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The Leverage Game: Teaching Growth, Leverage, and Risk in a Dynamic, Experiential Framework Arnold W. Oltmans Arnold W. Oltmans is an associate professor in the Department of Agricultural and Resource Economics, North Carolina State University. The author gratefully acknowledges the encouragement and suggestions during initial development of the game by Tom Frey and Nate Splett, the numerous helpful comments of reviewers, and the enthusiastic support of students in agricultural financial management at NCSU. Abstract Teaching abstract economic concepts to students who see the world in concrete terms can be enhanced through the use of games, simulations, and experiential learning activities. This article presents a valuable game technique for teaching the abstract concepts of financial growth, risk, leverage, and diversification in a concrete manner. The game vividly illustrates and allows students to personally experience the interactions among growth in equity, investment returns, cost of debt, leverage, and their own risk preferences. Students make financial decisions in a dynamic environment of changing expectations and variations in actual business performance. Response by students to the game is enthusiastic and positive; subjective and objective evaluations indicate learning is greatly enhanced. The game is easily adapted to various classroom and economic scenarios, and it has potential extension and research applications as well. Key words: abstract, concrete, learning style, ROA, ROE, leverage, equity growth, cost of debt, risk, probability, dynamic. Article <top> Experimental economics has established a niche in the economics profession as a research tool in the study of market behavior and for testing game theoretic hypotheses (Smith). Experimental economics techniques also have been applied in the classroom to demonstrate economic principles and to provide students with hands-on experience in making economic decisions (Wells). Games or simulations for teaching economic concepts have been reported in the general economic literature; examples include the free rider problem in public finance and the voting paradox (Sulock), stock market price determination (Williams and Walker; Bell), market exchange simulation (Williams), and the demand for money (Beckman). Fisher, Wheeler, and Zwick report that the experimental approach is not as widely used by agricultural and resource economists as by economists in general. However, Fackler states there is a growing interest in experimental approaches to agricultural marketing research. Recent work by Adam, Hudson, Leuthold, and Roberts, and by Forster and Roberts in marketing research attests to this. Lev demonstrates the educational use of a marketing game, as does Fackler. Applications of experimental and game techniques to farm management also can be found. In 1987, Edwards reported a simulation model for teaching farm management. Boehlje and Eidman in 1978 discussed the value of using a farm management game for teaching undergraduate classes, as did Menz and Longworth in 1976, Boehlje, Eidman, and Walker in 1973, and Schneeberger in 1969. Other teaching applications for games and simulations were demonstrated by Babb and Eisgruber in 1966 for grain merchandizing and feed supply business management, with updates toward agribusiness management since then. Conspicuous by their relative absence in the professional literature are games related specifically to financial management concepts for extension or classroom use. Games developed and published in the finance area have been primarily for research tools in measuring risk attitudes and subjective probabilities (Nelson and Bessler). Other games may have been developed and adopted in the classroom, such as bank management games, but not necessarily published. The limited availability, publication, and application of experimental/game tools for teaching financial concepts is unfortunate. Surveys indicate that undergraduate students in agricultural economics are predisposed (perhaps as high as 70% of students) toward a concrete learning style preference oriented to hands-on experiences and applications, games, and trial-and-error problem solving (Oltmans; Roberts and Lee).1 Research work on learning styles reveals four basic learning patterns arising from two types of mediation abilities—perception and ordering (Gregorc). In perceptual ability, individuals are predisposed toward either a concrete or abstract quality. A concrete quality indicates the ability and preference to grasp and mentally register information through experience and application of the physical senses. An abstract quality suggests the ability and preference to grasp and conceive information through reasoning and intuition, to perceive that which is invisible to the physical senses (Gregorc).2 1Preliminary results from Oltmans indicate no significant difference between students in agricultural economics courses in general and students in agricultural finance types of courses. 2The educational literature has much to say about learning styles, though not specifically related to agricultural economics students. These numerous works are not cited here. References cited by Roberts and Lee provide a good foundation to the learning styles literature beyond the work of Oltmans and of Gregorc cited here. Since major financial management principles, such as risk and leverage, are abstract concepts, bridging the learning gap between these abstract concepts and the concrete style of students is important to a successful teaching and learning experience. That games can be useful pedagogic tools for bridging this gap has been clearly established in the educational arena. French, in challenging the agricultural economics profession to bring more of the real world into the classroom, states, "I will not belabor the place of games and simulations.... They are proved, available, flexible, and motivational" (p. 1,165). Against this background and the noted paucity of educational games relevant to financial management, a game for presenting abstract financial concepts in a concrete manner for students to observe, experience, and reflect upon is offered here. This article describes a game approach to teaching the fundamental financial management concepts of leverage, risk, and growth, and their combined effect on financial decision making. It presents a game that is sufficiently complex with its dynamic nature to reasonably simulate a real-world economic process, while yielding realistically interesting (as opposed to simplistic or obvious) results that students can trace back to a cause-effect relationship. Yet it is simple enough to be administered easily and understood quickly by students without a large commitment of time in a typical classroom setting. Students are able to see not only the end results of the game process, but also to identify the economic principles at work. The game's structure contains options for either greater or less complexity, as desired. This game model hopefully will encourage others to search for similar applications in teaching, extension, and research to realize the enormous potential of such game techniques. Conceptual Model <top> Any business is financed by a combination of debt and equity claims to its assets. The return on assets represents the payments covering the costs of capital distributed between debt and equity capital according to their relative weights (Barry, Hopkin, and Baker). Equation (1) expresses this relationship as: ROA = (ROE)(E/A) + (COD)(D/A) (1) where ROA is rate of return on total assets, ROE is rate of return on equity, E is equity capital, A is total assets, COD is cost of debt (expressed as a rate), and D is debt capital. Assuming a profit motive of maximizing wealth accumulation over time, a business seeks growth in its equity capital, the ROE component of returns. To highlight the growth in equity, equation (1) can be rearranged as: ROE = ROA + (ROA COD)D/E. (2) Equation (2) clearly illustrates that equity growth (ROE) is a function of the total rate of returns, the cost of debt, and the amount of financial leverage (D/E) employed.3,4 In a nominal world of certainty and perfect flexibility of resources, the optimal strategy for growth is not particularly difficult. If ROA > COD, the optimal strategy is to use the maximum amount of leverage possible. If ROA < COD, leverage should not be used. However, this relatively simple strategy or decision rule has little practical significance in the real world of uncertainty where the precise relationship of ROA to COD is unknown (Levy and Sarnat). Also, business assets are not perfectly liquid and business organization is not entirely flexible in the short run. Thus, leverage cannot, in practical terms, shift from zero to maximum leverage from one business planning cycle to the next, even if it is known that the ROA-COD relationship is going to change. 3The tax rate also affects equity growth. Equation (1) can be expressed as an after-tax rate through multiplying by a factor of (1 t), where t is the tax rate. For simplicity, the tax effect is omitted here; it does not affect the primary intent of illustrating the relationships among growth, leverage, and risk. 4Barry et al. also include a consumption factor in their growth formula. Consumption is assumed to already be included in the ROA measure, consistent with the Farm Financial Standards Task Force measure of ROA, which includes the subtraction of capital withdrawals. The presence of uncertainty makes the optimal strategy for equity growth more interesting and also more complex. Equation (2) under uncertainty implies two types of risk conceptualized by Gabriel and Baker. Business risk (BR), the variability in net income or equity growth caused by changes in the biophysical environment and in markets, is embodied in the variance of ROA over time. Financial risk (FR), the additional variability resulting primarily from debt financing, is related to the degree of leverage employed and variation in the cost of debt. Risk balancing may occur in a tradeoff between BR and FR. A decline in BR may lead to the acceptance of greater FR or vice versa (Gabriel and Baker). Consequently, growth embodies a risk-return tradeoff decision on the optimal amount of leverage to use. Barry et al. explain that the optimal amount of leverage will differ among businesses, depending on the decision makers' risk-return preferences, or degree of risk aversion, and expectations about returns to assets and the cost of debt. Added to that is the notion here that the degree of asset liquidity and flexibility in organizational structure also affects the optimal choice of leverage. The interrelationships among growth, leverage, and risk are most often illustrated in the textbooks and classrooms through tables and graphs depicting various combinations of these financial elements. These illustrations add some concreteness that certainly helps students comprehend these important abstract concepts. Case studies are also useful in this regard. However, these instructional tools do not very well capture or illustrate the notion of risk aversion. Nor do they adequately illustrate the dynamic synergies over time of variability in returns and costs, leverage, risk relationships, and liquidity that affect financial management decisions. That inadequacy has left this author, over 12 years of teaching, with the frustrated feeling that "Yes, most students come to understand the basic nature of these concepts academically, but few really grasp how they work together or what their full implications are in making financial management decisions. Experience is the better teacher." Experience and hands-on application of these financial concepts can be simulated in the classroom through a game technique. The structure of such a game, referred to as the Leverage Game in this article, is presented in the following sections and is suggested as a valuable tool for teaching growth, leverage, and risk in the management process to students who are primarily oriented to a concrete view of the world. Game Objectives <top> The primary objective of the Leverage Game is to increase students' (hereafter referred to as players) understanding of the effect of leverage on equity growth and risk. The game illustrates the risk-return tradeoff associated with leverage through a dynamic simulation of business returns in an uncertain environment. Players experience the effect of making key financial decisions under risk. Secondary objectives include having players: (1) gain insight into their own degree of risk aversion compared to other people and how that affects their approach to financial management in a competitive economy; (2) examine the role of liquidity and financial diversification strategies for growth, leverage, and risk; and (3) observe risk-balancing behavior. Accomplishing these objectives enables students to discover the cause-and-effect relationships among growth, risk, leverage, and liquidity. The game is specifically targeted toward undergraduate classes in financial management at the junior/senior level where the concepts of leverage, growth, risk, and diversification are examined in detail. Basic Framework <top> Figure 1 presents a flow chart of game operations and illustrates the game's basic framework. Parameters of the game (such as the risk-free rate of return, cost of debt, beginning equity, expected ROA, and leverage choices) are presented in fixed terms for ease of explanation. However, the parameters can be adjusted to any level that most closely fits the instructor's view of reality or specific objectives being emphasized. A later section specifically discusses options to the basic framework and set of parameters illustrated.
Each player begins the game at year 1, with $50,000 equity to invest (item A in Figure 1) in either a risk-free bank fund yielding an 8% annual rate of return or in a business venture that the player will manage. There are no restrictions on the proportional amount of each investment (items B, B1, and B2 in Figure 1). As item 2.0 in Figure 1 indicates, the expected annual rate of return (ROA) for the business venture is 12%, the long-run average determined by the statistical probability properties of the game's structure. The actual ROA realized each year and the average ROA actually realized during the game's limited time span, however, are uncertain. The 12% is not risk free, as explained in greater detail later. After players decide how much to invest in the business, based upon their expectation of ROA (which changes each year), they must also decide how much money to borrow at a cost of 10% interest on debt (COD). Except for year 1, players have two opportunities to adjust the business leverage position (see items C1 and C2 in Figure 1) as more information about the expected return is revealed. The initial leverage position selected for the year represents the opportunity to adjust leverage from the prior year's position. It is followed by the opportunity to make an intra-year adjustment to a final leverage position for the year after ROA expectations are fully established. Players may operate with no debt at zero leverage, growing entirely on the initial equity capital and retained earnings. Or, players may borrow up to four times the amount of equity. To keep the game manageable in a noncomputerized format and to facilitate this discussion, only seven discrete leverage possibilities are illustrated here—0, .25, .5, 1, 2, 3, and 4—as indicated by item 4 in Figure 1.5 5There are no conceptual reasons for restricting the leverage choice to only seven discrete values. Leverage choice can be expanded to any number of discrete possibilities or incorporated as a continuous random variable at the instructor's discretion. However, expanding the leverage choice set dramatically increases the number of possible outcomes summarized in Table 4, making the use of Table 4 impractical and requiring outcomes to be calculated by formula. This may reduce students' ability to easily "see" the outcome of their leverage choices, which is a primary objective of the game. Increasing leverage choices, while more realistic, also makes operation and monitoring more difficult. Computerized operation and scoring of the game becomes a necessity. The ROE, or rate of return on equity (item D in Figure 1), is determined after the D/E leverage ratio is established and the actual ROA realized for the year becomes known from the roll of dice (item 7 of Figure 1). The ROE percentage converts to a dollar amount of growth based on the amount originally invested in the business (item E2 of Figure 1). This amount of growth in business equity for the year plus the amount earned on the bank investment (item E1 of Figure 1), when added to the beginning value of investment, determines the ending amount available for the following year. This general process, with some additional details described in the following sections, is repeated for as many years as players agree.6 The game's design allows 8-10 years of business activity to be accomplished in a typical 50-minute class setting, depending on the instructor's and students' familiarity with the game and its underlying concepts.7 An alternative is to play the game over an extended period of class meetings, with 5-10 minutes of each class devoted to a one-year cycle of the game's time frame. This would allow players to study yearly results, discuss strategy and/or outcomes to date, and to put greater thought into financial decisions. Players are evaluated on the basis of the amount of equity accumulated at the end of the game. A lower limit of $20,000 exists as a type of safety-first utility function. If a player's equity falls below $20,000, the player must liquidate the business investment and must leave any equity in the risk-free bank fund for the remainder of the game. 6A game may be of any length. Initial experience indicates that a 10-year cycle works best. A shorter cycle does not seem to capture a desired range in variability of returns. A longer cycle takes too much class time and results in players losing interest and making poor decisions towards the end of the game. 7To realistically complete a full 10-year cycle in 50 minutes, a prior practice round of one or two years is advisable to answer questions, to orient all players to the process and concepts involved, and to make necessary adjustments. Changing the Investment Mix and Amount of Leverage <top> After the first year and as the game proceeds, players may adjust the amounts invested in the bank fund and in the business. The bank fund may be increased or decreased by any amount at the beginning of each year. The business investment may also increase by any amount each year. However, players are restricted to decreasing the amount invested in the business by no more than 10% from one year to the next (item 3 of Figure 1). Players wanting to decrease their business investment by more than 10% must liquidate the entire business and invest all funds in the bank fund for that year and the following year. Liquidated players are allowed to reinvest in the business again after two years. This 10% limitation rule on business asset contraction and liquidation represents the lack of complete liquidity of business assets, a certain degree of asset fixity and liquidation costs. Experience with the game has shown this type of limitation to be necessary to get players to adopt a thoughtful long-run investment strategy rather than a short-run, in-and-out gambling type of behavior. Players may also, as previously indicated, adjust the amount of leverage in their business. However, this adjustment is limited to moving only one degree of leverage (in the range of seven discrete possibilities) at a time from the previously established level (item 5 of Figure 1). The reason for this limitation, as experience has also shown, is similar to that discussed for the limitation on changes in the investment mix. For example, a player could move from a leverage of 2 to a leverage of 1 or 3 in a single adjustment to the leverage strategy, but not to a leverage of 0. For this reason, the initial leverage chosen to begin the business is important since there is a related effect upon the following years. Decisions in subsequent years are partially dependent upon and limited by decisions of previous years. Expected Annual Returns <top> There are seven possible expected ROA levels for the business investment in any single year, as listed in Table 1. These represent the variation from the long-term average of 12% in the expected economic performance of the entire industry, or in a broader sense the general economy, in any given year. The game begins at level D of Table 1, with an expected return of 12% to business investments. After year 1, the expected ROA may be higher or lower than the previous year. However, the expected ROA after year 1 is not completely random among levels A through G. The yearly change in expected ROA is dynamic, but dependent upon the previous year's level and limited in its movement; the industry or general economy will not move from boom to bust or vice versa in one year. The expected ROA for all years other than year 1 develops in two steps, according to the change mechanism of Table 2. The flip of a coin is the first step that determines the anticipated direction of a change in the economy or industry. If the coin flip is heads, there is a 5/6 probability in Table 2 that the expected economic performance will be better than the previous year, and a 1/6 probability that it will be worse. If the coin flip is tails, the exact opposite is true. Knowing the expected direction (item 2.2 of Figure 1) but not the magnitude of change in ROA from the previous year, players must make some management decisions. Players choose a new investment mix for their accumulated equity, and they also choose an initial leverage strategy for their business for that year (subject to the restrictions previously mentioned).
The second step is the roll of a single die, which determines the actual direction and magnitude of change in the expected industry or general economy performance for the year, as indicated in Table 2. The coin flip of step one, followed by the roll of a single die, establishes the new level of expected ROA for the year (items 6.1 and 6.2 of Figure 1). At this point, knowing the expected ROA for the year, players make one last financial management decision for the year. They adjust their initial leverage and establish their final leverage position (item C1 of Figure 1), typifying an intra-year business adjustment to the external economic environment. They may not, however, change the amount or proportion of their investments. This two-step process for determining business ROA and leverage positions is repeated for each year. For example, assume at the beginning of year 2 that the coin flip result is heads. Knowing there is a 5/6 probability that the economy and general business performance will improve in year 2, players decide how to invest their accumulated equity and establish an initial leverage position for the year, which may or may not be different from their leverage in year 1.8 Next, assume a die is rolled and comes up 3. The change in expected ROA from the previous year, according to Table 2, is an increase of one level. Since expected ROA in year 1 was 12% at level D in Table 1, the expected ROA for year 2 is level E, or 15%. Players now establish their final leverage position and wait for the actual ROA for the year to be revealed. Actual ROA Realized During the Year <top> On average, over the years and over repeated runs of the game, the business investment will perform at the expected 12% ROA level, but the presence of business risk means actual ROA realized in any single year relative to expected ROA is uncertain. In any year, individual businesses may perform at an ROA better or worse than the industry average, and better or worse than the general economy. The actual business ROA realized during a year for all players is a discrete probability distribution found in the rolling of a pair of dice, as revealed in Table 3. Following the previous example where the expected ROA in year 2 is 15%, Table 3 reveals that actual ROA realized for year two may range from 0% to 30% in a single roll of the dice. This represents the business risk peculiar to an individual business, which may or may not perform at the average level of the industry as a whole at a specific point in time. The variation in Table 3 occurs in incremental steps of 3%, with decreasing probability for each increment away from the expected value of 15%. However, incremental steps of any magnitude can be substituted into Table 3 at the discretion of the instructor. Players have access to the information in all the tables at all times, allowing them to be aware of the range of possible outcomes and to update their subjective probabilities in making their investment and leverage decisions.
8Recall that a change in leverage can be only one degree different from the previous leverage position.
Note: ROE = ROA + (ROA COD)D/E. Growth in Equity (ROE) <top> The business performance during the year for each player will depend on the amount of equity invested in the business, the leverage position, the actual ROA realized for the year, and the cost of debt. The individual ROE percentage is calculated by each player (item D of Figure 1) according to equation (2). Table 4 lists the possible ROEs produced by equation (2) for various combinations of ROA and leverage amounts at a 10% cost of debt.9 The ROE percentage multiplied by the dollar amount invested in the business yields the dollar amount of growth in equity from the business. This, combined with the dollar amount earned from the 8% bank fund, determines the total gain (loss) in equity. The total gain or loss added to the equity investment at the beginning of the year is the amount of equity available for investment the next year. 9The cost of debt may be any amount; 10% is the default level used here for illustration purposes. Revealing Risk Attitudes <top> One objective of the Leverage Game is to reveal individual risk attitudes, risk management strategies, and subsequent results. However, when players have nothing to gain or lose other than the thrill of victory or the agony of defeat, their game management strategy may not be a true reflection of their risk attitudes. To partially alleviate this and to prevent "wild" gaming strategies that may not be realistic, it is useful to have a monetary reward at stake. Linking Leverage Game performance to a grade, while useful in this regard, creates ethical problems and should not be done. Classroom Results <top> Initial development and testing of the Leverage Game involved two groups of students in agricultural finance classes at two land grant institutions. Response from students was positive and led to the final version outlined here. Its further use in agricultural finance classes has demonstrated that it is an extremely valuable and effective teaching/learning tool because it actively involves students in the learning process and provides concrete experience of the abstract principles at work. Validation of the game's effectiveness as a teaching tool to enhance learning, as with any teaching technique, requires both subjective and objective evaluation. Subjective evidence from student evaluations and student analysis has revealed extremely favorable results from using the game. Course evaluations and individual comments of students indicate the game is a definite aid to understanding the concepts of leverage and risk. Students comment that it is stimulating and a delightful change of pace in course activity that renews their interest in the application of economic concepts. Students overwhelmingly indicate the game should be kept in the course syllabus, with several suggestions for expanding the activity beyond regular class hours. Graduates, informally recollecting their experiences in the class later, frequently cite the Leverage Game concepts as the things they remember most in the course. Instructor observation and student comments reveal that one of the most valuable aspects of the game is the post-game summary—with a comparison of individual player outcomes, discussion of risk-leverage strategies employed, and discussion of how the presence of risk affected individual management decisions. Here, students can reflect on what happened during the game, what various events meant to them, and how varying degrees of risk aversion affected management strategy. Through group discussion of the results, students affirm the validity of their own management decisions and beliefs as well as obtain additional insights from others. A prepared set of discussion questions elicits responses specifically related to the learning objectives of the game. Perhaps the most valuable insight gained by students and revealed in the discussion of the game's outcome is how important the timing of uncertain events and management decisions is to business success. No single investment or leverage strategy has emerged as the dominant strategy for success. The wide variations in returns for high-leverage players are vividly illustrated in the post-game summary, although they are emotionally well illustrated by some players during the game itself. By statistical probability, high leverage should dominate the list of high-return players. To date, however, seemingly high-leverage players have only succeeded to dominate the lower quadrant of returns. This has produced valuable points of discussion on the possible cause of such results. Objective validation of the game's effectiveness has been limited to a four-year comparison of grades on a common-unit exam. The course on agricultural financial management at North Carolina State University has been taught by this author over a four-year period—two years with using the game in the unit on leverage and risk, and two years without. A unit exam of similar content and style was given each year. Table 5 summarizes the statistical analyses of test results over the four years. Panel A of Table 5 is a comparison of exam scores and other grade characteristics of the group of 34 students taught without using the Leverage Game to the 41 students taught by using the Leverage Game. The average exam score of students improved by more than five percentage points through use of the game; this difference in mean scores of the two groups is statistically significant at the 0.05 level.
*Indicates significance at the .05 level. **Indicates significance at the .01 level. aLeverage Game dummy variable with a value of 1 if the student was in class using the Leverage Game, 0 otherwise. It does not appear that the difference in exam performance is due to a difference in academic ability of students. The grade point average of students in the two groups is not significantly different at 80.9% and 79.5%. Also, performance in the course prior to the unit on leverage and risk is nearly identical at 77.3% and 77.1%. Thus, assuming the testing instrument was unbiased over time (a reasonable assumption based on the consistency in teaching methods and testing procedures employed in the course over the years), the results indicate that use of the Leverage Game positively influenced learning, as measured through written testing. Panel B of Table 5 presents a slightly different analysis of the data, with similar results. A simple linear regression model, as shown in equation (3), uses the common-unit exam grade of all 75 students as the dependent variable. Exam Score = β0 + β1 Prior Grade + β2 Leverage Game. (3) Explanatory variables are the average grade achieved in the course prior to the leverage and risk unit, and a zero-one dummy variable for students who took the course when the Leverage Game was or was not used. Consistent with the previous statistical measures, the dummy variable is a significant factor, indicating that students taught via the game technique improved their exam grade by 5.06 percentage points. Caution is advisable at this point to recognize that a test score is neither the ideal measure nor the final word on the validity of a game for learning (Fels), even where more rigorous controls and measures of all variable factors of learning, beyond the simpler ones available and presented here, can be applied. The literature on economic games and experiments (Wells; Spencer and Van Eynde; Williams and Walker; DeYoung; and Fels, as recent examples) shows that primary evaluation and validation of economic educational games has been mostly via subjective measures, even where conditions for formal testing may have been adequate.10 While acknowledging the desirability of additional research using more sophisticated controlled experimentation and empirical testing and analysis of games for teaching, this author agrees with Fels, who further asserts, "Intuitive judgment is what we ordinarily use—must use—in deciding how to teach" (p. 369). 10An extensive literature review of the use of games and experiments for teaching, not research, turned up one citation by Babb and Eisgruber of a Harvard study, which conducted a controlled experiment for measuring the effect of using a simple economic game simulation. The experiment appeared to be rather limited in scope. Additional Options and Extensions <top> The basic parameters of the Leverage Game, illustrated here with fixed values, can be changed to any desired level, with combinations of different parameters limited only by the time available to reconstruct tables and by the level of complexity that can be handled. Various values are possible for the risk-free rate of return, cost of debt, and expected ROA. The seven possible leverage ratios can be changed to any number and combination of discrete possibilities. Incremental changes in the ROA levels of Table 1 can be adjusted, as can the number of levels. Table 2 can be changed to reflect more or fewer opportunities for change in expected ROA, and the discrete probability distribution of actual ROA realized in Table 3 can be adjusted as needed. An interesting option not presented here is to allow the risk-free return and the cost of debt to change (while maintaining a certain basis spread to reflect net interest margins) as the expected ROA—the proxy for the general economy—changes. Likewise, the cost of debt to individual players could vary positively with their leverage position. The requirement for doing this would be separate ROA and COD versions of Table 4 for every possible level of COD allowed. Making COD dynamic adds another element of financial risk and another layer of realism, but it also adds a layer of complexity. While technically appealing, this option and its necessary rules have not yet been tried by this author. Instructors should individually decide whether or not such added realism and complexity would enhance the primary learning objective. Another option for extending the game is to computerize the process. This would allow continuous rather than discrete values for all parameters, and would facilitate the inclusion of a variable cost of debt. The probability distribution characteristics of the coin toss and roll of dice could be replaced with other probability distributions judged to be more realistic. A computerized game would add statistical realism and sophistication that would be desirable. However, doing so would also remove much of the game's dynamic flow from the hands and eyes of the players, the essence of concrete learning, to the more abstract flow of a computer model. Computerized sophistication has definite advantages for designing, operating, and extending the game, but it is not obvious that it would necessarily enhance the learning process or advance the attainment of the learning objectives in this case. A useful first step in computerization of the game would be a spreadsheet for scoring, which would remove the more mundane computational tasks and allow students to concentrate on management strategies. A method of multiplying the teaching/learning potential of the game is to allow a student to play more than one management strategy at a time. By simultaneously operating differing strategies under the same economic conditions, a player would be able to contrast firsthand the performance of different strategies. A final option to consider is the incorporation of a simple credit scoring model as a method for determining the amount of leverage allowed and/or the cost of debt. As presented, the game allows a range of leverage, but the leverage choice is controlled entirely by the player without regard to past performance levels or current equity position. A scoring model based on current financial position, recent ROE, and expected ROA that would define the leverage choice set available and cost of debt to each individual player would add realism to the leverage decision process. It would also incorporate another conceptual area of financial management. The major costs of adding such an option would be a greater time requirement, greater complexity, and the possibility that students would lose their focus of the primary learning objectives. While the Leverage Game has been described for and applied to a classroom setting in undergraduate teaching, it also has the potential for extension and research applications. In extension education, the game could be used to vividly demonstrate risk, uncertainty, and growth strategies (i.e., the relationship of leverage, diversification, and the cost of debt to growth). The game could be employed as a research tool in controlled experiments to measure individual response to variable factors. Research relating players' outcomes to risk preferences, learning styles, personality types, and other factors could lend additional insights. This discussion of suggested options of the game is certainly not an exhaustive one. The basic framework of the game hopefully will be extended by others to enhance its use and adaptation for a wider variety of purposes in the financial management arena. Summary <top> The Leverage Game represents a useful technique for teaching the abstract concepts of risk, leverage, growth, and liquidity in a concrete manner, especially to students who prefer a concrete learning style. It can be a valuable addition to the limited set of experimental and game tools available for teaching financial concepts. The structure of the game, as presented in this paper, is sufficiently complex and dynamic to present a realistic business decision-making environment that captures students' interest. However, it is also simple enough to be easily administered in a typical classroom and to be quickly understood by student participants with a limited knowledge of risk and leverage. A variety of options exist that grant instructors the opportunity to customize the game to their standards. The game vividly illustrates and allows students to experience the basic concept that growth in equity over time is a function of returns (ROA), cost of debt (COD), and leverage (D/E). Several built-in parameters for risk cause student players to examine their own risk attitudes in developing a strategy for financial growth. Choosing between a risk-free rate of return and a risky business venture with the capacity to leverage the business investment, players must make yearly financial decisions based on reasonable expectations of business performance that are, nonetheless, uncertain and variable. The dynamic but not totally random structure of the game allows players to develop a long-run management strategy and make adjustments to that basic strategy as events become known. Initial applications of the game in agricultural finance courses show an enthusiastic, positive response by students to this teaching tool. Subjective student evaluations and personal assessment by this author strongly indicate it is a valuable aid to teaching and learning abstract financial concepts. Limited objective evaluations of test scores reveal that students exposed to this learning tool achieve greater understanding of these concepts. The generic nature of the game makes it easily adaptable to a wide variety of classroom settings and specific financial content, with potential for extension and research applications as well. Appendix <top> The following comments are offered as additional information that the author believes may provide further insights to interested readers considering the use of the Leverage Game in the classroom. As a demonstration of the classroom results obtained from use of the Leverage Game, Table A1 summarizes numerical outcomes from four sets of students playing the game. No statistical inference as to the game's properties is implied, but it usefully demonstrates a range of activity the game may produce in different sets of players and circumstances.
NA = Not available due to an error in recording and storing the information. The process for keeping track of players' equity was implied in the article. Table A2 is presented here as an example score sheet that also provides some insight into the operation and progression of the game through each year. Table A2. Record of Earnings for the Leverage Game Year 1:
All Other Years:
The article has discussed the desirability of having a monetary reward as an incentive for players to be guided by their personal risk attitude and to avoid uncharacteristic wild gaming strategies. A monetary scheme that has been used successfully by the author is for the instructor to contribute cash into a purse with predetermined payoffs—for example, a payoff to the player with the highest ending equity, the lowest equity, and the equity closest to a certain amount announced in advance. Further, it is desirable to allow (but not require) players to contribute cash into the purse as well. Caution is urged here not to violate ethical rules governing forced student participation in classroom activities. Every player becomes eligible to receive the payoff from the instructor-donated purse. Only players who choose to participate in the players' money pool are eligible to receive the players' purse. A description of the Leverage Game suitable for distributing to students that explains the game process in detail is available upon request from the author. References <top> Adam, B.D., M.A. Hudson, R.M. Leuthold, and C.A. Roberts. "Information, Buyer Concentration, and Risk Attitudes: An Experimental Analysis." Rev. Agr. Econ. 13(1991):5971. Babb, E.M., and L.M. Eisgruber. Management Games for Teaching and Research. Chicago: Educational Methods, Inc., 1966. Barry, P.J., J.A. Hopkin, and C.B. Baker. Financial Management in Agriculture, 4th ed. Danville, IL: The Interstate Printers and Publishers, Inc., 1988. Beckman, S. "A Microcomputer Program that Simulates the Baumol-Tobin Transactions Demand for Money." J. Econ. Education 18(1987):287308. Bell, C.R. "A Noncomputerized Version of the Williams and Walker Stock Market Experiment in a Finance Course." J. Econ. Education 24(1993):31724. Boehlje, M.D., and V.R. Eidman. "Simulation and Gaming Models: Application in Teaching and Extension Programs." Amer. J. Agr. Econ. 60(1978):98792. Boehlje, M.D., V.R. Eidman, and O. Walker. "An Approach to Farm Management Education." Amer. J. Agr. Econ. 55(1973):19297. DeYoung, R. "Market Experiments: The Laboratory versus the Classroom." J. Econ. Education 24(1993):33552. Edwards, W. "FARM-MAN: An Interactive Simulation Model for Teaching Farm Financial Management." Symposium paper abstract. Amer. J. Agr. Econ. 69(1987):1082. Fackler, P. "Experimental Markets Using the Electronic Market Place (EMP)." Unpublished workshop paper presented at North Carolina State University, November 1993. Fels, R. "This Is What I Do, and I Like It." J. Econ. Education 24(1993):36570. Fisher, A., W.J. Wheeler, and R. Zwick. "Experimental Methods in Agricultural and Resource Economics: How Useful Are They?" Agr. and Resour. Econ. Rev. 22(October 1993):10316. Forster, D.L., and C.A. Roberts. "Oral and Electronic Double Auction Markets: An Experimental Comparison." N. Cent. J. Agr. Econ. 9(1987):99105. French, C.E. "Selected Alternative Programs for Bringing the Real World to the Undergraduate Classroom." Amer. J. Agr. Econ. 56(1974):116375. Gabriel, S.C., and C.B. Baker. "Concepts of Business and Financial Risk." Amer. J. Agr. Econ. 62(1980):56064. Gregorc, A.F. An Adult's Guide to Style. Columbia, CT: Gregorc Associates, Inc., 1993. Lev, L.S. "Market Manager: An Educational Commodity Marketing Game." Symposium paper abstract. Amer. J. Agr. Econ. 70(1988):1216. Levy, H., and M. Sarnat. Capital Investment and Financial Decisions, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1986. Menz, K.M., and J.W. Longworth. "An Integrated Approach to Farm Management Education." Amer. J. Agr. Econ. 58(1976):55156. Nelson, R.G., and D.A. Bessler. "Subjective Probabilities and Scoring Rules: Experimental Evidence." Amer. J. Agr. Econ. 71(1989):36369. Oltmans, A.W. "Learning and Teaching Styles in Agricultural Economics Classrooms and Extension Audiences." Paper presented at the Southern Agricultural Economics Association annual meetings, New Orleans, LA, 1 February 1995. Roberts, D.Y., and H.Y. Lee. "Personalizing Learning Processes in Agricultural Economics." Amer. J. Agr. Econ. 59(1977):102226. Schneeberger, K.C. "Gaming as a Farm Management Teaching Device: A Development and Analysis." S. J. Agr. Econ. 1(1969):5358. Smith, V.L. "Game Theory and Experimental Economics: The Early Years." J. Econ. Perspectives 3(1989):15169. Spencer, R.W., and D.F. Van Eynde. "Experiential Learning in Economics." J. Econ. Education 17(1986):28994. Sulock, J.M. "The Free Rider and Voting Paradox `Games.'" J. Econ. Education 21(1990):6570. Wells, D.A. "Laboratory Experiments for Undergraduate Instruction in Economics." J. Econ. Education 22(1991):293300.
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