon <\z mmomn. acmumaoo .N usaouuuoam enema. ooooo. nues“ muqua umaamcoo .H sameness. a “wannabe ensue. moses. Amumaaonv mmumofiuauuuu mmaa>am .s mwoo~.I mmoea. Amumflaovv musmoaau mmao>am .m «\z Hemmw. announce .N emawsumuae «mafia. oqwna. xmuas manna umaamaoo .H owoommom. museums: <\z omaoa. uamumcoo .m uouugvan «mass. caqnm. Amumfiflocv mmumofimsuumo mwaa>am .4 a awesome smsmm. moons. A.muuum no .oav .uamc awas>wm .n can: NQNN¢. nmomm. A.muoow mo .Oav .muoum Hmflomumm .N vmuQUOHH< ommma. Nessa. smug“ «aqua “manuaoo .H mqmmnoma. sauce mumoo <\z mflmmo. gamumaoo .~ nooufieca aomma. ooooo. xmvafl manna acoumaoo .H aaoammmm. Hauoa mumoo «\z cacao. namumaoo .N goonscaH «Home. ooooo. xmuca «aqua “masmaou .H eaHQQNAa. gonna. knowoumo ponoaoo Amocmoamacwam ummumouw mo umpuo ch mucowowwmooo ShowOuoo ance and: manuaum> NH Hm>ma OH. um mmaausum> an emawmaaxm umoo cocoaum> mo pacemadxm huoumcwadxm ucmoamwcwwm coauoauo> coauoaouuoo oocmfium> no mo cowuuomoum cofiuuoooum Ammv Avoaaauaoov q mqmmm .c Hanan. momma. nova“ mowue amasmcoo .m <\z memes. uamuaaoo .~ «cannons oowma. comes. Amumasocv .uamu .m>m so amasauam .H oHNmmmma. mosoaaam soaks. wmoaa. Amumaaouv .ame .w>m ao mwcflaumm .k <\z momma. accumaoo .o huowoumo wouoaoa AmocmoHMficwam amoummuw mo novuo owv woodwoammooo huowouoo umoo nuaz mHanum> NH Ho>oq OH. on moanmwum> ma poofioaoxm umoo oocouuo> mo cmcwmaexm huoumsmaoxm oomo«m%:wwm doauowuo> cowuoaouuou oocmwum> no mo soauuoeoum coauuoooum ANMV Auoaaauaoov q man