INCREASING SIMULATION REALISM THROUGH THE MODELING OF STEP COSTS COST BEHAVIOR IN BUSINESS SIMULATIONS Development In Business Simulation & Experiential Exercises, Volume 18, 1991 38 INCREASING SIMULATION REALISM THROUGH THE MODELING OF STEP COSTS COST BEHAVIOR IN BUSINESS SIMULATIONS Kenneth R. Goosen, University of Arkansas at Little Rock ABSTRACT This paper addresses some of the theoretical problems involved in the modeling of fixed costs in business simulations. The theoretical nature of fixed costs as a special case of step costs is clarified. In addition, a mathematical technique is presented for the effective modeling of step costs within a computerized simulation model. Also, some of the consequences of significant amounts of step costs are illustrated. INTRODUCTION Creating a sense of realism in selected areas of decision- making activity is a goal of business simulation. Without an appearance of realism, the learning experience from a business simulation is not likely to be accepted. One aspect of business activity that appears easy to simulate is cost behavior. However, the author’s experience with developing business games has been that realistic cost behavior is much more difficult to achieve than is commonly believed. Furthermore, many simulations that appear to have realistic models of fixed cost behavior may need improvement. Fixed costs, in fact, are a subset of a category of costs that may be labeled step costs. Step costs are lightly discussed in economic and management accounting textbooks and literature. Because of this inadequacy in literature, the author believes inadequate attention to step cost behavior has also carried over into business simulations. The major problem in programming fixed costs is that these costs are not really “fixed.” They are fixed only in the short run relative to sales or production activity. Kaplan, an accounting theorist has recently called attention to this point (1987). In a simulation some fixed costs can change because they represent a decision made by a game player. For example, the amount of advertising may be increased or decreased at the whim of the decision-maker. However, once the decision is made, advertising will remain constant during the period regardless of the activity that is generated by the processing of decisions. The same would be true for other fixed costs such as the salaries of salesmen. In most simulations there are some fixed costs that cannot be directly controlled by the decisions of game player. For example, salaries of top management, salaries of secretarial and clerical staff, salaries of engineers, etc. are often internal values. These costs are often referred to as administrative. These types of costs are parameters and are preprogrammed into the game model. However, it is highly unrealistic for these internally generated fixed costs to remain constant at all levels of activity. The problem expressed in the form of a question is: When should an increase in these internal fixed costs be triggered? Also, what mathematical equation if any, can be developed to easily compute the required increase in the total fixed cost? COST BEHAVIOR IN BUSINESS SIMULATION In this paper, the primary emphasis is on the modeling of fixed cost. Although major questions may be asked concerning the modeling of variable costs in simulations, this paper does not directly address those issues. The modeling of variable production costs has been partially addressed by Gold and Pray (1989) and Gold (1990) Fixed costs by definition are constant and, therefore, supposedly unrelated to changes in activity. It would appear that in simulation modeling the correct approach would be co treat fixed costs as parameters whose value do not change throughout the play of the simulation. This view, for reasons which will be presented, is incorrect. A commonly accepted definition is that fixed costs are those costs that do not increase or decrease with changes in activity. What this definition states is that changes in volume (sales or production) per se do not affect the amount of fixed cost expenditure. Changes in fixed costs occur for reasons other than volume changes. Examples of fixed costs include machine rental, building rent or depreciation, supervisory cost, secretarial cost, and equipment. Fixed costs are often classified as discretionary and committed. An example of a discretionary fixed cost is advertising or a cost budgeted for the training of employees. Discretionary fixed costs lack the long term contractual nature of committed cost. A 10-year lease on a building would be another example of a committed fixed cost. In business simulations, discretionary fixed costs are usually generated by external decisions, that is, decisions explicitly made by the game player. What definitions of fixed costs imply but do not directly state is that a fixed cost is “fixed” only for a single period; that is, per month, per quarter, or per year. It is important to understand that business simulations are never played for a single period but involve decision-making over multiple periods of time. Consequently, for any given fixed cost to remain constant over the entire range of possible sales or production activity is unrealistic. An important question for simulation designers is: What is the proper view of fixed costs over multiple periods of time? The answer to this question requires an analysis and discussion of the relationship between fixed and step costs. A major premise of this paper is that all so-called fixed costs are actually a special case of step cost behavior. RELATIONSHIP OF FIXED AND STEP COSTS In order to understand the approach for modeling fixed costs that will be presented later in this Development In Business Simulation & Experiential Exercises, Volume 18, 1991 39 paper, it is first necessary to understand the relationship of fixed costs to step costs. The relationship is quite easy to illustrate. Fixed cost as illustrated in Figure lB is simply one step in the stair case of steps as shown in Figure lA. The graph of step cost behavior as shown in Figure 1A illustrates that at certain defined levels of activity, additional service units must be acquired in order to have the capacity required to attain the desired level of activity. In order for volume in the range of Q1 - Q2 to be attained, another service unit must be acquired. The acquisition of this service unit causes the total cost to increase to $2,000. Theoretically, the preparation of a step cost graph as illustrated in Figure 1A can be prepared only after management has carefully evaluated resource requirements at different levels of production activity. It management decides that the most likely volume level is greater than Q2, then the required service units at that level create a fixed cost of $3,000 for the current period. An understanding of the nature and cause of step costs is essential. The following is a brief outline of the salient factors. 1. Underlying the incurring of each type of fixed cost are identifiable service units. For example, factory supervisory cost is simply the total number of supervisors times average salary. Each supervisor is a separate service unit. Similarly, depreciation can be traced to separate identifiable machines or equipment units. Each machine is a service unit. 2. Each service unit provides production benefits over a measurable range of activity. That is, each unit has a maximum production potential or benefit. For example, a factory supervisor might have the capacity to supervise 10 workers. The ratio of maximum number of factory workers that one supervisor may manage or supervise may be called the capacity ratio or capacity range. 3. The attainment of a certain level of production or gales may sound a signal for the acquisition of another service unit. If this fixed cost resource is not acquired then the constraints imposed by current resources will prevent sales from rising to actual demand because of inadequate production. A simulation that allows substantial increases in production without increases in fixed costs is not realistic. 4. The event that triggers the actual purchase of an additional service unit should be a forecasted or planned activity and not the actual activity of the current period. 5. The decision to increase or decrease a step cost expenditure will be made at regular and well-defined intervals, e.g., monthly, quarterly or yearly. During the time between these decision points, the cost is committed and will not increase or decrease due to a difference in actual activity versus planned activity. That is, the commitment to a certain step or level of cost is inescapable during the current period of activity. Some step costs have the peculiar nature that they can be easily increased at regular increments in activity, but cannot be decreased when production or sales activity decreases. The game designer must explicitly take into account that some costs when incurred are committed for a number of periods. 6. In the design of simulations, step costs must be designated as either explicit decisions made by the game players or designated s internal to the game. For example, if the number of supervisors is a decision to be determined by the game player, then no equation is required to determine the total cost at different levels of activity. However, if the salaries of supervisors is internal to the game, that is, not a factor to be decided by the game player, then in order to achieve a step cost effect some means of achieving this effect must be programmed into the simulation. 7. The acquisition of a fixed cost service unit does not mean that all its service potential will be immediately used. Inherent in the nature of fixed cost service unit is the potential for idle or unused capacity. 8. The incurring of significant amounts of fixed cost resources or service units greatly increases risk of a business for $ 1 $ 2 $ 3 Q1 Q2 Q3 (000's) $ 1 $ 2 $ 3 Q1 Q2 Q3 (000's) Graph A Graph B Figure 1 Relationship of Step costs to Fixed Costs Development In Business Simulation & Experiential Exercises, Volume 18, 1991 40 failure in the event of a decrease in demand. In a simulation three types of costs require modeling: fixed, step and variable. The difference between a step cost and a variable cost may be summarized as follows: Variable costs are tied to individual units of actual output. Step costs are tied to a range of output based on planned production or planned sales. Step costs are determined at the decision interval between operating periods. Variable costs are incurred during the operating period at the same rate as actual production takes place. A fixed coat is determined at the start of the period. AN EQUATION APPROACH FOR THE MODELING OF STEP COSTS Theory In order to develop a mathematical model for determining the amount of a specific fixed cost at different volume levels, the following values or parameters must be determined. 1. The cost of a single unit of the fixed cost resource (service unit). 2. The capacity ratio; that is, the ratio of the range of output to 1 service unit. If one supervisor can manage 10 workers, then output is 10 supervised workers. 3. A sales forecast and a production budget for the current period. The objective here is to develop an general equation which will properly compute the required number of services units and the associated total cost at the proper volume intervals. The required resource units generated by these equations must be integer values. A fractional part of a supervisor or a fractional part of a machine can not be purchased. In order to illustrate how to develop a simulation equation for determining the amount of a specific fixed cost, assume the following: Capacity ratios: Output per factory worker 220 Workers per supervisor 10 Planned sales/production 12,000 Salary of a supervisor $3,000 Intuitively, an evaluation of the above data suggests that 55 factory workers are required: (12,000/220) Therefore, mathematically, the equation for the number of workers is: NW = SF/WOR SF - Sales forecast WOR - Worker output ratio Since the capacity ratio is 10 workers to 1 supervisor, the required number of supervisors would be 6 (55/10); this is, NS NW/WSR where: NS - number of supervisors WSR - ratio of workers to 1 supervisor The actual answer was 5.5. However, since one- half of a supervisor cannot be hired, then 6 supervisors must be hired. Since non-integer values cannot be allowed, an integer function must be used. Integer functions exists in computer languages such as BASIC or FORTRAN. Also, the integer function is found in electronic spreadsheet software such as Lotus 1- 2-3. The above analysis for supervisors can be stated mathematically as follows: TSSC = INT((NW/WSR)+.999) x SAL TSSC - Total supervisors salaries cost INT - Function for computing integer values as defined in BASIC or electronic spreadsheet software such as Lotus 1 – 2 - 3. WSR - Capacity ratio of workers to 1 supervisor NW - Number of workers; the capacity range of 1 supervisor SAL - Average salary of supervisors In the equation, the term INT(NW/WSR) +.999 determines the number of necessary supervisors. This statement uses the Integer function. The Integer function rounds all fractional values down to the next lower integer. For example, 1.8 would be rounded to the value of 1. Therefore, the inclusion of the .999 parameter ensures that rounding up rather than down will take place. The equation developed for computing total supervisory cost may be generalized for all types of step costs as follows: TFC = INT((DF/CR) +.999) x CPRU TFC = Total fixed cost INT - Integer function CR - Capacity range of DF - Demand factor CPRU - Cost per resource unit This equation will automatically compute the service units required at each activity level and the total fixed cost. Application and Illustration This paper addresses only those fixed cost resources that the game designer has deemed internal. The first step is to define these resources. Examples of fixed costs that are often internal to a simulation are illustrated in Figure 2. The above listed service units can be expressed mathematically in a manner similar to the equation established above for supervisors. In order to do this, let’s assume the following data and capacity ratios: Capacity Ratios: Output per worker 220 Required workers per mach. 5 Maximum workers per supervisor 10 Admn. details per admin. Personnel 1000 Staff per manager 1 Parameters: Budgeted production 12,000 Cost per machine per pd = $10,000 Salary per supervisor = $ 3,000 Salary per administrator = $ 4,000 Salary per staff = $ 2,000 In a business an increase in activity, e.g., production creates the need for additional support activity. Output requires machines and machines require workers, Workers require supervision and supervisors require staff support. The common Development In Business Simulation & Experiential Exercises, Volume 18, 1991 41 Figure 2 Examples of Service units that Provide Capacity SERVICE UNITS DEMAND FACTORS(Output measures) CAPACITY RATIO Machines Units of Product Units of prod to 1 machine Factory Supervisors Supervised workers No. workers to 1 supervisor Administrative personnel Admin. details Admin. details to 1 mgr. Staff (e.g. clerks, Processed paper Units of paper to 1 clerk denominator in the above list of service units is output in the form of production or sales. The major factor in modeling step costs is to establish a ratio between each service unit and output. A capacity ratio may be stated directly in terms of specified output or indirectly to other factors which are related directly to output. Based on the above assumed data, step cost functions for each of the above listed service units can be developed as follows: Number of workers: NW = (BP/OWR) = 12,000/220 = 55 Number of machines: NM = (NW/WMR) = 55/5 = 11 TCM = 11 x 10,000 = 110,000 Number of supervisors: NS = (NW/WSR) = ( 55/10) = 5.5 (= 6) TCS = 6 x 3,000 = $18,000 Number of administrative personnel: NAP = (BP/OAPR) = (12000/1000) = 12 TAPC = 12 x 4000 = $48,000 Number of Staff: NST = (NS/SSR) = (6 / .5) = 12 TCST = 6 x 2,000 = $12,000 A general equation for all of these calculations may be simply expressed as follows: A general equation for all of these calculations may be simply expressed as follows: Number of fixed cost units = Demand factor/ capacity ratio Total cost = No. fixed cost units x cost per unit The capacity ratio is simply the maximum output that can be provided by one unit of the fixed cost resource. The demand factor can be a derived demand, that is, directly related to some measure of output. In all cases the ultimate determining factor for the demand factor is planned activity (production/sales). The number of supervisors is determined by the demand for workers, and the demand for workers is determined by the demand for the product. Consequently, the demand for supervisors can be also stated in terms of a capacity ratio based on units of sales or production units. Example Using the Step Cost Equation A simple simulation-using Lotus 1 - 2 - 3 was developed based on the above step cost equations. Results based on specified levels of demand are shown in Figure 3. The same results are shown graphically in Figure 4. In this illustration in which five types of step costs are simulated, net income at each level of sales has been calculated. Both variable and step Costs have been computed at each assumed level of activity. Some interesting results should be noted. As sales (units) increases net income appears, increases, and then disappears. These pockets of net income can be easily seen in Figure 4. At certain intervals the increased demand causes an increase in one or more step costs sufficient to eliminate any profit that was reported at a lower level of activity. Further increases in activity again results in profit. The profit may then disappear when another jump in step costs occurs. This type of behavior is very common to many businesses. In this instance, the modeling of step costs created a more realistic cost behavior pattern. If significant amounts of step costs are built into simulations then students may have the opportunity to experience what many real world companies have learned: substantial growth in sales does not necessarily mean an increase in profit. Evaluation The above approach is a simplified approach to the modeling of step costs. It requires that capacity ratios for each service or resource unit be established. A basic assumption is that additional units acquired are homogeneous. Implementation of this approach is easy and involves a minimum of programming. In many businesses, a substantial growth in activity allows for existing smaller units of equipment or machines to be replaced with larger, more expensive units that have a considerably larger capacity range. For example, a small computer can be replaced with a larger computer. The mathematical model just presented can be adapted to allow replacement of equipment to achieve an increase in the economy of scale. Of course, complexity of programming to achieve this effect would be increased somewhat by the need to compute gains or losses on the retirement of old equipment. The general equation just presented for modeling step costs represents an effective means of increasing simulation realism by allowing fixed costs to assume their true nature as step costs over the entire range of activity that occurs in multiple periods of simulation play. Development In Business Simulation & Experiential Exercises, Volume 18, 1991 42 REFERENCES Gold, Steven C.(1990), “Modeling Cost Functions in Computerized Business Simulation: An Application of Duality Theory and Sheppard’s Lemma”, Developments in Business Simulation and Experiential Exercises, 17, 70 - 72 Gold, Steven C., and Thomas F. Pray (1989), “The Production Frontier in Computerized Business Simulations”, Developments in Business Simulation and Experiential Exercises, 16, 24 - 30. Kaplan, Robert S, “Regaining Relevance” Cost Accounting, Robotics, and The New Manufacturing Environment, Sarasota, Fl., American Accounting Association, 7.2 - 7.29 Figure 3 Example of a Simulation with Step Costs FIXED COST SIMULATION Parameters: Capacity ratios Price 50 Var. selling rate 20 Output to 1 worker (OUR) 220 Material per unit 5 Workers to 1 supervisor (WSR) 20 Wage rate 10 Workers to 1 machine (WMR) 10 Hours per month 176 Supervisors to 1 staff (SSR) 0.5 Cast of 1 machine 240000 Sales (units) to 1 salesman (SLSMR) 1000 Supervisor salary 3000 Prod. (units) to 1 bldg. (PUBR) 50000 Staff worker salary 2000 Salesman salary 2500 Budgeted prod. 100000 Useful life-mach. 120 Sales 80000 Rent-1 bldg. 500000 EQUATIONS Volume Volume Volume Volume Volume Volume Volume Volume Volume 10000 20000 30000 40000 50000 60000 70000 80000 90000 NW = INT(BP/OWR) 46 13 182 228 273 319 410 TWC = (NW * (WR * HPWPM)) 80960 160160 241120 320320 401280 480480 561440 640640 721600 NS = INT(NW/WSR) 3 5 7 10 12 14 16 19 21 TSC (MS * 55) 9000 15000 21000 30000 36000 42000 48000 57000 63000 NM = INT(NW/WMR) 5 10 14 19 23 28 32 37 41 TMC = (NM * CPM) 1200000 2400000 3360000 4560000 5520000 6720000 7680000 8880000 9840000 DEPR = TMC/UL 10000 20000 28000 38000 46000 56000 64000 74000 82000 NST = INT(NS/SSR) 6 10 14 20 24 32 38 42 TSTC NST * SS 12000 20000 28000 40000 48000 5600 64000 76000 84000 NSM = INT(SL/SLSMR) 10 TSMC = (NSM * SSM) 25000 5000 7500 NBR INT(BP/PUBR) 1 1 1 1 1 2 2 2 TNBC = NBR * Rent 500000 500000 500000 500000 500000 1000000 1000000 1000000 1000000 Development In Business Simulation & Experiential Exercises, Volume 18, 1991 43 Figure 3 (continued) INCOME STATEMENT Volume (units) 10000 20000 30000 40000 50000 60000 70000 80000 90000 Sales 500000 1000000 1500000 2000000 2500000 3000000 3500000 4000000 4500000 Expenses Variable: Mater ist 50000 100000 150000 200000 250000 300000 350000 400000 450000 Variable selling 200000 400000 600000 800000 1000000 1200000 1400000 1600000 1800000 Workers’ wages 80960 160160 241120 320320 401280 480480 561440 640640 721600 Total 330960 660160 991120 1320320 1651280 1980480 2311440 2640640 2971600 Fixed Depreciation 10000 20000 28000 38000 46000 56000 64000 74000 82000 Supervisors’ sal 9000 15000 21000 30000 36000 42000 48000 57000 63000 Staff sslaries 12000 20000 28000 40000 48000 56000 64000 76000 84000 Salesmen’s sal 25000 50000 75000 100000 125000 150000 175000 200000 225000 Rent 500000 500000 500000 500000 500000 1000000 1000000 1000000 1000000 556000 605000 652000 708000 755000 1304000 1351000 1407000 1454000 Total var. & fixed Net income 886960 1265160 1643120 2028320 2406280 3284480 3662440 4047640 4425600 -386960 -265160 -143120 -28320 93720 -284480 -162440 -47640 74400 Figure 4 Graph of Simulation Results Graph of Sales and Total Cost (effect of Step Costs on Net Income) Net Loss Net Income S al es a nd c os t (M ill io ns ) Sales (Thousand units) 10 30 50 70 90 4.5 0.5 1.0 Table of Contents Volume 18, 1991 Personality Types and Total Enterprise Simulation Performance Using DIS 'n DAT as a Decision Support System for a Marketing Simulation Game Theoretical Derivation of a Market Demand Function for Business Simulators The Ethnographic Case Study: An Experiential Approach to Teaching Retail Management Electronic Bulletin Board Systems (BBS): Support Software for Computer Simulations The New Budget Game Negame: A Cross-Cultural Role-Play to Introduce Students to the Familiarization Stage of Negotiations Modeling Short-Run Cost and Production Functions Using Sheppard's Lemma in Computerized Business Simulations Increasing Simulation Realism through the Modeling of Step Costs Predicting Simulation Performance: Differences Between Groups and Individuals A Facility Location Case to Stimulate Classroom Interaction Educational Effectiveness of Business Simulation Gaming: A Comparative Study of Students and Practitioner Perspective Ethical Dilemmas in Experiential Learning: Issues and Strategies A Critical Review and Assessment of ABSEL's Award-Winning Procedures and Protocols Political Risk: A Simulation for Business Practitioners Upside Down: A Cross-Cultural Game in Experiential Learning Gorby's Dilemma: From Communism to Free Enterprise in Two Hours Strategic Market: Planning with the COMPLETE Product Portfolio Analysis Package: A Marketing Decision Support System Career Concepts and Total Enterprise Simulation Performance Experiential Learning in Human Resources: A Performance Appraisal Application Managerial Motivation and Realism Among MBA Student as Viewed through The Looking Glass, Inc. Simulation An Experiential Approach to Teaching Data Analysis Using MYSTAT: Rationale, Procedures and Results Practicing What Was Preached: A Sequential Learning Model put to the Test Student Attitudes about Policy Course Simulations An Investigation of the Relationship Between Simulation Play, Performance Level and Recency of Play on Exam Scores The Effect of Leadership and Cognitive Processing Styles upon Peer Performance Evaluation: Implication for the Utilization of Simulations in Business Pedagogy On the Transfer of Market Oriented Business Games to Socialist Cultures An Application of Financial Analysis of the Business Firm in a Simulated Competitive Environment Collective Bargaining Simulation: An Exercise based on a Familiar Theme Making Business Policy a Strategic Management Experience A Student Exercise for Intergrating the Concepts of Power and Motivation The Boundaries Extended: An Experiment Comparing Dialectical Inquiry, Devil's Advocacy and Consensus Using the Executive Game Using a Simulation Package to Develop a Simulation Exercise in Cost Accounting Success Factors in Experiential Training for Creative Problem-Solving Teams An Experiential Approach for teaching Quality management Critical Success Ratios: A Comparison of Two Business Simulations in a Multi-Year Environment Stocklogs: A Classroom Exercise for Teaching the Logistical Relationship of Location and Inventory The Organizational Leadership Program Simulating Business Decision-Making: Using Statistical Cases for Classroom Exercises Scripting for the Classroom Upgrading the Business Strategy and Policy Game Developing Student Team-Building and Leadership Skills Using Computer-Aided Experiential learning Strategies Organizing and Outward Bound Field Trip An Architecture for Extensible Simulation Games Performance in the Capstone Business Course: What is the effect of Pedagogy, Learning Styles, and Student Motivation? Operational Strategy with Participant-Modifiable Parameters An Example of a Personal Selling Case Transformed into a Role Play Scenario Instructional Software: It's Evolution and Current State of the Art in the Business Curriculum Ascertaining Performance Variables for use in Determining Student's Grades in Courses Employing a Business Simulation Designing Management Seminars Using Business Simulations The Accounting Information Systems Course: Bridging the Gap between the Classroom and the Real World The Good Cooks Guide to Training Excellence: Working with Passion A Demonstration on Multiple Data Collection Methods: Seeing Strategic Issues Through the Looking Glass Simulation Systems Analysis and Design: Why Undergraduate Education gets a Failing Grade Accommodating Organizational Culture: An Evaluation of Management Development Delivery Modes in Varying Organizational Cultures Modeling Total Quality into Business Simulations The Political Futures Game Meeting Meeting Objectives