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FD! ‘t..£..~ M. ‘5 I“, 2 . o. 1.1.. .. 1 1 ... I 31. 1 1 | 1'...) i ’ ll 1’ N, 'I Iillli ANALYSIS OF THE EFFECTS OF SELECTED VARIABLES ON CORN HARVESTING SYSTEMS UTILIZING SIMULATION AND DYNAMIC PROGRAMMING By Robert Alexander Milligan A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1971 .45! 1’. [1| , :. ..h‘ yUJ‘ “U 7519?. 1 c .33: ACKNOWLEDGEMENTS The author wishes to acknowledge his co—major professors, Dr. Larry J. Connor and Dr. David L. Armstrong, for their invaluable advice and constructive criticism. Without their assistance and en- couragement this thesis would have been only a dream. Appreciation is also expressed to Dr. J. B. Holtman and Dr. L. R. Pickett for their guidance in the development of this study and to George Perkins for his help in development of the model. Thanks are expressed to Dr. Dale E. Hathaway and the Depart- ment of Agricultural Economics for the financial assistance and the facilities that made my Masters program possible. Finally, the author expresses a special word of sincere thanks to his wife, Karen, for her patience, understanding and encouragement. ii u..- \ h... \ ...... TT ... I—l <1 LIST OF TABLES . . . LIST OF FIGURES. . . Chapter I. INTRODUCTION. Objectives. Organization of the T Footnotes . TABLE OF CONTENTS II. A CONCEPTUAL FRAMEWORK. Economic Theory . . Simulation. Replacement Theory. Replacement Models. Footnotes . III. THE MODEL USED TO STUDY hesis. . . . . THE Corn Harvest Simulator. . The Machinery Replacement Footnotes . HARVESTING SYSTEM . Routine . IV. RESULTS FROM THE SHORT-RUN HARVESTING Loss. . Size. . . Length of Wor k Day. Grain Moisture Criterion. Opportunity Cost of Labor Average Temperature . Additional Rainfall Price . . . Yield . . . Footnotes . iii PERIOD. Page vi XV \JO\-l-\ 16 20 24 34 36 36 44 47 48 56 57 65 69 74 74 77 82 82 86 V. VI. VII. ANALYSIS OF THE EFFECT OF THE SELECTED VARIABLES IN THE HARVESTING PERIOD. Ranking of the Effect on Income . Effect of Changes in Variables on Choice of a Combine . . An Analysis of Each Variable. Size of the Enterprise. Price . . . . . . . . . . Temperature . . . . . . . Yield . . . . . . . . . . Opportunity Cost. . . . . Hours . . . . . . . . . . Grain Moisture. . . . . . Rainfall. . . . . . . . . Loss. . . . . . . . . . . Footnotes . . . . . . . . . RESULTS FROM THE LONG—RUN REPLACEMENT Repair Function . . . . . ROUTINE . The Shape of the Repair Cost Function . Number of Hours of Machine Use. Level of Machinery Management . Obsolescence Charges. . . Increasing Cost . . . . . Interest Rate . . . . . Optimum Replacement in the Corn Harvesting System . . . Footnotes . . . . . . . . . ANALYSIS OF THE REPLACEMENT RESULTS AND OF THE SHORT-RUN AND LONG-RUN ANALYSIS. INTEGRATION Analysis of the Long-Run Replacement Results. Repair Function . . . . . Shape of the Repair Cost Function . Number of Hours of Machine Use. Level of Machinery Management . Obsolescence Charges. . . Increasing Cost . . . . Interest Rate . . . . . . General Conclusions . . . Integration of the Short-Run and Long-Run Analysis . . . . . Size of the Enterprise. . Price . . . . . . . . . . Yield . . . . . . . . . . Opportunity Cost. . Hours . . . . . . . . . . Grain Moisture and Loss . iv Page 87 88 99 103 104 106 107 107 108 108 110 111 112 112 113 113 115 117 118 129 132 133 134 134 137 138 138 139 140 140 141 145 145 146 146 148 150 150 151 151 151 152 ...-c- l..-- -.b' vA-v—q VIII. SUMMARY AND CONCLUSIONS IX. IMPLICATIONS FOR FUTURE RESEARCH. BIBLIOGRAPHY . . . APPENDICES APPENDIX A. APPENDIX B. APPENDIX C. APPENDIX D. INPUT VALUES FOR CORN HARVEST SIMULATOR SUPPORTING DATA ON THE EFFECT OF THE SELECTED VARIABLES ON THE HARVESTING PERIOD SUPPORTING DATA ON RANKING OF VARIABLES SUPPORTING DATA ON REPLACEMENT ROUTINE Page 153 . . . . . . 160 . . . . . 163 O I O O O O 166 . . . . . . 169 . . . . . . 191 . . . . . . 208 LIST OF TABLES Table Page 1. Characteristics of the Three Base Years Used in Studying the Corn Harvesting System . . . . . . . . . 49 2. Three Year Averages for Different Sizes of Corn Enterprise Using a Two-Row Combine and a Four—Row Combine Assuming All of the Corn is Harvested. . . . . . . . . . . . . . . . . . . . . . . . 51 3. The Values Used for Each of the Nine Variables when that Particular Variable was Being Studied. . . . . 53 4. Income and Expense Figures for Each of the Three Years for a Two-Row and a Four-Row Combine Using Base Values. . . . . . . . . . . . . . . . . . . . 54 5. Income and Expense Figures for Each of the Three Years for a Two-Row and a Four—Row Combine Using Base Values with a 500 Acre Enterprise . . . . . . 55 6. Three Year Averages of Acres Harvested and Income from a 200 Acre Corn Enterprise Using Alternative Loss Functions for the Acres not Harvested by December 1 for a Two—Row and a Four—Row Combine. . . . . 58 7. Three Year Averages for Acres Harvested and Income from a 500 Acre Corn Enterprise Using Alternative Loss Functions for the Acres not Harvested by December 1 for a Two-Row and a Four-Row Combine. . . . . 59 8. Three Year Averages of Acres Harvested and Income from Different Sizes of Enterprise with a 40 Per Cent Loss on the Corn not Harvested by December 1 . . . . . . . . . . . . . . . . . . . . . . . 61 9. The Effect of Corn Acreage on Management Income for the Individual Years for Each Combine. . . . . . . . 62 10. Three Year Averages of Expenses for the Two-Row and the Four-Row Combines by Corn Acreage. . . . . . . . 63 vi Table 11. 12. l3. 14. 15. 16. 17. 18. 19. 20. 21. The Three Year Average Composition of Machinery Expenses by Per Cent for a Two-Row and a Four- Row Combine as the Size of the Corn Enterprise Increases. . . . . . . . . . . . . . . . . . . . . . The Effect on the Average Acres Harvested and on Average Income of Increasing the Length of the Work Day for a Two-Row and a Four-Row Machine with 200 Acres of Corn . . . . . . . . . . . . . . . The Effect on the Average Acres Harvested and on Average Income of Increasing the Length of the Work Day for a Two-Row and a Four-Row Machine with 500 Acres of Corn . . . . . . . . . . . . . . . . The Effect of the Length of the Work Day on Management Income for Each Year for 500 Acres. . . . . Results for Each Combine on 200 Acres with Different Criteria Concerning the Grain Moisture Content . . . . . . . . . . . . . . Results for Each Combine on 500 Acres with Different Criteria Concerning the Grain Moisture Content . . . . . . . . . . . . . . . . . . . The Effect of Alternative Grain Moisture Criteria on Management Income for Each Year with a 200 Acre Corn Enterprise. . . . . . . . . . . . The Effect of Alternative Grain Moisture Criteria on Management Income for Each Year with a 500 Acre Corn Enterprise. . . . . The Effect of the Opportunity Cost of the Combine Operator on Averages for Hours Required, Labor Expense and Income with a 200 Acre Enterprise. . . . . . . . . . . . . . The Effect of the Opportunity Cost of the Combine Operator on Averages for Hours Required, Labor Expense and Income from a 500 Acre Enterprise. . . . . . . . . . . . . . . The Effect of Temperature Changes on a 200 Acre Corn Enterprise with a Two-Row and a Four—Row Combine . . . . . . . . . . . . . . vii Page 64 66 67 68 70 71 72 73 75 76 78 Table 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. The Effect of Temperature Changes on a 500 Acre Corn Enterprise with a Two-Row and a Four-Row Combine . . . . . . . . . Effect of Additional Rainfall During the Harvesting Season with a 200 Acre Corn Enterprise for each Combine. . . . . . . Effect of Additional Rainfall During the Harvesting Season with a 500 Acre Corn Enterprice for each Combine. . . . . . . The Consequences of a Change in Price with a 200 Acre Corn Enterprise and a Two—Row and a Four—Row Combine . . . . . . . The Consequences of a Change in Price with a 500 Acre Enterprise Using a Two—Row and a Four-ROW combine 0 o o o o o o o The Effect of Variations in Potential Yield on a 200 Acre Corn Enterprise. . . . The Effect of Variations in Potential Yield on a 500 Acre Corn Enterprise. . . . . . A Summary of the Situation Existing in the Three Harvesting Periods Studied . . The Rank of the Magnitude of the Effect of the Given Changes in the Nine Selected Variables on Management Income with a 200 Acre Enterprise for a Two-Row and a Four- Row Combine. . . . . . . . . . . . . . The Rank of the Magnitude of the Effect of the Given Changes in the Nine Selected Variables on Managment Income with a 500 Acre Enterprise for a Two-Row and a Four-Row Combine . . . . . . . . . . . . The Direction of the Change in Management Income from Changing the Variables with and without Completion of Harvest During the Harvesting Period. . . . . . . . . . The Ranking of the Variables and the Percentage Change in Management Income when Harvest is and is not Completed for a 200 Acre Enterprise for a Two-Row and a Four-Row Combine . . . . viii Page 79 80 81 83 84 85 85 90 91 92 95 96 a. .J H4. 2%. q Table 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. Page The Ranking of the Variables and the Percentage Change in Management Income when Harvest is and is not Completed for a 500 Acre Enterprise for a Two—Row and a Four-Row Combine . . . . . . . . . . . . 97 The Ranking of the Variables and the Percentage Change in Management as to the Effect on the Choice Between a Two-Row and a Four—Row Combine. . . . . 101 The Effect of Increasing the Size of the Enterprise 100 Acres when Harvest is and is not Completed . . . . . 105 Gain or Loss in Income Due to an Increase of Two Hours in the Length of the Work Day. . . . . . . . . 109 Effect of an Increase in the Maximum Allowable Grain Moisture During Harvest. . . . . . . . . . . . . . 111 The Cost of Keeping and Trading the Two—Row Combine Used 200 Hours per Year with the Two Sets of Data . . . . . . . . . . . . . . . . . . . . 116 The Optimum Replacement Period and Its Cost for Each Set of Data for a Two-Row Combine Used 200 Hours . . . . . . . . . . . . . . . . . . . . . 116 Summary of the Optimum Replacement Period for the Eight Different Distributions for the $10,560 of Total Repair Costs. . . . . . . . . . . . . . 127 The Effect of Different Hours of Use on the Optimum Replacement Pattern and the Cor— responding Cost Using the First Set of Data. . . . . . . 128 The Optimum Replacement Pattern and Corres- ponding Costs for a Two—Row Combine Used 100, 200 and 300 Hours per Years Using the Bowers Data. . . . . . . . . . . . . . . . . . . . . . . 128 The Effect of Alternative Levels of Machinery Management on the Optimum Replacement Pattern and Cost for a Two-Row Combine Given the Assumption that Management Affects only Repair Costs . . . . . . . . . . . . . . . . . . . . . . 130 The Effect of Alternative Levels of Machinery Management on the Optimum Replacement Pattern and Cost for a Two-Row Combine Given the Assumption that Management Affects Repair Cost and Trade-in Value. . . . . . . . . . . . . . . . . 131 ix Table 46. 47. 48. 49. 50. 51. The Effect of Alternative Levels of Machinery Management on the Optimum Replacement Pattern and Cost for a Two-Row Combine Given the Assumption that Management Affects Repair Costs, Trade—in Value and Obsolescence Charges . The Effect of Different Levels of Obsolescence Cost on the Optimum Replacement Pattern and Cost for a Two-Row Combine . . . . . . . The Effect of Increasing Purchase Cost for a New Two-Row Combine on the Optimum Replacement Pattern. O O O C O O I C C O O O O I O O O O O O The Optimum Replacement Policy for the Two-Row and Four-Row Combine Used in the Corn Harvest Simulator for 200 and 500 Acres. . . . . . . . . The Effect on Cost of an Additional 100 Hours of Use Versus an Additional Year of Age on Repair Costs for a Two-Row Combine. . . . . . . . . . . The Optimum Replacement Frequency and Corresponding Average Cost for Each Management Level and Each Assumption Concerning the Effect of Machinery Management on Keeping and Trading Costs for a Two-Row Combine. . . . . . . . . Appendix Table Simulation Input Data 0 O O O O O O O C O O O O 0 Income and Expense Figures for Each of the Three Years for a Two-Row and a Four—Row Combine Using Base Values with a 300 Acre Enterprise. Income and Expense Figures for Each of the Three Years for a Two-Row and a Four-Row Combine Using Base Values with a 400 Acre Enterprise. . Income and Expense Figures for Each of the Three Years for a Two-Row and a Four—Row Combine Using Base Values with a 1000 Acre Enterprise . Average Incomes from 300 Acres of Corn Using Alternative Loss Criteria for the Acres not Harvested Before December 1 for a Two—Row and Four—Row Combine. . Page 132 133 135 136 142 144 166 169 170 171 172 Appendix Table B. 5. 10. ll. 12. 13. Average Incomes from 400 Acres of Corn Using Alternative Loss Criteria for the Acres not Harvested Before December 1 for a Two—Row and Four-Row Combine. . . . . . . . . . . . Average Incomes from 1000 Acres of Corn Using Alternative Loss Criteria for the Acres not Harvested Before December 1 for a Two-Row and Four-Row Combine. . . . . . . . . . . . . . Three Year Averages of Acres Harvested and Income from Different Sizes of Enterprise with a 20 Per Cent Loss on the Corn not Harvested by December 1 . . . . . . . . . . . . Three Year Averages of Acres Harvested and Income Received from Different Sizes of Enterprise with an Increasing Loss Function on the Corn not Harvested by December 1 . . . . Three Year Averages of Acres Harvested and Income Received from Different Sizes of Enterprise with a Second Increasing Loss Function on the Corn not Harvested by December 1. . . . . . . . . . . . . . . . . . The Effect on Average Acres Harvested and Income Received of Different Sizes of Corn Enterprises with a Ten Hour Work Day for a Two-Row and a Four-Row Combine . . . The Effect on Average Acres Harvested and Income Received of Different Sizes of Corn Enterprises with a Twelve Hour Work Day for a Two-Row and a Four-Row Combine . . . The Effect on Average Acres Harvested and Income Received of Different Sizes of Corn Enterprises with a Fourteen Hour Day for a Two-Row and a Four-Row Combine . . . The Effect on Average Acres Harvested and Income Received of Different Lengths of Work Days on a 200 Acre Corn Enterprise when 40 Per Cent of the Corn not Harvested During the Harvesting Season is Lost for a Two-Row and a Four-Row Combine . . . . . . . xi Page . . . 173 . . 174 . . . 175 . . . 176 . . . 177 . . . 178 . . . 179 . 180 . . . 181 Appendix Table Page B. 14. The Effect on Average Acres Harvested and Income Received of Different Lengths of Work Days on a 400 Acre Corn Enterprise when 40 Per Cent of the Corn not Harvested During the Harvesting Season is Lost for a Two-Row and Four-Row Combine . . . . . . . . . . . . . 182 B. 15. The Effect on Average Acres Harvested and Income Received of Different Lengths of Work Days on a 1000 Acre Corn Enterprise when 40 Per Cent of the Corn not Harvested During the Harvesting Season is Lost for a Two-Row and a Four—Row Combine . . . . . . . . . . . . 183 B. 16. The Effect on Average Acres Harvested and Income Received of Different Lengths of Work Days on a 200 Acre Corn Enterprise when 20 Per Cent of the Corn not Harvested During the Harvesting Season is Lost for a Two-Row and a Four-Row Combine . . . . . . . . . . . . 184 B. 17. The Effect on Average Acres Harvested and Income Received of Different Lengths of Work Days on a 500 Acre Corn Enterprise when 20 Per Cent of the Corn not Harvested During the Harvesting Season is Lost for a Two-Row and a Four-Row Combine . . . . . . . . . . . . 185 B. 18. The Effect on Average Acres Harvest and Income Received of Different Lengths of Work Days on a 200 Acre Corn Enterprise when the Percentage of the Corn Lost When Harvest is not Completed During the Harvest Season Increases as the Number of Acres Increases. . . . . . . . . . . . . . . . . . . . . . . 186 B. 19. The Effect on Average Acres Harvested and Income Received of Different Lengths of Work Days on a 500 Acre Corn Enterprise When the Percentage of the Corn Lost When Harvest is not Completed During the Harvest Season Increases as the Number of Acres Increases. . . . . . . . . . . . . . . . . . . . . . . 187 B. 20. Three Year Average Income Received Using Each Combine on 300 Acres with Alternative Criteria Concerning the Grain Moisture Content. . . . . . . . . . . . . . . . . . . . . . . . 188 xii Appendix Table Page B. 21. Three Year Average Income Received Using Each Combine on 400 Acres with Alternative Criteria Concerning the Grain Moisture Content. . . . . . . . . . . . . . . . . . . . . . . . 189 B. 22. Three Year Average Income Received Using Each Combine on 1000 Acres with Alternative Criteria Concerning the Grain Moisture Content. . . . . . . . . . . . . . . . . . . . . . . . 190 C. 1. The Effect of Changes in the Variables with a 200 Acre Enterprise in Each Year . . . . . . . . . . 191 C. 2. The Effect of Changes in the Variables with a 500 Acre Corn Enterprise in Each Year. . . . . . . . 193 C. 3. Economic Ranking of Variables in Each Year--200 Acres. . . . . . . . . . . . . . . . . . . . 194 C. 4. Economic Ranking of Variables in Each Year--500 Acres 0 o o o o o o o o o o o o o o o o o o o 196 C. 5. Effect of Changes in the Variables With and Without Completion of Harvest- 200 Acres. . . . . . . . . . . . . . . . . . . . . . . 198 C. 6. Effect of Change in the Variables With and Without Completion of Harvest-- 500 Acres. . . . . . . . . . . . . . . . . . . . . . . 199 C. 7. Economic Ranking of Variables Depending upon Completion of Harvest-—200 Acres. . . . . . . . . 200 C. 8. Economic Ranking of Variables Depending upon Completion of Harvest--500 Acres. . . . . . . . . 201 C. 9. Effect of Changes in Variables on the Choice of a Combine with a 200 Acre Corn Enterprise. . . . . . . . . . . . . . . . . . . . 202 C. 10. Effect of Changes in Variables on the Choice of a Combine with a 500 Acre Corn Enterprise. . . . . . . . . . . . . . . . . . . . 203 C. 11. Ranking of Variables According to Their Effect on the Choice Between the Two Combines . . . . . . . . . . . . . . . . . . . . . . . 204 xiii ..qafl’: .... u -..-n . . o " .. ’ E .U-. 90 LL. Appendix Table C. 12. Ranking of the Effect of Changing Variables on the Choice of Machine by Categories Concerning Completion of Harvest . . . D. 1. Additional Input and Output Using Armstrong Data with 200 Hours of Use . . . . . . . D. 2. Additional Output Using Bower's Data for 200 Hours. . . . . . . . . . . . . . . . xiv Page 206 208 209 13. 14, 15. Figure 1. Cost of Production Diagram . . . . . . . . . 2. Cost of Production with One Variable Input . 3. Cost of Production with Two Variable Inputs. 4. Cost of Production with One and Two Variable Inputs 0 O O O O O C O O O C O O C O I O O 5. Asset Fixity Diagram for One Variable Input. 6. Computer Simulation as an Iterative Problem Solving Process. . . . . . . . . . . . 7. Optimum Replacement with a Duplicate Machine 8. Optimum Replacement with a Different Machine . 9. A Flow Diagram of the Corn Harvest Simulator 10. The Sequencing of Daily Decisions. . . . . 11. Procedure to Determine Soil Moisture . . . . 12. Diagram of the Calculation of Harvest Performance Criteria . . . . . . . . . 13. A Flow Diagram of the Machinery Replacement Routine. O O O O O O O O O O I I I O O 14. The Distribution of the $10,560 of Total Repair Costs Through Years Two Through Seven Using Armstrong's Function . . . . . 15. The Distribution of the $10,560 of Total LIST OF FIGURES Repair Cost for Years Two Through Seven for a Two-Row Combine with the Costs Spread Uniformally . . . . . . . . . XV Page 12 12 l3 13 15 19 22 22 39 42 42 43 45 119 120 “J in \A) IL- I'\ Figure 16. 17. 18. 19. 20. 21. The Distribution of the $10,560 of Total Repair Cost for Years Two Through Seven for a Two- Row Combine with a Steadily Increasing Function. The Distribution of the $10,560 of Total Repair Costs for Years Two Through Seven for a Two- Row Combine with a 1 - Exponential (A = .2) Distribution . . . . . . . . . . . . . . . . . . The Distribution of the $10,560 of Total Repair Costs for Years Two Through Seven for a Two- Row Combine with a 1 - Exponential (A = .3) Distribution . . . . . . . . . . . . . . . The Distribution of the $10,560 of Total Repair Costs for Years Two Through Seven for a Two- Row Combine with a 1 - Exponential (A = .4) Distribution . . . . . . . . . . . . . . . . . . . The Distribution of the $10,560 of Total Repair Costs for Years TWO Through Seven for a Two- Row Combine with a 1 - Exponential (A = .5) Distribution . . . . . . . . . . . . . . . . . . . The Distribution of the $10,560 of Total Repair Cost for Years Two Through Seven for a Two- Row Combine with a 1 — Exponential (A = 1.0) Distribution . . . . . . . . . . . . . . . . . . . xvi Page 121 122 123 124 125 126 CU CHAPTER I INTRODUCTION Regardless of the type of management during the planting and growing seasons, the farm manager has only losses to show for his efforts if he fails to harvest his cr0p. Many management decisions must be made prior to the harvest seasons. Should the present har— vester be traded for a new one? Should a larger harvester be purchased? Should new or larger equipment be purchased to handle the crop? Many more decisions are necessary during the harvesting season. When should harvest commence? How much labor should be hired to shorten the har- vesting time? Farm manager's answers to these questions, and many more, affect the income he and his family receive. Wrong answers can result in large quality losses, or in the case of corn harvest the cr0p may remain in the field long after the snow has fallen. As farm firms continue to increase in size, the importance of the harvesting system increases. With increased size, investments in the harvesting system necessarily increase. Combines now cost $16,000 and up (1). Transportation and drying equipment are becoming increas- ingly important and expensive. Also, with increased acres, the pres- sure to complete harvest without large losses increases. The number of potential harvest days remains constant regardless of the acreage to be harvested. A day lost because of a breakdown or because the hired l 2 man skipped work or because of a poor management decision becomes even more expensive. Many different factors affect the answers to the above mentioned questions and the farm manager's income. What is the effect of size in good years and in bad? Are the price of the output and the yield the most important variables as farm managers commonly believe? What is the effect on harvest and income of the temperature and of rainfall? How does a farm manager decide when to trade for a new harvester? The importance of these and other factors must be determined before a farm manager can make optimal decisions. The reader has probably already realized that the above deci- sions involve different time periods. Some of the decisions affect only the present harvest period while the effect of other decisions is felt for several years. Two different time periods are of primary importance for the harvesting system. The first is the individual harvesting period. The second time period must involve several years since many decisions, notably machinery replacement, affect harvest for several years. For the individual harvest period, which is referred to as the short-run, the land, buildings, machinery and acreage to be harvested must be assumed fixed. Since only the harvest period is being studied, the conditions previous to harvest must be assumed. These conditions include potential yield, grain moisture content, and the condition of the crop especially with respect to lodging and field conditions. In this time period the decisions concerning when to harvest are crucial. The factors of importance are the number of acres to be 3 harvested, the price for the crop and its yield, the weather condi- tions and the grain moisture content. For the period of several years, which is referred to here as the long-run, the major decision relevant to the harvesting system alone is the choice of and/or replacement of the harvester. Decisions regarding size and other machinery must consider more than the har— vesting system. Optimum replacement policy is very important and relatively complex. In 1968 farm managers enrolled in TelFarm, the Michigan State University farm records project, spent an average of $8,998 or 20.5 per cent of their total expenses on power and machinery (2). The investment in machinery averaged $21,994 or 13.22 per cent of the average total investment on these farms (3). Of course not all of this machinery was owned or used in harvest; however, the expensive machines-~combines, tractors, trucks-~are used exclusively or at least substantially during harvest. The importance of machinery is not limited to one type of farm. Saginaw Valley cash crop farms that were enrolled in TelFarm in 1968 incurred $10,856 in machinery ex- penses which was 23.19 per cent of the total expenditures on these farms. These same farms had a machinery investment of $22,245 which was 7.99 per cent of their total investment (4). For cash grain farms the machinery expenses were $8,792 or 26.05 per cent of the total expenditures with a machinery investment of $19,758 (5). The impor- tance of machinery is only slightly less on livestock farms. Cattle feeding farms enrolled in TelFarm in 1968 incurred 19.89 per cent of their expenses on machinery (6) and specialized southern dairy farms spent 19.49 per cent of their expenses on machinery (7). 4 Farm managers need a more accurate criterion than the one ex- plained by a farm manager recently, "We trade when repair costs get high." In order to minimize costs over time the criterion should be to use the policy which minimizes average yearly cost using an appro— priate discount rate. Determining this optimum policy is not easy since repair costs, trade-in value and various obsolescence charges must be included in the calculation. Since in most instances the farm manager is trading for a non-identical machine, further problems are encountered. In the long—run, as in the short-run, many variables affect this optimum policy. Objectives Many decisions made by the farm manager are important in deter- mining his income. A simulator and a replacement model are used as a techniques of analysis to achieve the following objectives: 1. To determine the effect of selected variables on corn har— vesting systems for individual harvesting periods (short-run). 2. To evaluate the effect of selected variables on machinery replacement for the harvest system for corn (long—run). 3. To determine the effect on the optimum replacement policy of changes occurring in the individual harvesting period, and to determine the effect of changes in the optimum replacement policy on income from the individual harvesting period. The overall objective of this study is to determine the effect of various variables on the harvesting system. Knowledge of these effects can be used by farm managers to improve their decision—making abilities during harvest. Since the simulator as presently developed .-.-n; uduuh . . A"! - t .- .5“). . : ..-4v tic-II: . "an“. .65-”: 5 simulates southern Michigan conditions for corn harvest and uses input-output coefficients typical of this area, this study is most concerned with farm managers in southern Michigan who raise corn either as a cash grain or for feed. The short-run variables are studied using the corn harvest simulator (8). The following nine variables are studied extensively using the simulator: 1. Loss due to failure to complete harvest. 2. Size of enterprise. 3. Hours in the work day. 4. Grain moisture criterion. 5. Opportunity cost of the Operator of the harvester. 6. Average temperature. 7. Additional rainfall. 8. Expected price. 9. Potential yield. The results from using several values for each of the above variables are used to determine the short—run effects of each of these variables on income from the harvesting system. Changes in long-run variables effect the optimum replacement frequency. The magnitude of the effect of the following seven vari- ables is analyzed: 1. The source of the cost data. 2. The shape of the repair cost function. 3. The number of hours the machine is used. 4. The level of machinery management. 5. The rate of obsolescence. 6 6. Increasing cost to purchase a new machine. 7. The interest rate. This magnitude is measured using a dynamic programming replacement model. The third objective is attained by considering the effect of changes in variables in each time period on the other time period. The effect of changes in replacement policy on the individual har- vesting period is evaluated. Conversely, the effect of short-run changes on the optimum replacement policy is analyzed. Organization of the Thesis The remainder of this thesis is concerned with the following main ideas. Chapter II develops a conceptual framework with a look at relevant economic theory, simulation and replacement theory. Chapter III is devoted to a detailed look at the model. The results from studying the variables affecting the individual harvesting period are contained in Chapter IV. Chapter V contains the analysis of these short—run results. The results of the variables affecting machinery replacement are then presented in Chapter VI. The analysis of these long-run results and an integration of the short—run and the long-run are presented in Chapter VII. Chapter VIII contains the summary and conclusions. The implications for further research are presented in Chapter IX. .1 A .\.—1-. ..u nw~au 0.4 .- Pw~ n... 7. U {0‘91 A5 tdo A5 «L IRAQ tin-to 7 Footnotes 1. According to machinery dealers in the Lansing, Michigan area farm managers pay approximately $16,000 for a model 4400 John Deere combine with a four-row corn head. 2. Hepp, Ralph E. Michigan Farm Business Analysis Summary-- 1968 Data, Research Report 95, Michigan State University Agricultural Experiment Station, East Lansing, October 1969, P. 4. 3. Ibid., P. 5. 4. Kyle, Leonard R. TelFarm Business Analysis Summary for Saginaw Valley Cash Crop Farms, 1968, Agricultural Economics Report 122, Department of Agricultural Economics, Michigan State University, East Lansing, June 1969, P. 2. 5. Harsh, Stephen B. TelFarm Business Analysis Summary for Cash Grain Farms, 1969, Agricultural Economics Report 133, Department of Agricultural Economics, Michigan State University, East Lansing, August 1969, P. 4. 6. Kyle, Leonard R. TelFarm Business Analysis Summary for Cattle Feeding Farms, 1968, Agricultural Economics Report 135, Depart- ment of Agricultural Economics, Michigan State University, East Lansing, June 1969, P. 2. 7. Brown, L. H. and John Speicher, TelFarm Business Analysis Summary for Specialized Southern Dairy Farms, 1968, Agricultural Economics Report 137, Department of Agricultural Economics, Michigan State University, East Lansing, June 1969, P. 2. 8. The simulator is being developed under a Michigan Agricul- tural Experiment Station project titled "Analysis of Agricultural Pro- duction Systems" by a multidisciplinary task force. Present members of the task force are Dr. J. B. Holtman, Assistant Professor, Agri- cultural Engineering; Dr. L. K. Pickett, Assistant Professor, Agri- cultural Engineering; and Dr. L. J. Connor, Associate Professor, Agricultural Economics. Dr. D. L. Armstrong, Associate Professor, Agricultural Economics and Assistant Dean of the College of Agricul- ture and Natural Resources was a member until he became Assistant Dean on August 1, 1970. L ..- ‘0‘.! A: V. M t 8 a 818 v U Q 111 Or] CHAPTER II A CONCEPTUAL FRAMEWORK Several areas of static economic theory are needed to provide a background for the actions of the farm firm. In order to understand how a simulator can be used to improve the farm manager's knowledge of the harvesting system, simulation or system theory is developed as it relates to the corn harvest simulator. Assuming that the farm manager is a profit maximizer, how does he determine his optimum replacement policy? This question is answered by elucidating the relevant aspects of replacement theory. TO illustrate the workings Of this theory, several replacement models are examined. The replacement model used in this study is described in detail to illustrate how the model deter- mines the Optimum replacement policy. In this chapter these areas of theory are used to construct a conceptual framework for studying the harvest system. Economic Theory Several areas of static economic theory of the firm are developed in order to understand what decision rules a farm manager should use to maximize income from his harvesting system. In order to understand why a farm manager's decision would be different in the short-run and the long-run, the length of run theory is presented. Since minimizing cost is a major contributor to profit maximization, the cost theory of 8 9 the firm is outlined. The theory Of asset fixity is introduced to answer questions related to asset acquisition and disposal. In order to avoid confusion and confine the discussion to a relevant area, two assumptions are made. The first is to assume per- fect competition at all times. This assumption means that no matter how many inputs the farm manager purchases or how many outputs he sells, his actions will have no effect on the prevailing price. This assumption is realistic with the sizes of farm firms studied. The second assumption is that the farm managers are strict profit maxi- mizers. In general, this assumption is realistic; however, other goals usually have some influence on the farm managers decisions. These other goals are extremely difficult to quantify. Intermediate level economic theory differentiates between the short-run and the long-run. The short-run is defined as any period of time in which there are certain inputs whose level of usage cannot be altered even with a large change in output. All costs are considered as either fixed costs, which must be borne, or variable costs. Addi- tional units of variable inputs should be purchased as long as that unit costs less-than the value Of its corresponding addition to output, i.e., until the marginal value product of the additional output equals- the price of the input. In the long—run all inputs are variable; additional units should be added until the value Of the additional output equals the cost of the additional input. More advanced economic theory, particularly production economics, indicates that the length of run is more complex than simply short-run or long-run. The concept Of fixed inputs is again basic to the theory. Common sense indicates that anywhere from none to all of the inputs 0.16 q?‘ ... y. ... n a: 7:61 n 13.9115 while 10 may be fixed depending upon the relevant time period and the stage of the production process. Thus, simply using short-run and long-run is an oversimplification. Before proceeding, some notation must be adopted. Y's will represent outputs and X's will indicate inputs. The equation: Y = f (X1, X2,...,Xn) indicates that the level of output Of Y is a function of the level of the inputs X ...,Xn. All units of each input and each output are 13 assumed to be homogeneous. As indicated above, the length of run is a function Of the number of fixed inputs. Therefore, this notation is adopted: Y = f (x1, x2,... xd,|xd+l,..., Xn) with X X ., X being variable inputs and X ., Xn being 1’ 2’ " d d+1’ " fixed inputs. The I (slash) will always mark the division between variable and fixed inputs--all inputs to the left are variable; all inputs to the right are fixed. The shortest possible length of run is the one in which all inputs are fixed: Y = f (0,|xd+l, . xn) while the longest has all inputs variable: Y = f (x1, x2,...,xd,I0). This latter length of run with no variable inputs was called the long run in the simple dichotomy. In this study the short-run is represented by the single harvest period. Its production function could be represented by: Y = f (X x2,|x3, x4, x 5) where Y is the yield of corn in a particular year, X1 and X2 (variable 1! \ 3.2125 .' are I \ 12:1:5 ) re; 1: me har‘: u . q n '1‘ . n~kr .S h ‘4‘... (r) 1 .‘ I! . *— :"evt N-b yo. \— ‘ 1 Mefiea ~~1 I my I 'l )IVAQ' : "Rh-ASSIST; rs) ‘\ 11 inputs) are the harvesting criteria, and X3 and X4 and X5 (fixed inputs) represent machinery, land and the state of the system prior to the harvest. The long—run is represented by a period of several years so that machinery is a variable input to the farm manager. In this length of run Y is average yield. Since the concept Of costs will be important in this thesis, the effect Of the length of run on the cost structure must be dis— cussed. The following seven cost functions form the basis for this discussion: 1. Total Fixed Cost = TFC = ZPXi Xi’ i = d+l, ... n 2. Total Variable Cost = TVC = ZPXi X 3. Total Cost = TC = TFC + TVC 4. Average Fixed Cost = AFC = Igg- TVC Y ATC = AFC + AVC 5. Average Variable Cost = AVC = 6. Average total cost 7. Marginal cost = MC = the additional cost of producing the last (marginal) unit of output. The cost per unit of output is at a minimum where MC = ATC. In Figure 1 this cost minimizing point is at output "a" with average cost "b." If the price Of the output y is "d," additional units Of output should be produced until output "c" is reached. At this point, MC = MR, and profit is a maximum. Figures 2-4 illustrate the effect Of the length of run on the cost functions average total cost and marginal cost. Figure 2 shows the average total cost (ATCl) and the marginal cost (MCl) for the pro— duction function Y = f (X1,IX2, X ). Note the steepness Of the average 3 total cost and marginal cost curves. For the case with two variable "'E ,u \ ..gu. S d b Figure 1. Figure 2. 12 ATC MC \\ 1 .1 l _ ._.__...r . \ x: I \111.- .11 J a c Cost of Production Diagram ATCl MCl OJ—-—-——-—J Cost of Production with One Variable Input l3 ATC2 $ MC ...2 ,/’ > 7‘ VJ" ‘ g _ ’ I J b Y Figure 3. Cost Of Production with Two Variable Inputs s MCI .6 MC //, ATCl ,x 2 ‘ATCZ .\‘ ,~/ I ,/ , / , \\" \\.\ . ’/ /’ L ' " T \\\_ ‘ . _ __ _- . __,,-- — ’ I l J a b Y Figure 4. Cost of Production with One and Two Variable Inputs VF -‘I .-a 1 g :oztinue Qeg . n dinner ' 0 6». ___. ‘4: 44h- 14 inputs [(Y = f(X1, X2,|Y3)], Figure 3 illustrates the average total cost (ATCZ) and the marginal cost (MC2)° The increased flatness Of these curves should be Observed. Figure 4 superimposes the two pre- vious diagrams. Note once again the increased flatness Of the ATC2 and MC2 with two variable inputs. This flattening of the cost curves continues as more inputs become variable. The increasing flatness explains why a wider range of outputs must be considered by the farm manager as more inputs become variable. The usual method for increasing the number of variable inputs is to expand the planning horizon. One further concept must be added in order that the theoretical conditions approach those faced by the farm manager. This concept is the distinction between acquisition and salvage prices of fixed assets. Acquisition price is the cost of purchasing a fixed asset while salvage price is the price that would be received if the fixed inputs were to be sold. These prices represent acquisition and salvage price of the same fixed input at a point in time, not the new price and the scrap price of the input. At this point, the term marginal value product must be intro— duced. The marginal value product (MVP) is the value of the increase in output corresponding to a one unit increase in an input. The theory says that additional units of an input should be used as long as the MVP of the input is greater than its cost. Using the above definitions, the absolute fixity of any input can be defined as any point where its MVP is less than its acquisition price or greater than its salvage price. In the following diagram levels of input usage less than "A" should result in purchase Of the input until point A is reached. If input usage is beyond point B, 0" ' r .u 'v- Lag“. a..... A I. .1 '71." ‘K'sua‘ v I .'v., h‘t SQCO 15 units Of the inputs should be sold at salvage value until point B is reached. For levels of usage between points A and B, the inputs are absolutely fixed although the MVP's from the inputs are not enough to cover acquisition cost except at Point A. ,AMVP _ Output l,«*fi "*[ ”Irlmflrh_ P_acquisition $ /!’/ __ __ __ 11L _ __ ___'__ __!~V___ _ l " ~ - . J g 1::»- P salvage A B input Figure 5. Asset Fixity Diagram for One Variable Input Economic theory enables one to calculate the yearly cost of inputs whose life exceeds one year or inputs that are fixed in terms of the yearly production period. This calculation allows a manager to compare these inputs with those that are variable for the single production period. To illustrate, assume an input with a useful life of L years and no change in technology (1) X = Fixed input P = Price of one unit of X i = Interest rate C = present value of an infinite cost stream then: “PM—flaviafi...” (1+k) (1+i) ‘PVfith the first term representing the cost of the initial purchase, the Second term representing the discounted cost L years later, etc. F n u ”itflit‘ if ‘ UVJ-‘ga‘ULAAL v o. . . 5.... v H 5V... .: mates: 1 A 3’5. Have] 1 L , 'U f" Shed 16 Continuing: C = PX (1-+-—¥L—i:+--—l;—§i-+ ...) (1+1) (1+1) C = PX (1 + c_Ll + e-211 + ...) C=PX—-('l—)——,- —L1 l-e to convert this present value to a yearly cost simply multiply by the interest rate: One can think Of this process as depositing a sum C in the bank so that the interest would cover the yearly cost. Simulation The use of simulation as a research technique has become more and more common throughout the last two decades. A specific descrip— tion is difficult if not impossible because Of its general applica— bility; however, the following remark should be helpful. Morgenthaler (2) says, "to 'simulate' means to duplicate the essence of a system or ' MOrgenthaler concludes activity without actually attaining reality.’ that simulation is appropriate whenever the scientific method cannot be used for prediction and estimation. Its steps are (3): 1. Close observation Of the physical phenomenon. 2. Creation Of a theory or model which explains the Observation. 3. Prediction of observables from the theory by using mathe— matical or logical deduction. 4. Performance of experiments to test the validity of the model. mlenever these steps cannot be completed, completion can be accom- plished by simulating the system. 17 As is true of any research technique, simulation has advantages and disadvantages (4,5). The principle advantages are: 1. Simulation makes possible the study Of very complex systems. 2. It makes possible more adequate study of decision-making with less reliance on mathematical models. 3. It provides new approaches for studying the aggregation problem. 4. Simulation is the most effective method for studying problems under uncertainty. 5. It can be more easily used without high levels of mathe- matical proficiency. 6. Simulation solutions are more easily understood by non- technical personal. On the other hand, several disadvantages can be recognized: 1. It is very easy to build one's biases into the simulation model. 2. Simulation is not an Optimizing technique. 3. Parameters may be extremely difficult to estimate. 4. Specialization within some fields including economics may be encouraged. 5. Simulation can be time consuming and expensive. Simulation can be separated into two types--analog and digital (6). Analog simulation uses a model to represent the real physical world. The only requirement is that the important char- acteristics of the original system must be retained. Although this requirement does not restrict it to scaled-down models, analog simu- ilation will not be used in this thesis. On the other hand, digital Simulation using computer facilities is very appealing and will be LlEsed extensively. The use of hybrid simulation using both analog and 18 digital simulation is growing rapidly. All references to simulation will henceforth imply digital simulation. Depending upon the circumstances, a simulation can be determinate or stochastic. Deutsch (7) says, "A determinate model is one for which a unique input stimulus to any Of the subsystems will always yield a corresponding unique output stimuli. . . . On the other hand, a stochastic model of a system can be formulated so that when an input stimulus is applied, the model will on its own accord, make a random choice from among a set of permissible system parameters before generating the output stimulus." A determinate system is studied by perturbing the inputs. A stochastic system should be used when decision makers actions are to be studied. A large sample is needed to determine an accurate average. Two techniques commonly used in simulation are gaming and Monte Carlo methods (8). When gaming is used, the players, usually managers, are an integral part of the system being modeled. Monte Carlo methods integrate probability theory, into the simulation. This method is usually used when the action chosen is a somewhat random decision to be made from a set of alternatives. Any simulation project can be broken into four steps: problem definition, mathematical modeling and simulation, model refinement and testing and model application. The relationship among these steps is shown in Figure 6 (9). As the diagram indicates, feedback is an ianortant aspect in this process. Time spent in defining one's IDJrOblem very carefully and critically will usually result in great 'IZZIme-saving in the following steps. In the second step, a simulation 19 (1) PROBLEM DEFINITION (2) MATHEMATICAL MODELING & SIMULATION ”A ‘ u l | 1.77% _.____-— 1 MODEL \/ (3) REFINEMENT & TESTING (4) MODEL /\ APPLICATION It \/ ,M~JK—~. @213) Computer Simulation as an Interative Problem Solving Process Figure 6. d‘uav- _b.': - I.“ - “via. I. .' . ‘--.. .._ “W- >..A ...: . 23.: dec: - ‘ .- fl “:1 20 model is developed that crudely represents the system being simulated. The third and fourth steps comprise what is called sensitivity analysis. This analysis is a process of testing and refining the model so that it accurately represents the real work and is ready for application as a problem—solving technique. At this point the reader may be asking how can simulation help a farm-manager with his harvesting system. There are two ways. The first is that researchers can use the simulation model to increase their understanding of the harvesting system. They can then provide the farm manager with better advise. Although the cost of the farm manager would be greater, the second way is for the farm manager to use the model to simulate his own farm business. By simulating alter- native decisions he would then be able to improve his management decisions. Replacement Theory Replacement theory can be dissected into two parts. One part concerns the replacement of items that fail while the other concerns items that deteriorate. This study is concerned exclusively with items that deteriorate. When discussing replacement policy in either the short-run or the long—run, the Objective is cost minimization. When keeping a used machine, the costs include repairs both minor and major, in- fafficiency with respect to time and performance and technological obsolescence. The cost for trading is the difference between the purchase price of the new machine and the trade—in value Of the used IIIEiLchine plus the cost of repairs in the first year when needed to ...... 5. nova .1 . n 4". , .- lbtoio a. ...- luv .34; ‘v-.... using» I 0'!) 55... .J.. ...: (I‘ “I v—v rrn (yr) ‘_1. 21 complete the comparison. Differences in operating cost, i.e., fuel, Oil, grease, are not included. In this context a short-run decision is one in which the deci- sion to keep or trade is based solely upon the upcoming harvesting period. The manager will trade only if he expects the used machine to cost more in repairs and inefficiencies than the total cost of trading. Using this criteria most machinery would have a relatively large life span especially since the cost of inefficiency is usually underestimated. In the long-run a much longer time horizon is used so that cost can be minimized over time. The manager must now take into considera- tion the near certainty that repair and inefficiency costs will be less next year and in future years, if he trades this year. One could still think of this decision as one between the cost of keeping the used machine versus the cost Of trading in one year if he added to the cost of keeping the used machine the Opportunity cost of not having a new machine. There are, however, better methods of minimizing long-run costs. Kletke (10) states that when a machine is to be replaced by an exact duplicate, the replacement should occur when the average cost reaches its minimum. At this point marginal cost which is the cost each additional year equals the average cost. In Figure 7 point a represents the optimum replacement time. If replacement occurred at ii, the yearly cost would be shown by point c. Figure 8 illustrates the procedure for determining the Optimum t:Iime to replace with a different machine. MC and ATC are the mar- 0 0 Egitinal cost and the average total cost for the machine the farm manager A‘l’ 22 $/Yr. \\~ MCO ,\\ . \\\ / ATCO \ / r I Xi’“_“I"J' I a Years Figure 7. Optimum Replacement with a Duplicate Machine $/Yr. Figure 8. \ \ o ATC ‘\. ‘_ ATC ' l b a Years Optimum Replacement with a Different Machine I. J on- 0" AH. " v: 9.91; on.' .‘d ~.q h.‘ 23 is using presently. ATCl is the average total cost for the machine the manager is contemplating buying. The farm manager should replace when the current yearly cost (MCO) exceeds the minimum average cost for the machine to be purchased (ATCl). Point b in Figure 8 is there- fore the Optimum time to replace. This approach of replacing whenever the current yearly cost exceeds the average cost of the replacement appears adequate. A major problem arises however; this method does not consider time preferences. In order tO equate a dollar's expense today with a dollar's expense a year from today, the latter must be discounted. Discounting is neglected completely. Churchman, Achoff and Arnoff (11) correct this deficiency using a similar criteria. One should replace when the yearly cost of keeping the used machine becomes greater than the weighted average of previous costs. This criterion can be expressed mathematically as follows: trade when: (A+C + C +...+ C C > 1 2 n + n+1 1 r (1+r)n n with A = Acquisition cost C. 1 Cost in year i, i = l, 2,...,n+1 Interest rate r tfllis procedure assumes that all costs are incurred at the beginning of (Eéich period (year). This procedure corrects the discounting problem but implicitly assumes that the replacement will be an identical IIIialchine. 3'. O I... . ...: \r-dm - qa~| £.l , . rub. I Q.- ‘I 24 The above two procedures can easily be combined to provide a criterion for replacement with a different machine and including dis- counting. This criterion would be tO replace the machine when its yearly cost exceeds the weighted average of expected cost for the new machine. Mathematically trade when: A + B + B + B +... +B Cn+1 > 1 1 2 3 n (1+r) (Li-r? (l+r)"‘l n with A = Acquisition cost of the machine to be purchased B1 = Cost for keeping in year; the machine to be purchased, 1 = 1,2,...,n Cn+l = Cost of keeping the used machine another period r = Interest rate More sophisticated models using more advanced mathematics and the computer can be used. These models incorporate the replacement theory explained above. Models of this type will be discussed in the following section. Replacement Models In this section several models built around the long-run re- placement theory, presented in the previous section, will be presented. Only models that could be useful in machinery replacement will be surveyed. Three models using the criterion presented explicitly but in more involved terms will be presented. Two models using the theory in a less direct manner will follow. The first of these will use dynamic programming while the second will use dynamic programming and Markov chains. The latter model will be reviewed extensively. 25 The first model is a straight forward adoption of the model by Baumol (12). He commences with: V=A+C1+C2+C3 +...+Cn 1+1: (l+r)2 (1+r)"“l where V is the discounted present value of the repair cost for n years. Letting A equal the average yearly outlay for the n years, the following is true: V = A + A + A + . . . A l+r (1+r)2 (l+r)n_l By geometric progression the following is true: V=A+_A_+...+ A = [1-(1+r)“] 1+r (l+r)‘1 [l-(l+r)] Solving for A. A = [1-(1+r)] V [l-(l+r)n] Using this equation, the Optimal long-run replacement policy can be determined by finding the value of n which minimized A, the average yearly outlay for the n years. Smith (13) presents a much more intricate model which is par— ticularly useful when several replacements will be made within the time horizon. His repair cost function for the Kth machine in a chain of replacements is written E (u,kL,t) where u is the rate of equipment utilization, L is the life of the piece of equipment, kL is the time at which the machine was purchased new and t is the present age of the machine. E is measured in terms of some physical measure such as horsepower, width or number of rows capacity. E(u,kL,t) will usually increase with the age of the machine (t) and decrease as k increases due to technological advance. The author suggests the 26 following simple, linear relationship for a constant u: E(u,kL,t) = Eo - kL + Bt E0 is a constant representing initial repair costs. k is a parameter indicating the yearly reduction in E0 due to technological advance in the form Of model changes. B is a parameter indicating the increased repair cost due to increased age. This function can now be integrated into the full model to cal- culate a constant annual cost using discounted present value of all purchase cost and repair cost from an infinite chain of continuously improving machines. The general equation used to calculate this cost, w, is: 00 w = r z e‘rkL LE(u,k1,t) e-rtdt + w — Slu,L)e- k=O rt where all variables are defined above. In addition r is the interest rate W is the original cost of the machine and S (u,L) is the salvage value of the machine. e—rt is used to discount the costs for each rkL then discount machine to the date of purchase of that machine E- the cost to the present. Once again the criterion is to solve the model for the L that will minimize W. Terborgh (14) uses a simplified, linear version of the above equation. He also assumes the utilization rate, w to be constant. His expression is: W=E +( +B)L+w o 2 L +rW where all variables as above. As before, the Objective is to mini- mize w. 27 A somewhat different model develOped by Burt (15) is presented for two reasons. The model uses the alternative method of calculating the revenue from the machine. Secondly the concept of survival probability is introduced. A machine may fail to survive tO the next year because of fire, accident, or breakdown that cannot be economi- cally repaired. This probability will be used again later. This model will use discounted present values also. Before proceeding, the following notation must be introduced (16). P = The probability that an asset of age t will reach age t+l with normal productivity. H = Net revenue associated with an asset of age t in the absence of replacement due to random causes. D = Cost Of replacement cause by random factors. C = Voluntary replacement cost (cost of a new asset minus terminal value of the used one). Rt = Pt Ht - (l-Pt) Pt’ i.e., conditional expected value of net revenue during a time interval for an asset of age t (excluding cost Of planned replacement. T = Planned replacement age. B = l/(1+i), where i is the relevant interest rate for discounting. The interest rate includes a charge for price uncertainty. As the author indicates, the net revenues are often constant with machinery replacement and can be assumed as such. In this model, all revenues and costs are treated as occurring at the beginning of the period with replacement being made at the end of the period. An infinite planning horizon is assumed as are constant revenue, cost and probability parameters. v--.. u... n'\- ‘~~— 3A .... ( ‘1‘. v "D. ~‘l H“ 28 The expected present value of net returns from an asset over its life g(T) must first be calculated. The discounted revenue from any future year will be the net return in that year multiplied by the appropriate discount rate with the product multiplied by the prob- ability Of the machine reaching that age. Recalling that Rt = Pt Ht - (l-Pt) Pt includes revenue and probabilities for the final year considered in each term, the equation is: 2 g (T) - R1 + Bp1 R2 + B p1 p2 R3 + ... T-2 + B p1 p2 ... pT-2 RT—l + Bp1 p2 "' pTl (RT - pTC) From this the present value over the infinite time horizon, V(T), can be calculated as follows. L(T) V(T) = q (T) + E (B V(T)) where E indicates expected value. Solving for V(T), the equation is: V(T) = g(T) l-E BL ] where B is the discount rate. L(T) _ _ 2 _ E(B ) — B(1 pl) + B pl (1 P) + . T—2 +B P1 p2 . . . PT—2 (1PT_1) + B p1 p2 . . PT—l As a simplifying device let W1, W2, . . ., WT substitute for 2 T-l l,B . PT-l respectively. pl’ B p1 p2,. . . B p1 p2 . Substituting this equation into the one calculating V(T), yields T V(T) = l [ Z W R - W P C ]/T l—B tsl t t t t t X Wt t=l This equation calculates the average discounted present value of ex- Pected net revenues. The Optimal criterion is then to find the T that maximizes V(T). v ‘3 yL:_ tu‘: 29 These three models would all derive an Optimal solution, how- ever, they all require extensive calculations. The most logical solu- tion is to enlist the aid of a computer. Although used sparingly, dynamic programming is probably the most generally applicable method for solving replacement problems (17). Bellman and Dreyfus (18) present a general model for replacement problems. In this model the cost and returns are calculated for the two alternatives "purchase" and "keep" for each year. A solution is reached via dynamic pro- gramming that will maximize the net return. For machinery replacement, however a model using dynamic programming and Markov chains was found to be more relevant to the data available and to provide more flex- ibility. This model is explained and used by Howard (19). A user of this model must first decide upon the number of "states" in the model. Each "state" represents a decision period. For machinery replacement each "state" normally represents one year. States are represented by i. For each state the alternatives (k) must be defined. Alter- natives can range from "keep" and "trade" (for a new machine) to "keep" and "trade" for a new machine or a used one of any number of ages. A probability matrix and a reward/cost matrix must be calculated for each state. The probability matrix will contain for each alter- native the probability of going from the present state to each of the other states. This probability is called a transitional probability. The reward/cost matrix corresponds to the probability matrix and con- tains the reward or cost for each alternative of going from the present state to each of the others. The following table represents the model £N ,_ :3! (D A? Vex»; S‘ 30 as it would appear at this point. Four states with two alternatives each are used for illustration. state alternative probability reward/cost i k P..k c..k 13 1J 3= 1 2 3 4 j= 1 2 3 4 " 1. 1 1 '7? I. 1. 1 1 'If 1 1 P11 P12 P13 P14’} C11 C12 C13 C14 2 2 2 2 2 2 2 2 2 P11 P12 P13 P14 C11 C12 C13 C14 1 1 1 '1' 1 1 1 TI 2 1 P21 P22 P23 P24 C21 C22 C23 C24 2 2 2 2 2 2 2 2 221 P22 P23 P24 321 C22 C23 C24 1 1 1 1 1 1 1 3 1 P32 P33 P34 C31 C32 C33 C34 2 2 2 2 2 2 2 2 P32 P33 P34~_ C31 C32 C33 034. 1 1 1 1 ""7 1 1 1 7f 4 1 P41 P42 P43 P44 C41 C42 C43 C44 2 P 2 P 2 P 2 P 2 c 2 c 2 c 2 c 41 42 43 44, 41 42 43 This data is then used to calculate the immediate expected re- turn, qik, for each alternative in each state. This calculation is performed as follows: k qik = Z Pi.k Ci.k. for alternative 1 in state 1 Of the above table 1 1 l l l 1 l l l q1 ‘ p11 C11 ‘ p12 C12 ‘ p13 C13 + p14 C14 The maximum (reward) or expected immediate reward minimum (cost) in each state is then determined. This is the Optimum policy for the very short run. 31 A new matrix must now be formed using the transitional prob- abilities corresponding to the policy chosen above. Assuming that this policy chose alternatives 1, 2, 2, l for states 1, 2, 3, 4; this matrix would be used. :7 l P 1 P 1 P -I 11 12 13 14 P = P212 P222 P232 P242 P312 P322 P332 P342 [3411 P421 P431 P44i_ The corresponding qik values are also needed. the values in the reward/cost matrix are no longer needed since they represent short-run returns. The value-determination equations are solved next. The equa- tions are: N g + Vi = q1 + Z P j+i ij v. 1 =1, 2,..., N where N is the number of states. For the policy above the equations would be: g + V1 = q1 + P11 V1 + P12 V2 + P13 V3 + P14 V4 3 + V2 = q2 + P212 V1 + P222 V2 + P232 V3 + P242 V4 3 + V3 = q3 + P312 V1 + P322 V3 + P332 V3 + P342 V4 8 + V4 = q41 + P411 V1 + P42l V2 + P431 V3 + P44l V4 where g represents the gain from the policy chosen (1, 2, 2, l in the example) and the vi's represent the desirability of reaching state 1. One of the v's is set equal to zero and equations are solved simul- taneously for g and the other v's. The values for the V's now repre- sent the desirability of going to their respective states relative to the one set equal to zero. The policy-improvement routine is now used to calculate test quantities to replace the immediate expected return as the criterion for choosing a policy. This equation is used to calculate the test quantities for all alternatives in all states using the original q s, pijk's and the vj's from the value determination equations. q.k + P k v N 1 Z i' ' j=l J J For state 1 in the example the equations would be: 1 1 1 1 1 q12 + P11 v1 + P12 V2 + P13 V3 + P14 V4 2 2 2 2 2 q1 + p11 V1 + p12 V2 + p13 V3 + P14 V4 A new policy is now determined by choosing the maximum (reward) or minimum (cost) test quantity in each state. The probabilities and immediate expected returns (qik) corres- ponding to this policy will be used to solve value determination equa- tions again to get new test quantities. This iterative process should be :onzi: f. .. 1‘ {Cashj W U A- o .. 'V‘ bmta L! iii-ere B ifflpped With dis :F‘Ais S‘" S tin in to 90+ Sh e.“ ‘\. 33 be continued until two consecutive iterations determine the same policy. This policy will then be the optimal long-run policy and will maximize (reward) or minimize (cost) the grain g. The above model considers all dollars as equal with regard to time. To conform more to reality a discounted process is introduced (20). The process is the same but the equations are altered somewhat. The value determination equations are changed from: g + Vi = to where B is the discount rate [l/(l + interest)]. The g has been dropped because the concept of yearly gain or cost g is not relevant with discounting, and the v '3 represent the discounted present value. 1 This system of equations is now solved for all of the v's. The equa- tion in the policy improvement routine is also changed from N qik + Z Pi,k vj H 3 to N q k + B Z Pijk vj 1 i=j The above model both with discounting and without is the general formula. A number of adjustments are made for use in a specific re- placement model. These changes are discussed in the next chapter. One Should keep in mind that this model uses the principle shown in Figure 7 that the machine should be replaced when the current yearly DISTRIBUTION-YESTERDAY MOISTURE DISTRIBUTION-TODAY BUDGET SOIL TYPE Figure 11. Procedure to Determine Soil Moisture Once the soil moisture distribution is determined and the soil type is known, the tractability of the soil is determined by that sub- system. At the same time the grain moisture content is calculated based upon the grain moisture content yesterday and the weather today. 43 Given these calculations, the system can check the tractability and the grain moisture content and make the decision concerning whether to harvest. If the decision is to harvest and harvest has not been al- ready completed, the harvest performance is determined. Figure 12 shows the factors that are needed to calculate the harvest performance and the measure of harvest performance that are calculated. ..HARHESI_DEClSlONS______> .JMDLLHLJEMEL ) LODGING _;> CROP FACTORS > _BBEEARYE311LQ§SM_111__> HARVEST GRAIN M.C. HARVESTER LOSSES OR PERFORMANCE ROW SPACING > HARVESTER YIELD > HA V I W____> ..--13_1E__ST.__N,G..T-II€EE1_____9 WW9. Figure 12. Diagram of the Calculation of Harvest Performance Criteria For each set of variables the harvesting system is simulated for three years for each of two combines. One combine is a John Deere model 3300 with a two-row corn head costing $12,000; the other is a John Deere model 4400 with a four-row corn head costing $16,000. Both combines are assumed to be depreciated over eight years using straight line with 20 percent additional first year depreciation. 1966-1968 are used as base years. The basic weather data is taken from Monroe County, Michigan for those years. To be consistent corn prices quoted by the Michigan Elevator Exchange for those three years are used. Because only the harvesting system is simulated, a 44 maximum yield as of September 30 must be assumed. This maximum was 150 bushels in 1966, 100 bushels in 1967 and 125 in 1968. These yields are at least close to actual conditions on that date. A complete list of the exogenous inputs is present in Appendix A. These values are representative of those currently prevailing in Southern Michigan. Some Of these values are temporarily changed for analysis purposes. The Machinery Replacement Routine The replacement of machinery, particularly the combine, is Of crucial importance to the farm manager in managing his harvesting system. This decision is an investment decision rather than an operating decision. Since the simulator can only analyze short-run Operating decision efficiently, a machinery investment routine was developed by George Perkins (6) and this author. The machinery re- placement routine uses dynamic programming and Markov chains based upon Howard (7). The routine chooses an optimum replacement policy that minimizes the long-run expected costs subject to the conditions prescribed by the operator. The routine used follows from the theory presented in Chapter II with several adaptations. The major adaptation is that only one con- ditional probability is used for each alternative. For the alternative "keep" this probability is the probability that the machine will sur- vive until the following state. In this study each state represents one year. The probability of survival to the next state (year) in the last state must be zero. The conditional probability for an alternative involving trading the machine is the probability that the machine traded for will survive to the next state. Since the age of the machine 45 has little or no effect on returns from the combine, cost minimization is used. The cost for keeping the machine includes repairs (both routine and major) plus an obsolescence cost based on age. The cost of trading is the cost of the newly acquired machine minus the trade-in value of the original machine plus repair cost in the next state and Obsolescence cost (unless a new machine) for the newly acquired machine. Although several Options can be used, the basic format is the same in each formulation. Each has three subsystems. Figure 13 illustrates with a flow diagram the sequencing of the subsystems. only initially > moa>rwdruw \V .1. F.— E E O __J uNV POLICY Figure 13. A Flow Diagram of the Machinery Replacement Routine Each of the subsystems has a specific purpose: 1. VALUE determines which Of the alternatives have the smallest immediate expected cost initially and the minimum test quantity thereafter. The p's and g for each of the chosen alternatives are then prepared for simultaneous solution. This subroutine completes most of the value-determination Operation. 2. MATALG completes the value determination Operation by simul- taneously solving the equations. 3. POLICY calculates the new test quantities each iteration (policy-improvement). Subsystem VALUE is called from this subroutine. 46 Seven states and two alternatives are used. Each state repre- sented one year with the first state representing the decision to keep or trade a one year old machine. The two alternatives are to keep the old machine or to trade for a new machine. Although both the number of states and the number of alternatives could have been moved rela- tively easily, neither was removed because no significant limitations were imposed by the restrictions. Seven states were more than suffi- cient to determine an optimal policy, and the data needed to consider trading for used machine was not available at a cost that would justify its use in this study. As was mentioned above, this model makes available a number Of options. The user can present his data in one of two forms. He can simply supply the costs for each of the two alternatives in each of the seven states (years), or he can supply probabilities and corresponding costs for different types of repairs for each alternative. The second option concerns the interest rate. If no interest rate is used, the solution to the simultaneous equations will be six V 's repre- i senting the relative (V7 = O) desirability Of reaching state i and q indicating the annual yearly cost using the optimal policy assuming the user stated in state 1. When using discounting, however, the solutions will be seven Vi's representing the discounted present value of the stream Of expenses commencing in state i and using the Optimal policy. Dr. L. K. Dr. P. L. Dr! LI J. 3:. 1:25: Agricultu v .. :zltnan a t'?"‘l :1.“ ~ “d an: Where N i 4. FIJEESSOI Agricultu 5- ?lcxett f QE1i“,ere:‘ Of ASricu . 6- I: AgriCu 7- 1?]? TEE-fin "Cm Wile 47 Footnotes 1. The corn harvest simulator was designed in a project titled "Analysis of Agricultural Production Systems," established by the Michigan State Agricultural Experiment Station. The task force in- cluded Dr. J. B. Holtman, Assistant Professor, Agricultural Engineering; Dr. L. K. Pickett, Assistant Professor, Agricultural Engineering; Dr. P. L. Armstrong, Associate Professor, Agricultural Economics; and Dr. L. J. Connor, Associate Professor, Agricultural Economics. Dr. Armstrong has since been appointed Assistant Dean, College Of Agriculture and Natural Resources. 2. The first eight subsystems were developed by Dr. J. Ben Holtman and Dr. Leroy R. Pickett both Assistant Professors in Agricul- tural Engineering. The descriptions are the authors. 3. The formula used is: IIMZ SL equivalent — (depi - SL equiv.) tax rate (1 + interest rate)1 where N is the years of depreciation. 4. Formula developed by Dr. David L. Armstrong, Associate Professor of Agricultural Economics and Assistant Dean College of Agriculture and Natural Resources. 5. These component models were developed by Drs. Holtman and Pickett for a paper "Modeling of Corn Production Systems-A New Approach" delivered by Dr. Holtman at the 1970 Annual Meeting, American Society of Agricultural Engineers, Minneapolis, Minnesota, July 7-10, 1970. 6. George Perkins is a Graduate Assistant and Ph.D. candidate in Agricultural Economics at Michigan State. 7. Howard, Ronal A. Dynamic Programming and Markov Processes, The Technology Press of the Massachusetts Institute of Technology and John Wiley and Sons, Inc., New York, 1960, Especially pp. 54-59. CHAPTER IV RESULTS FROM THE SHORT-RUN HARVESTING PERIOD This chapter specifies the values used for each of the selected variables and presents the results obtained from using the Specified sets of variables to simulate the corn harvesting system. These re- sults are needed to determine the effect of these selected variables in the short-run. The format used for studying the selected variables is to simulate three years using yield, grain moisture and weather conditions from 1966, 1967 and 1968. Each Of these years has several unique characteristics so that three very different situations are studied. The years are referred to as first, second and third rather than by date since changes in the selected variables make the condi- tions quite different from those actually occurring. Several impor— tant characteristics of the three years prior to any variable changes are presented in Table l. A complete list Of the exogenous inputs is contained in Appendix A. Nine variables were chosen for study. The nine variables and their initial values are: 1. Loss due to failure to complete harvest during the harvest season -0.00 (l). 2. Size of enterprise - 200 acres. 3. Hours in the work-day--8 hours. 48 49 Table 1. Characteristics of the Three Years Used in Studying the Corn Harvesting System Year Unit Year 1 Year 2 Year 3 Maximum yield as of September 30 Bu. 150 100 125 Grain moisture on October 15 Per Cent 36.0 40.3 26.9 Tractability days during harvesta Days 37 16 32 Average price Dol. $1.23 $1.06 $.96 Date harvest startedC Date October 28 November 8 October 15 Tractability days after start of harvest Days 24 8 32 aTractability means the soil is dry enough so the combine can Operate in the field. There are 47 days in the harvest period. bAverage of price prevailing on harvest days including December 31. CThe first tractable day after the grain moisture content reached 30% or below. 50 4. Grain moisture criterion—-harvest can begin when the grain moisture content reaches 30.0 per cent. 5. Opportunity cost of the combine Operator's labor--$3.00 per hour (2). 6. Changes in average temperature——temperatures prevailing in 1966-1968 (see Appendix A). 7. The effect of additional rainfall--rainfall in 1966-1968 (see Appendix A) (3). 8. Price-—the prices prevailing in 1966-1968 (see Appendix A and Table 1). 9. Potential yield as of October 15 - 1966-1968 (see Table 1). Table 2 presents the average acreage harvested and several average income figures for the three years. The acreage harvested is that portion of the corn which is harvested during the harvesting period. The acres that are assumed to be harvested December 31 are not included. This definition of the acreage harvested is used through- out the study. Net cash income is the income the farm manager has after paying all cash costs. After he covers depreciation, Operator and family labor, and interest on his investment, the remaining income is the return for his management or management income. The $45.00 (4) subtracted from the harvesting income figure covers seed, fertilizer, herbicide, tillage expense, etc. to cover the expenses incurred prior to September 30. Table 2 quickly illustrates the need for a change in the assump- tion that all of the corn is harvested. Even when acreage harvested during the harvest period fails to increase with the size Of enterprise, S US: SC-QECC 3.5.l33... C. 1~:....: .quhQLflUZE CHOU .50 WQNHW UCthkkuQ MOM MNXEHN>< hawmwtw @QHSK. .N «£1325 .umw>um£ Ou m:OH>mum mumoo um>oo Ou monomuuasm ma muom\oo.mqwn .Hm nonsmoon pmumm>um£ on On possmmm we on Hmn5m>oz I ma Honouoo .wowuma wawumm>uma on“ maflusw kumopnm: uoa cuoom 51 mmmm ommq mman ommmq Hummm anmm momma omqnm owe 0mm oooH moHHI ml mmmam mmqmm mwwem Hmomm mwmmq Hmmnq mam 0mm oom NNqHI omen whooa momma mqama owmom muqmm ommwm wNm «om ooq mnwmn mmoal maooa mquH «oaqa mowqa qwmmm Nomwm How «mm oom omqml wmqml ommm «Nam «Nam omaoa NNHwH omHmH «ma mod com A.Hopv A.Hopv A.Hopv A.Hopv A.Hopv A.Hopv A.Hopv A.Hopv Ampopv Ampupv 3ou|¢ soulm 3oulq BOMIN zoulq BOHIN Boyle BOHIN 3oulq BOHIN wmuo< mEOocw pawsommcmz 1wdaumm>umn Eouw oEOocH ammo umz wcaumm>nm£ aoum mmuom wmumo>umm oEOoaH ucmamwmamz oaooaw ammo uoz wwwumm>umm ma auoo USu mo Ham waflasmm< magnaoo 3omausom m was ocfinaoo 3Om|039 m mcwmb mmfiumuouam cpoo mo mmufim uGOMOMMHn pom mmwmuo>¢ Ham» mouse .N manme 52 income continues to increase (or loss of income continues to decrease); furthermore, even with a 1000 acre enterprise, the two—row combine proves more profitable although it only harvests an average Of 270 acres during the harvest season. In order to represent the real world more closely, the base value for the loss due to failure to complete harvest during the harvest season was changed to 40 per cent. Table 3 presents the values used for each of the nine variables. The base value is the value used whenever another variable is being studied. The harvesting system is simulated for all possible combina— tions of the first three variables-loss, acres and hours--except the second sliding function for loss was only used with 8.0 hours. For the grain moisture criterion the system is simulated using each criterion and each of the sizes of enterprise. For the remaining five variables, the system is simulated for each of the chosen values with 200 and 500 acres. When the results are presented, three year averages are used primarily, with individual years used when a particular year is especially responsive to the changes being made. In order to illus- trate the conditions in the years being studied, Table 4 presents the important output figures from each of the output figures with all base values, except the size of enterprise is changed to 500 acres. Similar output for 300, 400 and 1000 acre enterprises is contained in Appendix Tables B. l, B. 2, and B. 3. As Tables 1, 4 and 5 illustrate, the first year is extremely profitable. The yield and the price are high and harvesting conditions are very good. The following year is financially disastrous with low yields and extremely unfavorable harvesting conditions. The price is 53 Table 3. The Values Used for each of the Nine Variables when that Particular Variable was being Studied Variable Base Value Other values Loss 40% 0, 20%, sliding l,a sliding 2b Acres 200 acres 300, 400, 500, 1000 Hours 8.0 10.0, 12.0, 14.0 Grain moisture 30% 28%, 32%, slidingC Opportunity cost $3.00/hour 2.00, 5.00, 8.00, 12.00 Additional rainfall Normald +1" on October 15, November 1, November 15 d Temperature Normal -1°, -5°, +1°, +5° Price Normald -.$01, -.05, -.10, +.Ol, +.05, +.10 Yield Normald —10 bu., +10 bu. a . Loss is 5 per cent for the first section not harvested, 6 per cent for the second, etc. bLoss is 5 per cent for the first acre not harvested, 5.5 per cent for the second acre, 6.0 per cent for the third, etc. cHarvest can start if grain moisture content fell below .26 before October 21, .28 before October 29, .30 before November 4, .32 before November 11, .34 before November 18, .40 before November 25. dNormal refers to actual conditions for 1966-68. These values are used as a base for years one, two and three. 54 .H Honouoo ou momma muom\oo.QOllmmmamaxm Ham mmpaaocH .pmumamaoo coszo n .thO wcwumm>ums aoumm on wNH mm «NH on mNH mm HmH pom: mcfinaoo musom I- .. oN\OH No\aa .. I- mo\HH mH\HH oppupaaaoo ump>pmn puma mmH an ooN oom «ma NOH CON oom wmumm>nm£ mmuo¢ mmmml omem: mqoml comm: mmawl mqmoal quq mmqm amaooofi ucoamwmawz mqmw wqqma woqm mmmm ooqq mama wNONH quma nmEOOOH :mmo umz nmmm Hmmm mmmH qoqm Hmw mmmal mcmma mmqqa mmaoocfl uamamwmamz mqmma wqqma wOOqH mmmmH ooqma wmmoa wmomm qumm mmaoocw :mmo umz mmmma qmmwa momma Hnmna omeH «Nona «mHHN mHooN mmmammxo HmuOH mmmm mmmm Heme qum mem mmam mqu mfiow momammxm smmo HOuOH omqm comm Mmqm NHmN Hmmm wmmm qum mmwm mmmamaxo humafinomz mmnqm Hmmmm omnow mmoHN Hwoma Newma mmqqm mmqem Amv mumflmomu HOuOH 3oulq 3OHIN 3oulq BOHIN Bound BOHIN 3OHI¢ BOHIN omammxm no maoocH mwmpw>< Ham» ppm ummm paw Hawk umH mosam> mmmm waHmD mafinaou Bodnusom m mam 3oMtoBH m Mom mummy mounH mfiu no comm How mmuawfim mmammxm dam maooGH .q OHLMH 55 .H Honouoo ou HOHHQ maom\oo.mqwllmomcomxm Ham mmpzaoaH .woumHmEou Gonzo n .haao waaumm>um£ Eoumm oma omm ska can Nwa mam mwa aam ppmp maapaoo mupom .. .. oa\aa I- u- .. m~\aa .. upmpmaaaoo ump>ums pupa mam cam com oas mwa moa com mam ppamp>upa mopua «was- omaa- ommw- papa- mmoam- maNpN- nomma aawa pmaouca pamamwmamz mwaam aROpa maeaa aaama «mom paw- mamas aammm pmaouaa ammo upz eaaaa amama aamma «mama mmma- mqam- Romaa ammom ppaooaa “spamwpapz mwame aammm mammm qammm ammqm «Ream Naqae awmmm ppaouaa ammo ppz mamas mmwwm mmmmm mmowm maomm mmmom amass okaae pmmapaxm apnea opaaa magma owmma mNaNa pamaa mamaa amawa momma mmcpaxp ammo appoa News moam aema 04am Gama maam mama emwm mpmamaxm appaaaomz maaoe «moan aommm amaom oamom «mama wmapw aaaaa amv mpaapupp appoa 3oulq aoulm Bowie aoHIN 3oulq 3OHIN soulq 3OHIN mmcomxm no maooaH mmmpo>< ummh ppm ummm can Hawk uma mmfiuaumucm wHo< oom m nua3 mosam> mmmm wcamb mcHnEOu BOMIusom m pom 3oMIoze w you mamow mounH onu mo comm pom mouawam mmcomxm was oaooaH .m OHQOH 56 slightly below the average for the three years. Although conditions during the harvest period are excellent, the third year is unprofitable, tfluough better than the second year, because the yield is only average and.the price is extremely low. Conditions in the three year period are slightly below average. In the following pages the results from changing the values of the variables are discussed for each variable individually. In some instances more than one variable will have a value other than its base value. Whenever any value other than the base value is used, the new value is specified. Loss Whenever corn is not harvested by the first of December, the possibility exists that the corn will never be harvested or will not be harvested until spring. The simulator as previously developed in- cluded losses from lodging, maturity, machine speed, etc. but did not include loss from failure to complete harvest. Furthermore, tract- ability data was unavailable for December so all corn not harvested by December 1 was assumed to be harvested on December 31. For this study the assumption that the remaining corn is harvested December 31 is retained since the tractability data is still unavailable, but five alternative functions are used to simulate the possibility of harvest not being completed. The first function assumes no possibility of loss while the second and third functions assume that 20 per cent and 40 per cent of the corn harvested on December 31 is lost. The fourth and fifth functions incorporate increasing losses per unit as the number Of unharvested acres increases. With the first of the two functions, 57 5 per cent of the first section harvested in December is lost (the total acreage is divided into 100 equal sized sections), 6 per cent Of tile second section is lost, etc. The fifth function assumes that 5 per cent of the first acre harvested December 31 is lost with an additional 0.5 per cent is lost on each succeeding acre not harvested. The two functions are the same for 200 acres only. Tables 6 and 7 summarize the results by three year averages for 200 and 500 acres respectively. By comparing the two tables the reader can easily observe the increased importance of the loss function as the size of the enterprise increases. This relationship is also apparent in similar tables for 300, 400 and 1000 acre enterprises that appear in Appendix Tables B. 4, B. 5 and B. 6. Size To study the effect of changes in size, five sizes of enterprise are used--200, 300, 400, 500 and 1000 acres. 200, 300, 400 and 500 acre enterprises certainly could be harvested with one combine although 400 and 500 acres are extremely large enterprises for a two-row combine. The 1000 acre enterprise is used more to determine the effect of such a large size than because the size is realistic since farm managers with that many acres Of corn would have a larger combine or more than one combine. The use of only one combine and no custom hire is assumed in this study. When considering the results, the reader should remember that the relative magnitude Of the changes in size of enterprise is larger than the magnitude of changes in other variables. This difference occurs for two related reasons. First, changes in the size of 58 .umw>um£ ou HOHum mmmamaxm Hm>oo Ou whom you oo.m¢m mmpoHouHo .H umpfimoon Ou HOHHQ woumm>Hms monom onu mamoa oaom pmumm>ammp .wmumo>um£ uoa whom wavamoosm sumo.ao umOH wchn Nm. HOCOHunvm cm nuHs H umpEooom kn vmumo>amc uoa muom umuHm onu Eoum umOH OH Nmo .wmumm>umn no: GOHuomm some now umOH wchn NH HmsOHquwm cm nuH3 H nonsmowm kn vmumo>umn no: OOHuomm umHHm mnu Eonm uOOH mH Nmn .woumm>am: on um>oc amo choo man umfiu huHHHnHmmom ocu Ou mac umOH mH Hm nonsmomm wmumo>amn on pHsoo umau choc msu mo mHo>Huoommou wow wow MONO quml OBHMI MHmm omwm «mom quw owowH wONNH qu me Om*waHpHHm quMI ONHmI MHmm omwm Nwom quw owowH qumH qu mmH nHk maHpHHm mmmmn mmqml nnmm Hmmm mqmm wqu qqmnH wquH qu me mmmOH Noe mmmml wqmmu qmqm mmom mmom mmmw NmmmH mmmnH qu me mmmOH Now omqmu wmmml ommm Nnmo NNHm omHOH omeH omomH qu me mmOH 02 anad A403 H403 A403 A403 A403 THoE TaoB 3.983 3938 Boyle Boaum zoalq aoalm Bonlq BOHIN zoulq. 3OHIN Boauq BOHIN mmao< mmaooaH unmammmcmz wsHumm>umn 80am wwEoonH nmmu uoz wsHumo>umn scum wwouom woumm>amm oaoocH unmamwmomz oaoosH ammo umz . OGHASOU 3Om|usom m can zomuoze a How H nonsmoon hp Opumm>hmm uoa mouo< on» How maoHuocsm mmOH O>HuoanouH< waHmD umHHauoucm choc ouo< cow m aoum oaooaH mam vOumm>umm mouo< mo mmwmuo>< snow moans .m OHQOH 59 .pOumo>um: uoc ouom wanoooosm some do umOH maHon Nm. HchHunwm om :uHB H nonsmoom on woumo>umn uoc whom umHHm OSu aoum umOH mH Nmo .ooumm>am5 uo: GOHuOom sumo How umOH mason NH HmaOHuHUvm cm :uHS H nonsmomn on amumo>am£ uoa GOHuoom umuHm man anm umOH mH Nmn .voumo>am£ on ao>oc awo choc msu uwsu ouHHHnHmmom ozu Ou mow umOH mH Hm nonsmoon woumo>pm£ on stoo umnu choc onu mo on>Huooamou Noq vow Noam oonl mmquI NommH Nme HnwwH o¢OHH HNMHq oqmmm mom CNN ONN onpHHm quql Nomnl mmNmH NOHmH mNmHN mHowH mmmqq NHmoq mom CNN QHN wchHHm «mmqn mqmol mHomH mmHmH quHN HmomH Hmomq Hummm mom 0mm momOH Noq qmwml NHmmI «NmoH mwwwH qumN wwwom qommq Noqmq mom CNN mmmOH NON mmHHI ml HmmHN momma mwwqm HmomN mwmmq Hmqu mom CNN mmOH oz Taog AHoE Taog A403 Taowv A403 A403 A403 3983 $9.83 aoulq BOHIN soslq 3OHI~ soulq soulm Boalq BOHIN 3OHI¢ zoulm moao< wEooGH ucoaommamz wcHumo>pmn aouw oEooaH ammo uoz mqumm>um£ Eoum mouom woumo>umm oaoosH uaoaowmamz oaoonH nmmo uoz oaHnEou Bomnusom a vow soMIoze a How H uonfiooon on OOumo>umm uoa mouu< man How mGOHuocom mmOH O>HumcuouH¢ wnHmD omHHnuouam cuoo whom oom m Eoum maoocH pom woumw>amm mouod How mowmuo>¢ umow mouse .n OHan 60 enterprise are much larger than changes in other variables. Second, the farm managers have the power to change the size of their enter- prise. With the other variables being studied the manager can either make changes within a rather small range, or he has no power to make changes. Table 8 illustrates the effect Of the alternative sizes Of enterprise on average income. For all sizes of enterprise, increasing acreage decreased management income although the other income figures increased; however, management income remains somewhat constant until the two-row combine exceeds 300 acres and the four-row combine exceeds 500 acres. TO illustrate further the effect of size on income, Table 9 presents management income for each year for the various sizes of enterprise. The picture is somewhat different for each Of the three years, with management income increasing in the first year until the two-row exceeds 300 acres and the four—row exceeds 500 acres. In the second year management income becomes increasingly negative as size increases. In this second year the management income from har- vesting is negative in every case except for the four-row with 200 acres. The third year behaves in a similar fashion to the three year averages. Tables in Appendix B illustrate further the effect of changes in size of enterprise. Appendix Tables B. 7, B. 8 and B. 9 illustrate the effect of size with a 20 per cent loss function and the two sliding functions. Tables B. 10, B. 11 and B. 12 show the effect of size with 10, 12 and 14 hour work days. Tables 10 and 11 portray the effect of increases in acreage on machinery expenses. Table 10 illustrates the savings in machinery .H aonfioooo Ou uOHao momaoaxo ao>OO Ou ouom you CC.mqm movoHocHn .H uo£Eoooa Ou HOHao Cmumm>umn moaom momma mmaom voumo>ummm 61 monHI HCQNNI wCNCN oommH CNNCm mHmCN CmNmm mHmmC Cmq CNN CCCH qwmql mqmol CHomH mmHMH quHN HNCCH Hwomq Hmmwm mom CNN CCm NquI CmCCt mummH CmoHH NqHNH Nwqu qumN Nmem wNm qu CCq NNHQI Homm: Cmmo oCmo mquH mNCNH mquN mNHCN HCN «MN CCm MNCMI oCmmI mnmm Homm mqow quw mqomH wqqu qu mmH CCN THoE Taonv A403 733 A403 A403 733 A403 $983 $303 Bowie BOHIN aohlq 3OHIN 3oalq BOHIN Boulc 3OHIN 3oulq BOHIN mmao< mEOOCH ucoaowmcmz n waHumo>Hms Boum oaoocH uaosowmcmz oaoocH zmmo uoz wcHumo>Hmn aouw p m oEOOaH ammo uoz mmHUN $0“ mflPHmm H HonEOOOQ on COumo>umm uoa cuoo on» do mmOH ucou “mm Cu m nqu momHaaaouam mo mONHm uCOHOMMHQ Eoum oaoocH Cam C0um0>umm mouo¢ mo mmwmuo>< umow oomSH .w OHan 62 Table 9. The Effect Of Corn Acreage on Management Income for the Individual Years for Each Combinea First Year Second Year Third Year Acres Two-row Four—row Two-row Four-row Two—row Four—row (dol.) (dol.) (dol.) (dol.) (dol.) (dol.) 200 5437 4343 —10249 -8169 -5596 -7045 300 10110 8905 —15566 —13411 —5917 -7861 400 8835 13697 —20932 -18634 —5993 -8331 500 7821 18807 —26243 —24035 -9616 —8526 1000 1646 15082 —53425 —50481 -30426 —l9469 is assumed lost. a40 per cent of the corn harvested after the harvesting season 63 Table 10. Three Year Averages Of Expenses for the Two—Row and the Four—Row Combines by Corn Acreagea Percentage Machinery Machinery Machinery of total expense expense expense expense .per acre per hour Acres 2-row 4-row 2—row 4—row 2-row 4-row 2-row 4-row (dol.) (dol.) (%) (%) (dol.) (dol.) (dol.) (dol.) 200 2801 3450 15.34 12.79 14.00 17.25 21.95 49.02 300 3116 3718 12.29 13.96 10.39 12.39 16.11 35.03 400 3438 3990 10.69 11.81 8.60 9.98 13.18 28.04 500 3765 4267 9.69 10.45 7.53 8.53 11.44 23.80 1000 5410 5691 7.43 7.65 5.41 5.69 8.03 15.42 corn not harvested by December 1. aAssumes an eight hour work day and a 40 per cent loss on all 64 .H HOQEOOOC on poumo>am5 uoc caoo HHm GO mmoH uaoo moo Cq m can omp xao3 ado: usto cm meowmcH omcmmxo umoo uHmoom umoo Homm no ummpoucH aOHumHoouaon OmommouocH omHumuoucm auoo onu mo ouHm onu mm oaHnsoo 3OMIusom m Cam BoMuose w you uaoo mom on mmmaoaxm huocHsomz mo :oHuHmoanu ommuo>< umow manna 05H .HH OHan 65 cost per acre and per hour as well as relative to total expenses with increases in size. The distribution by per cent of the six types of machinery expenses is shown in Table 11 for the five sizes of enter— prise. With increases in size the variable expenses--fuel cost and repair cost-—increase relative to the fixed costs—-depreciation expense, interest on investment, insurance and housing. Length of Work Day In contrast to nearly every other crop, corn harvest is not restricted to the hours of the day when no dew is present. This fact makes the length Of the work—day an important variable. In this study 8, 10, 12 and 14 hour days are used. 12 and 14 hour days would cer— tainly require hired labor or operations with more than one Operator. The same labor rate was charged for all hours. Under some circum- stances a farm manager would have to be charged higher rates for the additional hours. Table 12 and 13 indicate the effect on acres harvested and on income of the alternative lengths of the work-day for 200 and 500 acres respectively. These tables show that whenever a longer work-day in- creases the acres harvested, the income is increased. Table 14 illus— trates the effect of the length of the work day on management income in each year for 500 acres. Once again increased work—hours increases income except where harvest has already been completed. Harvest is completed with the four—row combine in the first and third year with any of the lengths for the work day considered but never completes harvest during the harvest season in the second year. Although the two-row never completes harvest during the harvesting season in the 66 on on Coadmmm mH Shoo wchHmSou OSH . Hm H0£EQUMQ @QU mm>HM£ .H umpEooom Ou HOHum pmumo>hm£ mmuom onu mH mHnH .H Monsooon ouomon opumopum: no: mouom HHm so pom: mH uooo you Cq mo mmOH «w waml NmoNI qum wHCm CHCC mmow CHNNH mmomH CCN qu «H Comma NonI CmNm wam omwm mNmC omwnH mNNNH CCN CwH NH Nomml Nmmml Cqu wqmm Cwom mmmw CwoNH mmmNH CCN CNH CH mNCmI omem: mnmm Hmmm meow mqu qquH wqan qu me w a.aopv a.aopv A.aopv a.aopv a.aopv A.aopv a.aopv a.aopv Ammpupv Ammpomv aoulq soHIN aoalq zouuN 3oulq BOHIN 3oulq soHIN sohlq soHIN mason oEooaH uaoaowmamz waHumo>am£ Eonm mEooaH smmo uoz waHumo>Hm£ anw Cmumm>am£ moao< oEOOaH uaoEmmmcmz oaooaH Some uoz n mauou mo mouo< CCN SuH3 ocHzomz BoMnusom o Cam BoMnose o How hon xuoz osu mo SumGOH onu waHmmouocH mo oaooaH omwum>¢ co Cam Coumo>umm mouo< owmuo>< can no uoommm 039 .NH oHan 67 .H amnfioomm .H uwnEooom Ou HOHHQ Commo>ama moaom onu wH mH:H n oaowon woumo>ums uoc moaom HHm so Com: OH uaoo pom C« mo mmOH mm CHN«I NCC«| ConH wo«CH omeN mH«HN omm«« mHom« C«« mom «H HC««| mmNmI oonH «mHNH CCCHN HmHCN wCH«« HmmN« mN« mom NH wmm«| m«NNI N«oNH «mN«H HHmHN Hmme HHC«« HmHH« CH« Cmm CH «wm«| m«mo| CHoNH mNCmH Hw«HN HNCCH Hwom« HNmmm mom CNN C a.aopv A.aopv a.aopv a.a0pv a.aopv a.aopv a.aopv A.aopv ammpomv Ammaomv 30a|« 3OHIN Bop|« 3OHIN Bou|« BOHIN zou|« 3OHIN Soul« 30» N mason oaoocH uooaowmcmz waHumo>Hm£ anw oaooaH ammo uoz wcHumo>um£ aoum Coumo>nms mouom oEoocH ucoaowmomz oaooaH ammo uoz n ocuoo mo mouo< CCm :uH3 ocHsomz Boxiasom m Cam SomuosH a How Non 3H03 onu mo nuwcoa O£u wcmeouooH mo oeooaH owmuo>< co Com voumo>umm mouo< owmuo>< man so uoowmm one .mH OHan 68 Table 14. The Effect Of the Length Of the Work Day on Management Income for Each Year for 500 Acres First year Second year Third year Length of Work Day Two-row Four—row Two-row Four-row Two-row Four-row (hours) (dol.) (dol.) (dol.) (dol.) (dol.) (dol.) 8 7821 18807 -26243 -24035 -9806 -8704 10 11802 18097 —25403 —22317 —6887 —9688 12 16089 17640 —24559 -20834 —7516 -10265 14 19424 17362 -23524 —19294 -8096 -10957 69 second year, harvest can be completed in the first year by working 14 hours per day, and completion occurs in the third year with ten or more hours per day. Appendix Tables B. 13, B. 14 and B. 15 contains tables similar to Tables 12 and 13 for 300, 400 and 1000 acres. The Appendix also contains tables showing the effect Of the different lengths of work—days on 200 and 500 acres with a 20 per cent loss function (Tables B. 16 and B. 17) and the first sliding function (Tables B. 18 and B. 19). Grain Moisture Criterion The grain moisture content is crucial to farm managers deciding when to commence harvest. Four criteria are considered for determining when to start harvest as related to the grain moisture. The first three criteria state that the grain is ready to be harvested as soon as the grain moisture content falls below 28, 30 and 32 per cent. If the moisture content returns to a level above the criterion, harvest stops. The fourth criterion once again has a sliding feature in that the maximum content increases as the harvesting season progresses. Specifically, the harvest could commence if the grain moisture content fell below 26 per cent before October 21, 28 per cent before October 28, 30 per cent before November 4, 32 per cent before November 11, 34 per cent before November 18 and 40 per cent before November 25. Tables 15 and 16 present the results of each of these criterion with the effect on harvest and average income. The effect on average income by changing the criterion is not great. Tables 17 and 18 show the effect on individual years. These tables show that in the first year the decision concerning which criterion to use effects management 7O whoapp mm. .mHo>Huoommou Nm. mpoapa oa. .mH Hmnao>oz ouomon «m. .mowmum>m Moo» mounu mum mmuome .HH umnao>oz ouomon Nm. .umo>um£ ou HOHHQ umoo muom Hon CC.m«m osu .HN Honouoo daemon CN. 30Hon HHom unoucoo ousumHoa :Hmum MH uumum CHsoo .Cm. .mN. 30Hon HHom ucoucoo ouaumHOs aHmuw oSu cons quum CHDOO .mumoo moan» .mHnmuomHu mmB CsmH map uwsu wouumum umo>um£ Houmm .mHnmuomHu mos HHom OSu Cam uoe mm3 aOHumano manumHoE m5u .mN Honao>oz .« Honao>oz maomon Cm. osu mo .mN Honouoo umo>awm m umo>ummo ovaHooH C owmuo>um£ onuow Houmm mono OHnmuomHH umo>umn mama woumo>ums mOHo< uaoucou ououmHOz chuo map wchuoocoo OHHOuHaC uGOHOMMHQ :uHa mouo< CCN so OGHLEOC zoom How muHsmmm .mH OHan .mN Honao>oz onomon C«. .CH Homao>oz ouomon «m. .HH Honao>oz ou0mon Nm. .« Honao>oz onomon Cm. .mN HonOuOC ouomon wN. .HN Honouoo ouommn mN. BOHOI HHom ucouooo unaumHofi aHmuw MH uamum CHsoo umo>ummm .NHo>Huoommoa Nm. .Cm. .CN. SOHOQ HHom uooucoo ousumHOa aHme onu dons uumum CHooo umo>ummo .mowmao>m Homm moaau mum moastm .uwo>nm£ ou HOHHQ umoo whom pom CC.m«m onu ovsHoaH C .mumON mouzu map wo mwmao>umn noumm mmmw mo Honsszn .OHQMuomuu mmB HHom onu Cam nos mp3 GOHHOuHHo ousumHOa onu umnu Now umuHmm 71 CoN«I mmmon oNNHN oNNmH mom CCN Hm C mN CH\CH wCNHH oN\CH wwcHCHHm wNHmI «Howl N«oCN mCmCH mom NmN Nm w wN mHNCH CCNHH «N\CH on. mwm«l m«mo| mw«HN HNCCH mom CNN Nm m «N mHNCH CCNHH CNNCH mom. mwmml CmHCHI CCCCN NCNmH NNm NmH Nm N NN mH\CH oCNHH Hm\CH owN. A.HOCV A.HOCV A.HOCV A.HOCV flux Chm MN CCN Hm umHH MOON Homm Hawk 30H|« 3OM|N 30a|« onIN Bou|« BOHIN Cum CON umH cOHamuHaC CmaoooH CmaoocH OCOHHOQ awouumum umo>hms «Couumum uaoEowmcmz ammo uoz umo>hmn wcHHoC Houmm mmmw OHnmuomHH umo>um£ oumm woumo>um£ mouo< ucouaoo musumHoz aHmuu map mcHahoocoo mHuouHuo uGOHOMMHQ auHB mmuo< CCm Go UGHQSOU 50mm How muHammm .3 flag 72 Table 17. The Effect of Alternative Grain Moisture Criteria on Management Income for Each Year with a 200 Acre Corn Enterprise First year Second year Third year Criterion Two—row Four—row Two-row Four-row Two-row Four—row (dol.) (dol.) (dol.) (dol.) (dol.) (dol.) .28a 5907 4924 -10664 -8811 —5596 -7045 .30a 5437 4341 -10249 —8169 ~5596 -7o45 .32a 4734 3318 -10252 -8178 -5596 -7o45 Slidingb 5602 4541 —10249 —8169 -5582 -6786 aHarvest can start when the grain moisture content falls below .28, .30, .32 respectively. bHarvest can start if grain moisture content falls below .26 before October 21, .28 before October 28, .30 before November 4, .32 before November 11, .34 before November 18, .40 before November 25. 73 Table 18. The Effect of Alternative Grain Moisture Criteria on Management Income for Each Year with a 500 Acre Corn Enterprise First year Second year Third year Criterion Two-row Four-row Two-row Four—row Two-row Four-row (dol.) (dol.) (dol.) (dol.) (dol.) (dol.) .28a 5866 17322 —26701 -24950 -9616 -8521 .308 7821 18807 —26243 —24035 -9616 —8521 .328 10016 17177 -26243 —24035 —9616 —8521 Slidingb 7076 19679 —26243 -24035 —9901 -8015 aHarvest can start whenever the grain moisture content falls below .28, .30 and .32 respectively. bHarvest can occur if the grain moisture content falls below .26 before October 21, .28 before October 28, .30 before November 4, .32 before November 11, .34 before November 18, .40 before November 25. 74 income significantly. The effect is small or nonexistant in the second and third years because the soil is not tractable on most Of the days the criteria affect. Tables with harvest and average income results similar to Tables 15 and 16 are presented in Appendix Tables B. 20, B. 21 and B. 22 for 300, 400 and 1000 acres respectively. Opportunity Cost of Labor The value of the labor of the combine operator can come from one of two places. If the operator is a hired laborer, the value is his wage. If the farm manager Operates the combine the value is his Opportunity cost during that time. Five values are used for this value which is labeled the opportunity cost of labor. These values are $2.00, $3.00, $5.00, $8.00 and $12.00 per hour. $8.00 and particularly $12.00 seem very high and unrealistic; however, in certain instances where the operator had tO leave other jobs, particularly fall plowing, these high rates may apply. Tables 19 and 20 show for 200 and 500 acres respectively the hours required, the labor expense and the resulting average income for each of the five levels of opportunity cost. The effect is very straight forward with income being reduced the amount of the labor expense. The effect is nearly the same in each of the three years. Average Temperature Changes in the average temperature are studied by increasing or decreasing the maximum and minimum temperature each day from October 1 tllrough December 31. Increases in average temperature reduce the glflain moisture content more rapidly. Five levels of average temperature 75 .mms GH mm ocHnEOo OSu mason m5“ NHouoa wH onanm mHsz aamm- aaoa- omoa mama mam mmma om mma oo.ma ammm- ammm- mama mmmm amm mmoa ca mma oo.m maom- maam- mmma amam mmm amm am mma oo.m mama- mama- aama mmoa aam mmm am maa oo.m aomm- «mam- mama mmaa aaa mmm ca mma oo.m a.aopv A.aomv a.aopv a.a6pv a.aopv A.aopv 3oul« BOHIN 30H1« BOHIN 3oul« BOHIN onI« BOHIN H50: pom oEoocH unmaommcmz QEOUCH Smmu “OZ wsHumo>Hm£ Mom omcooxo Hoan HmuOH Commooou mudom umoo Numasuuommo mono< CCN sums oaooaH Com monomxm momma .Coamsoom made: How mommao>< so Houmuomo OOHQEOC osu mo umOC NuHasuuoamC o5» mo uoommm 05H .oH OHQMH 76 .mm: OH mH osmnsoo ozu mason osu NHouoE mH oasmHm mmshm maam- ammma- aamOa maoma mmam mmam aaa omm oo.ma omom- mooaa- aooam mamaa mmma ammm aaa omm oo.m mmmm- maooa- ammam aamma mam mama aaa omm oo.m mmam- mmma- aoaaa amoma mmm ama aaa omm oo.m mmam- mama- mmoam aamma amm amm aaa omm oo.m a.aomv A.aomv a.aomv a.aomv a.aomv A.aomv 3OHI« BOHIN 3oal« 3OHIN BOHI« BOHIN BOHI« BOHIN moo: Mom umoo NuHcsuaoamC oEoocH ucoawwmamz oaoocH Smmo uoz womumo>Hm£ How mmaoaxo HOAMH HouOH mcoamowou mason omHamuoOom whom CCm m Eoum oaoocH Cam omaomxm Hoan .CouHsoom mason mom mommao>< so Houmuoao osmnaoo onu mo umou muHasuuomaC osu mo uoommm may .CN OHan 77 are used: the level that prevailed in 1966-68, that level increased by one and five degrees, and that level decreased by one and five degrees. Table 21 and 22 contain the results Of using the five selected temperatures. The higher the temperature; the greater the income. Only in the first year do changes in the average temperature have a noticeable effect on the number of tractable days after harvest began. When the average temperature was decreased five degrees, the harvest was never completed in the first and second years using a 30 per cent grain moisture criterion due to the assumption that the moisture con- tent must fall to that level. A four degree decrease in the first year and a three or four degree decrease in the second year created the same problem. To obtain the values in Tables 21 and 22 for a decrease of five degrees, the corn is harvested on December 31 regardless of the grain moisture criteria. Additional Rainfall The effect of rainfall is studied by additional rainfall since a reduction in rainfall can not be made uniform for the three years. The four levels of rainfall used are the actual rainfall in 1966-68, an additional inch on October 15, an additional inch on November 1 and an additional inch on November 15. The additional rainfall affects the soil moisture, and thus the tractability. The effect will also depend on the soil moisture conditions previous to the rainfall and the amount of rainfall on the given day and several days following. The effect of the four levels of rainfall on harvest, average drying expense and income is shown in Tables 23 and 24 for 200 and 500 78 .uOOo won on o>OnO OOB OHOumHoa OHOHC onu kaC m OOu mo OEHH .uOoo mom on O>onO mO3 OHOuOHOa OHOHC Onu mNOC oH onu mo Ooouusomn .CC. oponO OHOumHoE OHOHC :uHB Honaooon OH COuOHmaoo mma umo>HO£ N COO H OHOON OHC .OOCOHO>O HOOh mounu OHO OOHOCHm .uso COuOOHunOm OH umoo umO>HOOIOHO OHOO MOO CC.m«mm .OCOHO>O MOON OOHOO OHO OOHOCHC .ouaummoa uOOO MOO m.mH Ou ano Os» NHC ou umOCO .mHOON moan» Osu pom Common umo>nOO onu COHHOC CoumO>uOn OOHOO mo HOQEOO OCOHO>¢C .uoooo OOO umo>uO£ uOnu Loom OH HHOm Ozu uOnu CC. OOCOOOH uOOuOoo masummoa OHOHC OSO HOOMO mNOC mo HOAEOO OCHO .NHC OH HHOO map uOnu Cm. OOOOOOH uOOuOoo OHOumHoE OHOOC OOu HOuMO OuOC umummn .Hm HonEOOOQ I mH Honouoo Eoum NOC OOOO How OHOuOHOOEOu EOSHOHE may COO EsaHan Onu aouw OOOHCOC mo HOQEOO OuOHumOHQOO Oau mo OOHuOOHunOm no OOHuHCCO Ono OH OHOanOmaOu OH OOCOOOO OOHO maaa- oammu aaam omam mma aoa am am Haaa ma\oa mm\aa mo\aa mom- «oCCI mmNmn NHCN CC«N moH CCH NC C CN mHNCH CC\HH oNNCH 6H1 N«CNI NCmNI CNNH CH«H moH CCH NC C CN mHNCH CCNHH CN\CH om+ CCNCI CCHC! HCNN NCCH moH CCH NC C «N mHNCH CCNHH CNNCH oH+ CNCCI oC«m| momN oNHN moH CCH NC C «N mHNCH CCNHH CNNCH HOEqu A.HOCV A.HOCV A.HOCV A.HOCV MOON MOON MOON MOON MOON MOON BOHI« soalN 3OHI« soHIN Boul« BOHIN Cum CON OOH Cum CON umH moaooOH OOmOOmwO CCOumo>nOn ommmC OHnOuOOuH numo>uOO uOoaOCOOOz COHMMQ mmao< mo OuOC umumm OOOHCEOC 30mlunom O COO SOCIosfi O nuH3 OOHHQHOOOC OHOC ouo< CCN O Oo OOCOOfio OHOuOHOmEOH mo uoomwm OCH .HN OHCOH 79 .uOOo MOO CC O>onO OOB OMOMOHOa OHOMC Oau ONOC m Onu mo 039m .MOOO MOO CC o>onO OOB OMOMOHOa OHOMC Onu ONOC oH Onu mo OOOMMOONO .CC. O>OnO OMOuOHoE OHOMC nuH3 MOQEOOOQ OH COuOHCaOO OOB uOOpMOO N COO H OMOON OHC .OOCOMO>O MOON OOMOM OMO OOMOCHN .uoo COMOOMMQOO OH uOoo MOO>MO£IOMC OMOO MOO CC.m«Cm .OCOMO>O MOON OOMCM OMO OOMOCHN .OMOMOHOa uOOo MOO m.mH OM OMOO Ono NMC Ou MOOCO .OMOON OOMCM Osu Mom COHMOQ MOO>MO£ Ono COHMOC COuOO>MO£ OOMOO mo MOCEOO OCOMO>MOn uOsu OOOO OH HHOO OOM MOnu CC. OOCOOOM MOOMOOO OMOuOHofi OHOMC Osu MOMMO ONOC mo MOnaOO OOHO .NMC OH HHOO OOM MOCM CC. OOOOOOM uOOuOOO OMOMOHOa OHOMC Onu MOumO OuOC uOMHmn .HC MOLEOOOC I mH MOLOuOC EOMM NOC COOO Mom OMOMOMOOEOO EOEHOHB Osu COO EOEHOOE Onu SOMm OOOMCOC mo MOQEOO OMOHMCOMQOO Osu mo OOHOOOMMCOO Mo OOHuHCCO Oau OH OMOOOMOOBOM OH OOCOOOO OCHO NCNNHI «HCoHI mmHN CoCN mNN NNH NC am O.oH mH\CH CNNHH NCNHH Com: «NCmI «N«CH| CNmm H«m« moC mCN NC C CN mH\CH CCNHH oN\CH 6H: NNmNI HNNNI C«HC CCmN CoC CNN NC C CN mHNCH CCNHH CNNCH om+ CNCCI HoCCI mCH« moCC moC CNN NC C «N mH\CH CC\HH CNNCH oH+ «Cm«l m«Co| NCo« NCoC moC CNN NC C «N mHNCH CCNHH CN\CH HOSMOz A.HOCV A.HOCV A.HOCV A.HOCV MOON MOON MOON MOON MOON MOON 30M|« BOMIN BOMI« aoMIN BOMI« BOMIN CMC CON OOH CMC CON OOH wanoOH OOOOOme CCOMOO>MOO OONOC OHnOuOOMH nuOo>MO£ uOOEOCOOOz COHNMC OOMo< mo OMOC MOMHN OOOHOEOC soCIMOom O COO Bomlose O CuHa OOHMOMOuOm OMOC OMo< CCm O OO OOCOOOC OMsuOMOOeOH mo uOOmmm OOH .NN OHnOH 80 MOON OOMOO OMO OOMOCHO .xHCOOOOO OnO OH O3O£O OH HHOmOHOM :HOEMOz:O .OOO>MO£ OO MOHMO COMMOOOH OOOOO mo OMOO MOO CC.m«C OOO OOCOHOOH .OOCOMO>O C .COHMOO OOO>MOO OOO COHMOC COOOO>MOO OMOs OOOO AOCOMO>O MOON CV OOMoMOO OOOO OOOO OH HHOO OOO OOOO CC. OOsoOOM OOOOOOO OMOOOHoa OHOMC MOOmO ONOC mo MOQOOZ ..HDUUO GNU C .NMC OH COOOMC OOO OOLO CC. OOOOOOM OOOOOOO OMOOOHOB OHOMC MOOMO OOOC OOMHOO CNCCI C««CI momN CCHN CoH CCH NC C CN mHNCH CC\HH CN\CH mH >Oz :H+ Co«C| mmCCI Cm«N NooH CoH CCH NN C CH mHNCH CCNHH CNNCH H >Oz :H+ «m«C| CCCCI C««N moCN moH CCH CC C NN NH\CH CC\HH CN\CH mH OOC :H+ CNCCI oC«CI momN NoHN «oH CCH NC C «N mH\CH CCNHH CNNCH O:HOaMoz: A.HOCV A.HOCV A.HOCV A.HOCV MOON MOON MOON MOON MOON MOON 3OMI« SOMIN BOMI« aoMIN BOMI« 3OMIN CMC CON OOH CMC CON OOH COEooOH OOOOOxO OCOOOO>MO£ ONOC OHOOOOOMH OOOO>MOO OOOEOCOOOz COHNMC OOMo< O CO OOOC OOMHO OOHQOOC OOOO Mow OOHMOMOOOC OMOC OMo< CCN O OOHs OOOOOC COHOOO>MOm OOO COHMOQ HHOOOHOm HOOOHOHCCO mo OOOmmm .CN OHnOH 81 MOON OOMOO OOO>MO£ OOOO OMO OOMOCHO .NHfiGQQQ< GS“ CH G3O£m mH HHQHGHQH :HNEHOZ:$ .OOO>MOO OO MOHMO COMMOOOH OOOOO mo OMOO MOO CC.m«m OOO OOCOHoOH .OOCOMO>O C .COHMOO OOO>MO£ OOO COHMOC COOOO>MOO OMOB OOOO AOCOMO>O MOON CV OOMoOO OOOO OH HHOO O£O OOLO CC. OOOOOOM OOOOOOO OMOOOHoE OHOMC MOOwO ONOC mo MOnaOz . H5000 GNU C .NMC OH COOOMC OOO OOOO CC. OOOOOOM OOOOOOO OMOOOHoE OHOMC MOOHO OOOC OOMHOO oNNmI oCCCHI CoN« «HCC mNC CmN NC C CN mH\CH CCNHH CN\CH mH >Oz :H+ C«NNI CNoHHI CCC« onC C«C mHN NN C CH mHNCH CCNHH CN\CH H >Oz :H+ NCN«I NNNoI CmN« oNNC moC CNN CC C NN NH\CH CCNHH CN\CH mH OOC :H+ «Cm«| m«Cou Nmo« NCoC moC CNN NC C «N mHNCH CC\HH CN\CH O:HOaMOz: A.HOCV A.HOCV A.HOCV A.HOCV MOON MOON MOON MOON MOON MOON BOMI« BOMIN BOMI« BOMIN 30M1« 3OMIN CMC CON OOH CMC CON OOH CanoOH OOOOOxO OCOOOO>MO£ ONOC OHQOOOOMH OOOO>MOO OOOEOCOOOZ COHNMC OOMo< n mo OOOC OOMHO OOHnEoo OOOO Mom OOHMOMOOOm OMOC OMo< CCm O OOHB OOOOOC COHOOO>MOm OOO COHMOC HHOOOHOM HOOOHOHCCO mo OOOmmm .«N OHOOH 82 acres respectively. The additional rainfall increased income in cer— tain cases particularly with 200 acres, decreases income in others especially with 500 acres and had no effect in some other cases. In the cases where additional rainfall increases income, the reason is that after the rain the grain dried faster than the soil resulting in lower drying charges. When no effect is shown, either the soil is already saturated causing the additional rain to run off, or harvest has already been completed. Price Seven levels of prices are used. The prices prevailing in 1966-68 by weeks are used as the base. All corn is assumed to be sold the day it is harvested at the price for that week. The other six levels are the base price plus and minus one cent, five cents and ten cents. Tables 25 and 26 show for 200 and 500 acres respectively the expected relationship between changes in price and income. Yield Three levels of yield are used. The levels refer to the potential yield as Of October 15. The base level is the potential yield for each year that is typical of the yields for 1966—68. The second and third levels are ten bushels more and ten bushels less. Tables 27 and 28 present the results from the three levels for 200 and 500 acres respectively. The results are once again as expected. One should note the much greater effect on management income with a 500 acre enterprise. 83 .HC MOCEOOOQ .CC MOnEO>OZImH MOCOOOC .OMOON OOMOO OOO mo OOCOMO>O OMO OOMOCHM OOHO .OMOON OOMOO OOO MO>O CO>HOOOM NHHOOOOO OOHMO OCOMO>MOO OO OOHMO COHHHO>OMO mo OCOMO>HOOOM OMOON OOOO OMoo OOOEOCOOOZ OOOO OOz OOHMO OCOMO>< mo OOHMO OCOMO>< OOHAEOC 3omIMOOO O COO somlosa O COO OOHMOMOOOm OMOC OMo< CCN O OOH3 OOHMO OH OCOOOC O mo OOOOOOOOOOOC OOH .mN OHOOH .OMOON OOMOO OOO mo OOCOMO>O OMO OOMOCHC OOHO .OMOON OOMOO OOO MO>O CO>HOOOM NHHOOOOO OOHMO OCOMO>OZImH MOCOOOC "ONOC COHOOO>MOO Oo OOHMO COHHHO>OMO wo OCOMO>HOOOM OOHMO OCOMO>< OMOON OOOO OMoo mo OOHMO OCOMO>< NCCCHI NmH«H| NCCCH mCNHH CNo. NCo. CC. Co. CH.H CH.m| CNCNI o«NHHI N«NCH CCCCH CNC.H NCC.H Ho. HC.H CH.H mC.mI NCHmI oNCoI NCoCN CommH CCC.H NNC.H mo. mC.H NN.H HC.CI CoC oCm«I NCoCN mHCCN CNH.H NCH.H CC.H CH.H CC.H CH.O+ C«CHI N«oCI CNN«N mN«CH CNH.H NCH.H HC.H HH.H CN.H mC.m+ NCC«I mCCCI CCCNN NmmCH CCC.H NoC.H No. NC.H «N.H HC.C+ «Cm«l m«Co| HC«HN HNCCH CNC.H NCC.H Co. CC.H CN.H HOOMOz a.a6mv a.aomv a.aomv a.aomv a.aomv a.aomv a.aomv a.a6mv a.aomv BOMI« soMIN 3OMI« 3OMIN BOMI« 3OMIN MOON MOON MOON CMC CON OOH OOHQEOO zoMIMOOO O COO Bowlose O COHOD OOHMOMOOOm OMOC OMo< CCm O OOHS OOHMO OH OCOOOU O mo OOOOOOUOOOOU OOH .CN OHnOH 85 «CCI oNCCI mC«mN oCCoH m.CNH C.NHH C.mN C.CC C.CmH N.CNH mCH CHH CCH .OC CH+ «Cm«I C«CoI mC«HN HNCCH C.oHH «.oCH N.CC «.NC C.H«H C.CHH mNH CCH CmH HOaMOz o««CI NNCNHI CNCNH C«NNH m.oCH H.HCH C.CC N.Cm C.HCH «.oCH mHH Co C«H .OC CHI H.HOCV H.HOCV A.HOCC N.HOCV BOMI« zoMIN 30MI« BOMIN BOMI« BOMIN MOON MOON MOON BOMI« 3OMIN BOMI« BOMIN MOON CMC MOON CON MOON OOH CMC CON OOH OEooOH OBOOOH CHOHN HOOOo< CHOHN HOHOOOOOO OOOEOCOOOZ OOOO OOz OOHMOMOOOm OMOC OMo< Com O Oo CHOHN HOHOOOOOO OH OOOHOOHMO> mo OOmem OOH .CN OHCOH CooHI NNoHI NNmCH CCHCH o.CNH N.CNH C.oo C.HC N.CmH C.CmH mCH CHH CCH .OC CH+ CNCCI oC«CI C«oC C««C N.oHH H.oHH C.Co C.«N C.H«H N.H«H mNH CCH CmH HOaMoz NCNmI oHCmI NCCN CCCC N.oCH C.oCH C.NC «.NC o.HCH C.HCH mHH Co C«H .On CHI N.HOCV N.HOCV N.HOCV N.HOCV 30MI« 3OMIN BOMI« aoMIN BOMI« BOMIN MOON MOON MOON 3OMI« 3OMIN BOMI« BOMIN MOON CMC MOON CON MOON OOH CMC CON OOH anoOH OEOOOH CHOHN HOOOo< CHOHN HOHOOOOOO OOOEOCOOOS OOOO OOz OOHMOMOOOm OMOC OMo< CCN O OO CHOHN HOHOOOOOO OH OOOHOOHMO> mo OOOmmm OOH .NN OHCOH 86 Footnotes 1. The model as developed by the task force assumed all of the corn not harvested during the harvesting season is harvested on December 31. Field losses for corn harvested December 31 are deter— mined with the same functions used during the harvesting period. 2. Income is determined using a $960 charge for the operator's labor and $2.00 per hour for any hours in excess of 320; however, the income can easily be adjusted to reflect the Opportunity cost. 3. Additional rainfall is used since an equivalent reduction in rainfall could not be made in each of the three years. 4. The $45.00 per acre charge includes: seed $ 4.00 fertilizer 20.00 herbicide - 5.00 machinery and labor 'l6.00 Total $45.00 CHAPTER V ANALYSIS OF THE EFFECT OF THE SELECTED VARIABLES IN THE HARVESTING PERIOD In this chapter, the results presented in the previous chapter are analyzed and interpreted so that conclusions can be reached that will enable farm managers to improve their decisions relative to the harvesting system. The nine variables are ranked as to their effect on income for several situations. These same variables are then ranked as to their effect on income from the use of the two-row and the four- row combines. From these rankings and the magnitude of the changes, conclusions can be made as to which of the selected variables create significant changes in income under specified conditions. The chapter therefore, includes an individual look at each Of the nine variables to discuss that variable's impact on the harvesting system. The changes in management income are used as the basis for the ranking of the selected variables. Since management income is the return for the farmer's management, all costs, both cash and non-cash, have been subtracted from income. If any other income figure were used, some of the costs would not be subtracted. Therefore, changes in the unincluded expenses from changes in a variable would not be reflected in the ranking of the variables. 87 88 Ranking of the Effect on Income In order tO determine the effect of changes in variables, the magnitude of change for each of the nine variables had tO be established. The following nine changes are used: 1. 2. Failure to complete harvest by December 1: 20% to 40% loss. Size of Corn Enterprise: 100 acre change. Hours in the working day: 2 hour change. Criterion of how low grain moisture content must be: .02 change. Opportunity cost: $3.00 per hour change. Additional rainfall: one inch. Temperature: 5% change (1). Price: $.05 per bushel change. Yield: 10 bushel change in the potential yield as of October 1. Each of these changes has approximately the same probability Of occurring on a given farm situation. Although the decision concerning the magnitude of the change is somewhat arbitrary, the consequences Of possible inaccuracies are less serious because the effect of the changes in the variables relative to the other variables is most im- portant. The absolute change in each variable is of a lesser impor— tance since each set of changes would produce a different set Of abso- lute changes; however, each equivalent set Of changes should have a similar relative effect on the variables. In order to study more thoroughly the effect of the size of the enterprise, rankings were made for a 200 acre and a 500 acre corn 89 enterprise. For the 200 acre enterprise the magnitude of the effect of the change in size is determined by changing from a 200 to a 300 acre enterprise. For the rankings for a 500 acre enterprise, a change from 400 to 500 acres is used. Major emphasis is placed on the effect Of changes in the size of enterprise since the relevant range of sizes of enterprise is much larger than the relevant range for the other variables. Also, farm managers are especially concerned with the effect of changes in the size of their enterprise. The first situation used for ranking is the three individual years. Before presenting the rankings for the years, the conditions prevailing in each of the three years should be reviewed. The first year is characterized by excellent yields, high prices and ample har- vest time. In the second year the farm manager encounters low yields, prices slightly below average and disastrous harvesting conditions with very high grain moisture content and extremely wet field conditions. In year three the yield is average, conditions during the harvest period are excellent but prices are very low. The first year, there- fore, is highly profitable. The third year can be profitable with a favorable set of variables but seldom financially disastrous. However, the second year is financially disastrous especially as size increases. Table 29 illustrates the important characteristics Of the three years and presents management income using the base values specified in the previous chapter. The conditions prevailing in this three year period appear to be somewhat less favorable than average primarily because Of the conditions in the second year. Tables 30 and 31 rank for 200 and 500 acres respectively the effect of the given changes in the nine variables. Appendix Tables 90 Table 29. A Summary of the Situation Existing in the Three Harvesting Periods Studied Unit First year Second year Third year Maximum yield as of September 30 Bu. 150 100 125 Grain moisture on October 15 Per Cent 36.0 40.3 26.9 Average price Dol. 1.23 1.06 0.96 Harvest conditions Good Very poor Excellent Management incomea 200 acres 2-row Dol. 5,424 -10,351 -5,939 200 acres 4-row Dol. 4,326 —8,305 —7,503 500 acres 2-row Dol. 7,808 -26,345 -9,959 500 acres 4-row Dol. 18,790 —24,171 -8,984 a . USIng base values. Table 31 sar1aale 91 Table 30. The Rank Of the Magnitude of the Effect of the Given Changes in the Nine Selected Variables on Management Income with a 200 Acre Enterprise for a Two—Row and a Four-Row Combine Rank Variable lst year 2nd year 3rd year Averageb 2-row 4-row 2-row 4-row 2—row 4—row 2-row 4-row Size of enterprise 1 1 1 l 5 4 6 4 Temperature 2 3 3 2 6 2 2 2 Price 3 2 5 3 l l l 1 Yield 4 4 6 4 2 3 3 3 Grain moisture 5 5 8 6 8 6 5 6 Opportunity cost 6 6 7 8 3 5 8 5 Hours 7 7 4 5 4 7 7 7 Rainfall 8 8 9 9 7 8 9 8 Loss 9 9 2 7 9 9 4 9 aThe rank is based on the absolute value Of the change in management income. bIn summing the changes in the three years the sign of the changes is included. Increases in one year may offset decreases in another. A auurs Painfall LOSS 92 Table 31. The Rank of the Magnitude Of the Effect of the Given Changes in the Nine Selected Variables on Management Income with a 500 Acre Enterprise for a TwO-Row and a Four-Row Combine Ranka Variable lst year 2nd year 3rd year Averageb 2-row 4-row 2—row 4-row 2—row 4—row 2—row 4-row Size of enterprise 9 l 2 l l 7 2 8 Temperature 2 3 3 3 8 4 5 2 Price 5 4 4 4 2 l 4 1 Yield 7 5 5 6 5 2 6 3 Grain moisture 6 8 8 8 9 8 9 7 Opportunity cost 8 7 6 7 6 6 8 6 Hours 3 6 7 5 3 3 3 9 Rainfall 4 2 9 9 7 5 7 5 Loss 1 9 1 2 4 9 1 4 8The rank is based on the absolute value of the change in management income. bIn summing the changes for the three years the sign of the changes is included. Patt Fiel hOUI ‘n‘it‘r POII SUQ. 93 C. l and C. 2 present the dollar value of the change for 200 and 500 acres while Appendix Tables C. 3 and C. 4 provide the ranking in descending order of importance for each year and the average of the three years. The rank is based upon the absolute value Of the change with the direction of the change not considered. When the average effect is calculated, the sign Of the value for each individual year is considered to calculate the average, and then the rank is deter— mined from the absolute value Of the average. For several variables-- size of enterprise, hours, grain moisture and additional rainfall--the direction of the change depends upon the year. The size of enterprise where its importance is considerably less in the average than in the individual years is an excellent example of the offsetting directions Of the change. The rankings made by years fail to present any consistent pattern. The variables size of enterprise, temperature, price and yield appear to have the greatest effect. The variables loss and hours have a large effect in some years especially with 500 acres. With a two-row machine the variables loss and hours command more im- portance. Although the above generalizations can be reached, a more distinct pattern must be found. Much of the fluctuation in the rankings can be explained by the success or failure to complete harvest by December 1. The variables size of enterprise, hours, grain moisture and rainfall create opposite effects on income with and without completion of harvest during the harvest period. When the harvest is easily completed, increased size increases management income, however, when harvest is not completed 15 CC: and la e:able haul i: 94 during the harvest period the increased acres are harvested with the 40 per cent loss and thus creates a decrease in income. When harvest is completed easily, increased hours, increased maximum grain moisture and lack of rainfall produce less management income since these changes enable harvest to be completed earlier creating increased drying and hauling charges. When harvest is not completed during the harvesting season these same changes increase income by decreasing the loss from failure to complete harvest. Table 32 describes the effect of changes in each of the variables with and without completion of harvest during the harvesting period. Tables 33 and 34 present for 200 and 500 acre enterprises re- spectively the rankings and the percentage change for each variable with and without completion of harvest during the harvesting period. The rankings are made using absolute values of the average changes for each variable. The percentage is calculated by dividing the given change by the average management income using base values and the given size of enterprise and size of combine. For the 200 acre enterprise the harvest is completed within the harvesting season in the first and third years using either combine. Harvest is not com- pleted in the second year with either combine due to the adverse weather conditions. With a 500 acre enterprise the two—row never completes harvest during the harvesting period, whereas the four-row completes harvest in the first and third years. Appendix Tables C. 5 and C. 6 contain the actual values for the changes for a 200 and a 500 acre enterprise respectively. The ranking for completion and non— completion in decreasing order Of importance is contained in Appendix Tables C. 7 and C. 8 for the two enterprise sizes. Table 31 95 Table 32. The Direction of the Change in Management Income from Changing the Variables with and without Completion of Harvest During the Harvesting Period Variable Completion No Completion Size of enterprise Temperature Price Yield Grain moisture Opportunity cost Hours Rainfall Loss Increased income with increased size Small increases with higher temperature Increased income with price increases Increased income with yield increases Decreased income with increased maximuma Lower income with increased labor cost Lower income with increased hours Increased income with additional rainfall No effect Decreased income with increased size Large increases with higher temperature Increased income with price increases Increased income with yield increases Increased income with increased maximuma Lower income with increased labor cost Higher income with increased hours Lower income with additional rainfall Lower income with increased loss a . . Increased max1mum means an earlier harvest. .351 in: 96 Table 33. The Ranking of the Variables and the Percentage Change in Management Income when Harvest is and is not Completed for a 200 Acre Enterprise for a Two—Row and a Four-Row Combinea 2-row 4—row Not Not Variable Completed Completed Completed Completed b % c b % c b % c b % c Rank Change Rank Change Rank Change Rank Change Size of enterprise 1 60.0 1 146.8 1 49.0 1 141.7 Temperature 3 25.1 3 26.9 3 22.8 2 30.0 Price 2 35.9 5 20.6 2 30.3 3 23.6 Yield 4 23.5 6 17.2 4 21.5 4 20.0 Grain moisture 7 5.3 8 5.8 5 10.5 6 8.5 Opportunity cost 5 10.5 7 13.7 6 5.5 8 5.5 Hours 6 7.2 4 24.2 7 4.5 5 11.5 Rainfall 8 4.2 9 0.0 8 2.5 9 —0- Loss 9 0.0 2 43.1 9 —0- 7 6.8 8Completion of harvest means completed by December 1. bThe rank is based on the absolute value of the change in manage— ment income. cThe percentage change in each variable is based upon management income using the base values 2-row = $—3622, 4—row = ~$3827. 97 Table 34. The Ranking of the Variables and the Percentage Change in Management Income when Harvest is and is not Completed for a 500 Acre Enterprise for a Two-Row and a Four-Row Combinea 2-rowb 4-row Variable Not completed Completed Not completed c Z d c % d c Z Rank Change Rank Change Rank Change Size of enterprise 2 34.9 2 51.3 1 112.8 Temperature 5 22.4 4 42.6 4 43.6 Price 4 25.3 1 67.9 5 35.9 Yield 6 17.5 3 45.2 7 31.1 Grain moisture 9 8.1 8 0.7 9 9.6 Opportunity cost 8 10.4 6 10.1 8 11.4 Hours 3 27.2 5 16.9 6 35.5 Rainfall 7 14.2 7 9.1 3 43.7 Loss 1 50.9 9 -0- 2 107.1 aCompletion Of harvest means completed by December 1. bThe harvest was not completed using the two—row combine in any of the three years. CThe rank is based on the absolute value of the change in management income. dThe percentage change in each variable is based upon management income using the base values 2—row = $-9499, 4-row = $-4788. 98 When the harvest is completed before December 1, the size of enterprise, price, temperature and yield have major effects on manage- ment incomes. For the given changes, each of the four variables affected income by more than 20 per cent under each situation where harvesting is completed. None of the other variables consistently affect income as much as 10 per cent. The variable changes which in- crease the speed of harvest--increased hours in the work day, higher maximum grain moisture and lack of additional rainfall--create a minor decrease in income. The opportunity cost of labor has only a small effect since the labor expense for Operating the combine is not a major expense. When harvest is not completed during the harvest season, the rankings have less pattern than for completion of harvest but more than for the individual years. The reduction in the degree of similarity is created because each situation has a different proportion of the corn still in the field at the end of the harvesting period. Most farm managers seldom face this problem Of not being able to complete harvest; however, when they do, they are faced with a situation where at least six of the nine variables have a large effect on income. The four variables that are important when harvest is completed-—size Of enterprise, temperature, price and yield are still very important. The size of enterprise and average temperatures have a greater effect while price and yield have a slightly diminished effect. The variables loss and hours now consistently have a large effect on income. Only with a four-row combine and a 200 acre enterprise was the effect of loss less than 40 per cent or the effect of hours less than 20 per cent. The effect was much less with the four—row combine on a 200 acre f1 US (J1 99 enterprise because only 16 acres were left unharvested. Changes in the maximum grain moisture and rainfall seldom had a large effect be- cause on the days when the changes would have had an effect, the soil was usually not tractable. The opportunity cost of labor was the only variable that never showed a potentially large effect. These conclu- sions would indicate that when a farm manager reaches a situation either because of bad weather or poor management where he may not complete harvest on time, he will have to consider an increased number of variables. Effect of Changes in Variables on the Choice Of a Combine Changes in the nine variables being studied can also affect the choice of a two-row or a four-row combine. Using the same changes as in the previous section, the effect of the nine variables on the rela- tive income position created by the use of each machine is studied. For each variable the change in difference in management income received from the two machines (income using a four—row combine minus income using a two-row machine) is calculated. Appendix Tables C. 9 and C. 10 present for 200 and 500 acres respectively the actual change in the difference between the two machines for each of the three years and the average of the three years. Appendix C. 11 then shows the corresponding rankings in order of decreasing importance for 200 and 500 acre enterprises in each Of the three years and the average Of the three years. Once again the yearly rankings are scrambled because in some years harvest is completed during the harvest season while in others 100 it is not completed until December 31. The values for the individual years indicate that the variables size of enterprise, loss and hours in the work day are of major importance when a choice is to be made be- tween a two—row and a four—row combine.‘ Under certain conditions the grain moisture criterion and rainfall appear to be important variables. In comparing the two machines relative to completion Of harvest, three categories are needed: one in which both combines complete the harvest during the harvest season, one in which the two—row does not finish but the four-row does and one in which neither combine com- pletes the harvest. The first and third years with 200 acres fill the first category. The first and third years with a 500 acre enterprise occupy the second category while the second year for both enterprise sizes is contained in the third category. Since the years and acreages differ, the actual values are highly questionable; however, the relative values and the rankings from the changing variables pro— vide valuable insight into the effect Of these variables on the choice of machines. Appendix Table C. 12 lists the actual values ranked in descending order for each Of the three categories. Table 35 ranks each of the nine variables and shows a percentage change in income for each of the three categories. Since no logical base was available, the percentage change is based upon an average of the management in- come from the two machines used on the two enterprise sizes (—$5,434). A quick glance at the first part of Table 35 illustrates to the reader that changing the variables under study has little effect on the relative income position Of the machine when both combines complete harvest during the harvest period. Although the increase is small, 101 Table 35. The Ranking Of the Variables and the Percentage Change in Management as to the Effect on the Choice between a Two—Row and a Four-Row Combine Both 4-row Neither .Complete ., Complete . Complete % % % Rank Changea Rank Changea Rank Changea Size of enterprise 1 5.6 1 87.9 8 0.1 Temperature 6 0.4 9 1.8 7 1.7 Price 8 -0— 7 7.8 5 2.9 Yield 5 0.5 8 6.7 6 2.2 Grain moisture 3 2.0 5 16.6 4 3.1 Opportunity cost 2 3.1 6 8.4 2 5.6 Hours 4 1.3 2 78.4 3 3.6 Rainfall 7 0.1 4 22.3 9 -0— Loss 8 -0- 3 77.1 1 24.0 8The percentage change is the change in the difference in management income between the two combines divided by a base which is the average income from the two combines and the two sizes Of enterprise. Base = —$5,434. 102 the relative income from the four—row increases as the size of the enterprise increases. In addition to this relative increase, the value of the four-row increases with increasing size since the prob— ability Of the two—row failing to complete harvest increases. When only the four-row combine completes harvest during the harvest period, five variables provide a major influence on the rela- tive income position of the two combines. These five variables in decreasing order of importance are: Size (87.9 per cent), hours (78.4 per cent), loss (77.1 per cent), rainfall (22.3) and grain moisture (16.6 per cent). As size increases, the four—row quickly becomes more profitable since it is harvesting the additional acres during the harvesting period while the two-row is not. Increases in the loss on those acres not harvested during the harvesting season further increases the relative income position of the four-row. The other three variables of major importance affect the amount Of har- vesting time available. Decreases in the work day, decreases in the maximum grain moisture and additional rainfall shorten harvesting time and thus improve the relative income position of the four-row combine. Increasing labor costs, prices and yield all provide minor increases in the relative income position Of the four—row combine. When neither combine completes harvest, the only variable showing a major effect is the loss (24.0 per cent). Some or all of the vari- ables showing major effects in the previous category would probably have greater effects under different conditions. Only the second year fits this category so the figures have limited scepe. In this situation of failure to complete harvest, the real question would almost 103 certainly be which combine would minimize losses. The answer invari- ably would be the four-row as it would harvest more acres before the end of the harvest period. From the above analysis some conclusions can be reached con- cerning when each of the combines would be more profitable. When completion of harvest is a near certainty with either machine, the two-row is more profitable since its ownership costs for depreciation, interest, housing and insurance are $671.00 less than for the four-row and variable cost are very similar. The farm manager should keep in mind that the effect of increasing size by 100 acres when only the four—row completes harvest during the harvesting season improved by nearly $5,000.00 the relative income position of the four-row. Based upon the magnitudes of these two values, the farm manager would appear to be smart to choose the four-row whenever the probability of the two-row not completing harvest became very large. In making a deci- sion of this type, a farm manager must estimate values for the above figures based on his own Operation. An Analysis of Each Variable In this section each of the nine variables is analyzed indi- vidually. Particular attention will be directed to those variables the farm manager can control; size, hours and grain moisture criterion. A decision-making rule to determine the optimum value for each of these variables is sought. The variables are discussed in decreasing order of importance when harvest is completed during the harvesting period. 104 Size Of the Enterprise This variable has by far the greatest effect on a harvesting system. The size of the enterprise must be determined long before the harvesting season begins. Not only must the corn be planted but in- vestment decisions concerning the combine and other machinery must be made. Ownership costs including depreciation, interest, housing and insurance are very high for harvesting equipment. These costs average $2,013 and $2,684 for the two-row and four-row combines respectively using the coefficients in the model. To maximize profits these costs must be spread over as many acres as possible. As is illustrated in Table 10, page 63, machinery expenses for the four-row were $3,654 for 200 acres and $4,471 for 500 acres. On a per acre basis this is $18.27 and $8.94 per acre for 200 and 500 acres respectively. On the other hand, the ranking Of the effect of changes in variables illustrated that if harvest is not completed in the harvest season, large losses would result from increases in size. These losses amounted to approximately $5,000 a year. Table 36 presents the gain from increasing acreage when harvest is completed and the loss from increasing acreage when harvest is not completed before December 31 for the three years studied. 105 Table 36. The Effect of Increasing the Size of the Enterprise 100 Acres when Harvest is and is not Completeda Machine Completed Not completed 2-row gain $2,176.00 loss $4,316.00 4-row gain $2,166.00 loss $5,412.00 8All other variables given values used initially. From the above discussion the conclusion can be drawn that given constant values for other variables, the size of the corn enter- prise for harvesting purposes must be a function of the expected gain from increasing acreage when harvest is completed during the harvest season, the expected loss from acreage increases when harvest is not completed and the estimated probability of completing harvest. Since the loss from failure to complete harvest depends upon the number of acres not harvested, an accurate value would require analysis of many years and a probability distribution for the number of acres not har- vested. With this figure and a more accurate gain figure, the profit maximizing enterprise size can be determined. The enterprise size should be increased until the probability of not completing harvest gain ) equals (gain + loss A farm manager who places increased value on reducing risk and a stable income would reach his optimum with a smaller probability of not completing harvest and therefore a smaller acreage. Conversely, a manager wishing to gamble would increase his Size above the profit maximizing acreage. The reader must keep in mind that this optimum acreage only applies to harvest, and the actual acreage may be reduced by bottlenecks at planting time. 106 The fact that most farm managers begin harvest on about the same date each year would indicate that they are using a decision- making rule consistent with this conclusion. The manager's decision rule is certainly less formalized and precise; however, the above calculation would be made ex poste whereas the farm manager must make his decision ex ante. Price As any farm manager would say, the price of the corn being sold is an extremely important variable. When the harvest is completed during the harvesting period, the importance of price is second only to size. The magnitude of the effect of price is almost identical when harvest is and is not completed. Its rank, however, is much lower when harvest is not completed because of the increased effect of the variables affecting the duration of the harvesting period. As the size of the enterprise increases, the price assumes a greater role (assuming perfect competition). With very large enter- prises economic survival may depend On accurate price prediction. For the four-row combine a $.20 price change altered management income $4678.00 for 200 acres and $10,955.00 for 500 acres. The expected price will affect nearly every decision the farm manager makes. Increases in price are going to increase the profit maximizing size of enterprise by increasing the amount of gain when harvest is completed and decreasing the loss when harvest is not com- pleted during the harvest season. The price has a definite although relatively minor effect on the choice of a combine as increases in price increase the relative profitability of the four-row combine. 107 Temperature Changes in the average temperature result somewhat surprisingly in large changes in income. These income changes occur because in- creases in average temperature decrease the grain moisture content which diminishes drying and hauling charges with a resulting increase in income. This effect has dramatic and unexpected results when the temperature is decreased in the corn simulation model. With a 5 degree decrease the grain moisture in the first and second years failed to fall below 30 per cent long enough for harvest to be completed. By allowing harvest to occur above 30 per cent after the harvest season, harvest did occur; however, income from 500 acres with a four-row combine is $28,599.00 and $7,073.00 for the first and second years respectively (2). Since the effect of temperature appears to be greater when harvest is not completed prior to December 1. Although temperature changes have very little effect on the choice of a combine in the years being studied, the potential effect is great. Anytime that the temperature affects the length of harvest and the harvest is not completed in the harvest season, a large effect on the choice of a combine could result. Yield The same conclusions that were reached for the effect of changes in the price can be drawn for the effect of changes in yield. This Change refers to changes in the potential yield as of October 15 rather than actual changes. This variable also has a greater effect Vfllen harvest is completed since more of the additional bushels are 108 harvested or more of a reduction occurs. Furthermore, the effect is greater as the size of the enterprise increases and yield increases favor the larger four-row combine. Opportunity Cost Changes in the Opportunity cost of the combine operator have the most consistent effect on income. This effect is consistently relatively minor. Increases in this charge decrease income while decreases increase income. Also, increased labor charges are favorable to the choice of the larger four—row combine since harvest is com- pleted more quickly. This minor effect of labor charges is largely a result of the limited scope of this analysis. First, only the harvesting system is being studied. This restriction reduces the labor used greatly. Further— more, only the combine operator's time is counted. The transporattion and storage of the harvested corn is given a specific, unrelated change. Thus, the effect of the labor costs are greatly reduced in this model. Hours The effect of changes in the number of hours in the working day is quite small when the harvest is completed easily. Even when the harvest is not completed prior to the end of the harvest season, changes in the length of the work day are the easiest way of increasing harvesting time. The analysis of how to determine the maximum length of the working day must be divided into two parts. The first part Of the analysis involves conditions where a set length for the working days must be determined. The second part involves situations where the length can be varied. 109 For both analysis the other variables are assumed to be con- stant. The length of the harvesting seasons including the date or a decision—rule to determine the date for commencing harvest. In both parts of the analysis increased hours decrease income when the harvest is completed easily since drying and hauling charges are increased and increase income when harvest is not completed since a larger acreage is completed. Table 37 illustrates this gain or loss. Table 37. Gain or Loss in Income Due to an Increase of Two Hours in the Length of the Work Day Machine Completed Not Completed 2-row loss of $262.00 gain of $1728.00 4—row loss of $490.00 gain of $1069.00 When a constant length of the work day must be determined, this length will depend upon the loss from increasing the work day when harvest is completed easily, the gain from increasing the length when harvest is not completed before loss results and the probability of completing the harvest. If increasing the length of the work day re- sults in increased per hour costs, the gain and loss figures must be adjusted accordingly. As with the size of the enterprise, accurate values for the gain and the loss could be calculated. The length of the work day should be increased until the probability of completing *gain ) . . A risk averter would work gain + loss harvest is reduced to equal ( longer hours while a risk taker would reduce his work day. 110 In the case where the length of the work day can be varied, the same variables will be considered, however, these variables will be changing and will be evaluated daily or periodically. Thus, if har- vesting is going very well, the probability of completing harvest will increase and the length of the work day decreased. On the other hand, if rain or repairs delay the harvest, the length Of the day can be increased to maximize profit. Once again the farm manager from his ex ante position will be unlikely to be as precise as the preceeding examples. There is little doubt, however, that this type of analysis does occur. The farm manager would be most concerned with the probability of completing harvest. Grain Moisture The question of when should the harvest commence is important and difficult to answer. In the simulator this decision was a func— tion of the grain moisture content alone. Of course harvest could not actually begin until the first tractable day after this criterion was met. This criterion did not have a major effect on income; however, this small effect was largely due to the changes used and the rainfall conditions. The date at which harvest starts is, however, a major determinant of income especially when harvest is not completed. Once again this variable has Opposite effects depending upon whether harvest is completed during the harvesting season. As Table 38 illustrates, increasing the maximum grain moisture during harvest decreases income when harvest is completed and increases income when 1038 :results due to failure to complete harvest. 111 Table 38. Effect of an Increase in the Maximum Allowable Grain Moisture During Harvest Machine Completed Not Completed 2-row loss of $191.00 gain of $488.00 4-row loss of $220.00 gain of $392.00 Once again the maximum profit will be a function of loss when harvest is completed, the gain when it is not completed. Using the same method used previously, profit will be maximized when the prob— gain ) gain + loss ° ability of not completing harvest equals ( Rather than using the above calculations, a criterion could be develOped using the harvester size and the size of the corn enterprise to determine the starting date. With this criterion the grain moisture content would have no influence on the starting date. On the other hand, with the previous method the gains and losses were partially determined by the grain moisture content. Rainfall The effect of additional rainfall is very inconsistent because the effect depends upon the soil moisture and rainfall conditions when the additional rainfall occurs. When harvest is completed, additional rainfall has very little effect especially since the rainfall has little affect on the moisture content when harvest occurs. When harvest is not completed during the harvesting period, the significance Of additional rainfall depends upon the effect of the rain on the harvesting time available. Any reduction in this time decreases 112 income. In general additional rainfall increases the relative income position of the larger four-row combine. Loss As soon as failure to complete the harvest during the harvesting period occurs, the size of the resulting loss becomes important. With anything more than a few acres this loss has an important effect on the income. A function approaching real world conditions must have the percentage of loss increasing as the acreage not harvested in- creases. No satisfactory function has been found. Footnotes 1. 5° increase was used because the decrease had a very large effect since the grain moisture content remained above the minimum. 2. These figures were not used in the ranking of variables since there magnitude resulted largely from an unrelated assumption of the model. CHAPTER VI RESULTS FROM THE LONG-RUN REPLACEMENT ROUTINE In the previous two chapters the individual harvesting period was analyzed. The analysis now turns to a longer period of several years so that optimum machinery replacement can be considered. In the first part of this chapter the variables to be studied relative to their effect on Optimum replacement are specified and the results from using different values for each of these variables are specified. These results are needed to determine the effect of the selected variables on the long-run replacement decision. The second and final part of this chapter specifies the Optimum long-run replacement policy for the combines used in the corn simulator. Long—Run Results The effect of the variables chosen on long-run replacement decisions is studied using the dynamic programming replacement model discussed in Chapter III. The effect of the variables on the optimum replacement period and on the minimum cost level is presented in this section. The following seven variables are studied: 1. The source of the cost data. 2. The shape of the repair cost function given total repair cost. 3. The number of hours the machine is used. 113 114 4. Level of machinery management as reflected in repair costs. 5. Rate of obsolescence. 6. Increasing cost of the new machine. 7. The interest rate. The procedure used to study each of these variables is to deter- mine, for each of several values, the repair costs for the present machine for one additional year and the cost of trading the present machine for a new machine plus the repair costs for the new machine for the first year. These calculations are made yearly for the machine when it is one through seven years old. The optimum time to replace the machine is determined for six different interest rates. The interest rates are 0.0, 5.0, 7.5, 10.0, 12.5, and 20.0 per cent. The two-row combine used in the corn harvest simulator is used throughout. The results from using the selected values for the variables are presented for a specified interest rate as "keep x years" where x can be from one to seven. This result means that to minimize cost at the specified interest rate, the new two-row combine (initial cost = $12,000) should be kept x yearsand then traded for another new com- bine. If the interest rate is zero, the average yearly cost using the Optimum replacement policy is presented. When the interest rate is greater than zero, the discounted present value of the infinite cost stream commencing with and including the year in which a new combine is acquired by trade is presented as the cost figure. This figure assumes the Optimal replacement policy is followed. The cost for keeping and trading in each of the seven years and the Optimum policy for each interest rate with the corresponding minimum cost are 115 presented in Appendix D for the general case with each set Of data. Similar tables for all sets of variables are on file with the Depart- ment of Agricultural Economics, Michigan State University. In the following pages each of the variables will be discussed separately with the results presented. Unless specifically indicated otherwise, the cost of keeping the used machine is only repair costs, and the cost to trade is only the cost of the new combine minus the trade—in value of the used combine plus the first year repair cost for the new machine. Two hundred hours of use is used as a base. Repair Function Three sources are used to derive two sets of data. The first data set uses a repair cost function derived by Armstrong (1) and a trade-in value function derived by Peacock and Brake (2). The second set is developed by Bowers (3). Table 39 presents the cost of keeping and trading a combine used 200 hours per year using the two sets of data. There is a very striking difference between the cost of keeping the used machine with the cost being much lower with the Bowers data. The cost to trade increases more rapidly with the Bowers data because he has the value of the used machine dropping more rapidly. The resulting optimum replacement policy and its cost are pre- sented in Table 40. The optimum policy requires the manager to use the machine longer using the Armstrong data. Also the cost is less. Note that the optimum policy depends on the interest rate with the Bowers data. Higher interest rates result in keeping the machine longer since the large "trade" cost is delayed and thus reduced further by discounting for an additional year. The higher the interest rate 116 Table 39. The Cost of Keeping and Trading the Two-Row Combine Used 200 Hours per Year with the Two Sets of Data Cost to Keep8 Cost to Trade Age Of Machine Armstrong Bowers Armstrong Bowers (dol.) (dol.) (dol.) (dol.) l 734 228 5862 5244 2 899 480 _ 6306 5952 3 1158 816 6750 6600 4 1473 1248 7194 7176 5 1806 1784 7638 7680 6 2119 2376 8082 8148 7 2374 3072 8526 8556 3Cost to keep is the expected repair cost for the following year. bCost to keep is $12,000 minus the trade-in value of the given used machine plus the repair cost for the first year which is $710 for the Armstrong data and $60 for the Bowers data. Table 40. The Optimum Replacement Period and Its Cost for Each Set of Data for a Two-Row Combine Used 200 Hours Armstrong Bowers Optimum decision Keep 6 years for 0 Keep 5 years for 0 and 5% interest and 5% interest Keep 7 years for Keep 6 years for :_7.5% interest > 5% interest Yearly cost with no interest $2359 $2090 Discounted present Value with 7.5% interest $36,886 $32,978 117 the greater the discounting and thus the greater the savings from delayed expenditures. The Shape of the Repair Cost Function The shape of the repair cost function given a constant total repair cost affects the optimum replacement decision. For this study the total repair cost for years two through seven using Armstrong's function is $10,560. The first year is not included so that the cost of trading remains unchanging. Several shapes are used besides the normal one given by Armstrong's function. The first shape is to spread the repair cost uniformly over the six years for an average cost of $1761. For the second shape a steadily increasing function is used with each year being the same amount greater than the previous year. The remaining shapes all use the exponential probability density function with different A's. The procedure used in deter- mining the shape of the function is to determine the probability of each of the intervals (0, 1), (l, 2) ..., (5,6) for the given A. These six probabilities are then adjusted so they equal one. Then, since the exponential probability density slopes in the opposite direction of the desired slope, the order of the six probabilities is inverted, and the probability represents the prOportion of the total repair cost ($10,560) in that year. For example, the adjusted probability of being between 5 and 6 equals the prOportion of the total repair cost in the first of the six years which represents the repair costs for the second year for the machine. The values of A used are .2, .3, .4, .5, and 1.0. 118 Figures 14-21 Show the distribution of the eight functions along with the Optimum policy and its cost. Table 41 summarizes the optimal replacement periods. The reader should note the lack of any relation- ship between the length of time the combine is kept and the average cost of the Optimum replacement policy. The machine is kept for seven years with a uniform cost structure because the replacement model as presently developed only allows a machine to be kept seven years. The combine would be kept forever if the uniform cost were allowed to continue. Number of Hours of Machine Use The effect of the number of hours the combine is used depends on the set of data used. Both sets mentioned previously are studied. The first set using the Armstrong and Peacock-Brake data showed no effect on the Optimum replacement pattern by changing hours of use. The reason for the lack of change is that an increase in the hours used increases repair costs in all years an identical amount. The optimum replacement pattern and the average yearly cost without discounting are shown in Table 42 using this data for 100, 200, 300, and 400 hours of use. The "keep" cost for this data includes $360 (3 per cent of the new cost) for each year of age to cover Obsolescence costs. The optimum replacement policy is to keep the combine four years for all interest rates. The second set of data from Bowers shows significant change in the Optimum policy with different hours of use. The optimum policy and the average yearly cost are shown for 100, 200, and 300 hours of use ll9 Optimal Policy Average Yearly Cost: $2,339 Keep 6 years for 0 and 5% interest Discounted Present Value (7.5%): Keep 7 years for $36,886 :_7.5% interest Yearly Cost 7000 6000 a 5000 - (Dol.) 4000 _ 3000 _ _—EII§“* 2000 ~ 1806 1473 1158 1000 899 734 2 3 4 5 6 7 Age (Years) Figure 14. The Distribution of the $10,560 of Total Repair Costs Through Years Two Through Seven Using Armstrong's Function 120 Optimum Policy Average Yearly Cost: $1,761 Keep 7 years Discounted Present Value (7.5%): $42,266 Yearly Cost (dol.) 7000 6000? 50004 V 4000 U 3000 2000r 1761 1761 1761 1761 1761 1761 1000 V Age Figure 15. The Distribution of the $10,560 of Total Repair Costs for Years Two Through Seven for a Two-Row Combine with the Costs Spread Uniformly Yearly Cost (dol.) 7000 6000« 5000- 40004 30004 2000 I 1000 , 121 Optimum Policy Keep 5 years for 3_12.5% interest Keep 6 years for 20% interest 503 2011 Average Yearly Cost: $2,533 Discounted Present Value (7.5%): $38,546 3017 2514 Age Figure 16. The Distribution of the $10,560 of Total Repair Costs for Years Two Through Seven for a Two—Row Combine with a Steadily Increasing Function 122 Optimum Policy No interest Keep 5 years Average Yearly Cost: $2,645 Discounted Present Value (7.5%): Interest :_12.5% $40,441 Keep 6 years Interest 20% Keep 7 years Yearly Cost (dol.) 7000 6000' 5000 — 4000 - 3000 - 2726 2239 2000 _ 1838 1510 1000 - 1225 1014 2 3 4 5 6 7 Age Figure 17. The Distribution of the $10,560 of Total Repair Costs for Years Two Through Seven for a Two-Row Combine with a l-Exponential (A = .2) Distribution 123 Optimum Policy Average Yearly Cost: $2,497 Interest (:_12.5%) Keep 5 years Discounted Present Value (7.5%): Interest (= 20%) $38,194 Keep 6 years Yearly Cost (dol.) 7000 I 6000 5000 . 4000 I *7 3285—7 3000 2429 2000 ' 1796 1342 718 Age Figure 18. The Distribution of the $10,560 of Total Repair Costs for Years Two Through Seven for a Two-Row Combine with a l-Exponential (A = .3) Distribution 124 Optimum Policy Average Yearly Cost: $2,358 Keep 5 years Discounted Present Value (7.5%): $36,231 Yearly Cost (dol.) 7000 I 6000 5000*‘ 4000 \ 3834 3000 I 2567 2000 I 1711 1000 1151 I 507 782 Age Figure 19. The Distribution of the $10,560 Of Total Repair Costs for Years Two Through Seven for a Two—Row Combine with a l-Exponential (A = .4) Distribution 125 Optimum Policy Average Yearly Cost: $2,237 Keep 5 years Discounted Present Value (7.5%): $34,553 Yearly Cost (dol.) 7000 6000 I I 5000 4373 I 4000 3000 I 2662 2000 I 1616 1000 ______ __ _._____‘ 982' I 359 2 3 4 5 6 7 Age r——~———a { ‘591 '7‘ Figure 20. The Distribution Of the $10,560 of Total Repair Costs for Years Two Through Seven for a Two-Row Combine with a 1-Exponential (A = .5) Distribution 126 Optimal Policy Average Yearly Cost: $1,808 Keep 5 years Discounted Present Value (7.5%): $28,776 Yearly Cost (dol.) 7000 6676 6000 5000— 4000 I 3000 I 2461 2000 I 1000 T 897 NM“ 2 3 4 5 6 7 Age Figure 21. The Distribution of the $10,560 of Total Repair Costs for Years Two Through Seven for a Two-Row Combine with a l-Exponential (A = 1.0) Distribution 127 .OOOOO mo OOOHCMOCOM OMOON OO>OO MOOMO COOOHOOM OH OOHOOOE OOHO CHCN NCCN CmCN CHHC NH«C CoCC CHCC «HCN OOOO NHMOON OCOMO>< m m m C N C N N NC.CN m m m m C m N N Nm.NH m m m m C m N N NC.CH m m m m C m N N Nm.N m m m m C m N C NC.m m m m m m m N C NC.C C.H n H m. u H «. u H C. u H N. u H OOOOMoOH OEMOCHOD COOMOOEMO OOOM OOOMOOOH :OOOm: MOON mo MOnEOz OOOOC MHOOOC HOOOH mo CCm.CHC OLO MOO OOOHOOCHMOOHQ OOOMOCCHC OOCHC OOO Mom COHMOO OOOOOOOHOOm ODOHOOC OOO mo NMOOEOC .H« OHCOH 128 Table 42. The Effect of Different Hours of Use on the Optimum Replacement Pattern and the Corresponding Cost Using the First Set of Data8 Average Yearly Cost Optimum replacement 100 hours 200 hours 300 hours 400 hours patternb (dol.) (dol.) (dol.) (dol.) Keep 4 years 2736 3036 3336 3636 aThe "keep" cost include $360 per year for obsolescence cost, i.e., one—year old machine has $360 obsolescence cost, two-year old machine has $720 obsolescence cost, etc. bThe Optimum replacement policy is identical for all hours of use. Table 43. The Optimum Replacement Pattern and Corresponding Costs for a Two—Row Combine Used 100, 200 and 300 Hours per Years Using the Bowers Dataa Hours of Average yearly use Optimum policy cost (dol.) 100 Interest :_12.5% keep 5 years 2405 Interest = 20.0% keep 6 years 200 Keep 4 years 2715 300 Interest :_12.5% keep 3 years 3068 Interest = 20.0% keep 4 years 3The costs for keeping include $360 (3% of new cost) per year of age for Obsolescence. 129 in Table 43. With this data the length of time the machine is kept decreases as the hours of use increase. Level of Machinery Management The ability of the farm manager with regard to handling machinery has a large effect on the level of machinery repair costs. The level of machinery management is reflected in the maintenance of the machines, in the handling of minor repairs and problems and in the operating of the machine. Three assumptions are made as to how the management of machinery affect the costs of keeping and trading machinery. The three assumptions are: 1. Management affects the level of repair costs but has no effect on trade-in value and obsolescence. 2. Management affects the level of repair costs and the trade-in value but has no effect on obsolescence. 3. Management affects the level of repair cost, the trade— in value and obsolescence. The effect of machinery management on optimum machinery replace- ment is studied using each of the assumptions. Six management levels are used. The levels are: .75, .90, 1.0, 1.1, 1.25, and 1.50 where each level means a person in the given management level will incur that prOportion of the repair costs indicated by the Armstrong function. The repair costs using the function are given in Appendix Table D. 1. For instance, the level .75 is the best management level with these managers only incurring 75 per cent of the repair cost indicated by the function. Using the first assumption that only repair costs are affected by management, the cost of keeping changes as much as the repair cost 130 with the three per cent per year obsolescence remaining constant. With the trade-in cost constant the cost of trading only changes as much as repair costs in the first year change. Table 44 pictures the optimum replacement pattern for each management level for each interest rate and the average yearly cost without discounting for each management level. As the level of management declines repair costs increase in each year. The Optimum frequency of replacement increases as do the average yearly costs. Table 44. The Effect of Alternative Levels of Machinery Management on the Optimum Replacement Pattern and Cost for a Two-Row Combine Given the Assumption that Management Affects only Repair Costsa Number of Years "Keep" Interest rate .75 .90 1.0 1.1 1.25 1.50 0.00% 4 4 4 4 4 4 5.00% 4 4 4 4 4 4 7.50% 4 4 4 4 4 4 10.00% 5 4 4 4 4 4 12.50% 5 5 4 4 4 4 20.00% 5 5 5 5 4 4 Average yearly cost 2818 2949 3036 3124 3254 3473 aUses the first set of data and includes three per cent of new cost per year of age charge for Obsolescence. With the second assumption that management affects repair costs and trade-in value only, the cost of keeping is the same as with the 131 first assumption; however, the trade-in value of the machine is now assumed to be partially dependent on machinery management level of the manager. The trade-in value is now determined by dividing the value calculated with the Peacock-Brake function by the various management level: .75, .90, 1.0, 1.25, 1.50. Table 45 presents the optimum number of years to keep the combine with each management level and the resulting average yearly cost. With this second assumption the optimum frequency of replacement increased as the management level deteriorated; however, note also the much larger increase in average cost with declining management. Table 45. The Effect of Alternative Levels of Machinery Management on the Optimum Replacement Pattern and Cost for a Two-Row Combine Given the Assumption that Management Affects Repair Cost and Trade-in Valuea Number of Years "Keep" Interest rate .75 .90 1.0 1.10 1.25 1.50 0.00% 3 4 4 4 4 4 5.00% 3 4 4 4 5 5 7.50% 3 4 4 4 5 5 10.00% 3 4 4 5 5 5 12.50% 3 4 4 5 5 5 20.00% 4 4 5 5 5 5 Average yearly cost 2298 2796 3036 3249 3530 3932 3Uses the first set of data and includes three per cent of new cost per year of age charge for obsolescence. 132 With the third assumption repair costs, trade-in value and Obsolescence charges are all affected by the management level. The repair costs and the trade—in value are affected as in the previous assumptions and the Obsolescence charges are affected like repair costs. Table 46 presents the optimum replacement frequency and the average yearly cost for this assumption. No overall pattern is shown in the frequency as the management level changes, but the costs in— crease rapidly as the management level deteriorates. Table 46. The Effect of Alternative Levels of Machinery Management on the Optimum Replacement Pattern and Cost for a Two-Row Combine Given the Assumption that Management Affects Repair Costs, Trade-in Value and Obsolescence Chargesa Number Of Years "Keep" Interest rate .75 .90 1.00 1.10 1.25 1.50 0.00% 3 4 4 4 4 4 5.00% 4 4 4 4 4 4 7.50% 4 4 4 4 4 4 10.00% 4 4 4 4 4 4 12.50% 4 4 4 4 4 4 20.00% 4 5 5 5 5 5 Average yearly cost 2208 2742 3036 3302 3665 4202 8Uses the first set of data. Obsolescence Charges As the machine the farm manager is using increases in age, his present machine becomes increasingly inefficient in comparison to a 133 new machine. The degree Of inefficiency depends on the type of machine, its age, and the improvements in the new machine. For this study Obsolescence charges are calculated as a per cent per year of the new cost. Four levels are used: 0.0, 3.0, 6.0, and 10.0 per cent. The new cost of the two-row combine is $12,000. Table 47 illustrates the effect of the rate of Obsolescence of the optimum replacement frequency and corresponding average yearly cost. The length of time before trading decreases and the cost increases as the obsolescence rate increases. Table 47. The Effect of Different Levels of Obsolescence Cost on the Optimum Replacement Pattern and Cost for a Two-Row Combine Number of Years "Keep" Interest a rate 0.00% 3.00% 6.00% 10.00% 0.00% 6 4 3 3 5.00% 6 4 3 3 7.50% 7 4 3 3 10.00% I 7 4 3 3 12.50% 7 4 3 3 20.00% 7 5 4 3 Average yearly cost (dol.) 2359 3036 3514 3994 a3, 6, and 10 per cent per year of age. Increasing Cost When a farm manager decides to purchase a new machine, he usually finds that the price is considerably above the amount he paid 134 for the machine he presently owns. This price rise can be a large increase with a constant price thereafter or a gradual increase. Two different price increases are used here. The first increase is of $1000 the year after the farm manager purchased his new combine while the second increase is 5 per cent of the new cost of the first machine per year ($600 per year for the two-row combine). Repair costs, trade-in value and Obsolescence charges remain the same. The Optimum Policy and Corresponding Cost for the two types of increases and no increase is shown in Table 48. Note that the one-show increase delays the trade-in time significantly and the steady increase delays trade- in slightly under certain circumstances. Interest Rate The previous tables have adequately illustrated the impact of increasing interest rates in delaying optimum trade-in time. As the interest rate rises future costs are discounted more and more. Since the largest cost of machinery is at trade-in time, higher interest rates often delay the Optimum trade-in time one year. Optimum Replacement in the Corn Harvesting System Using the base values except for size of enterprise, the aver— age hours of use for the two—row combine are 128 and 330 for 200 and 500 acres respectively. For the four—row an average of 70 hours and 179 hours are used for 200 and 500 acres respectively. The optimum replacement frequencies and costs are found in Table 49 using the Armstrong repair costs function and the Peacock—Brake function for trade-in value and no Obsolescence charge. The two-row combine has a 135 Table 48. The Effect of Increasing Purchase Cost for a New Two-Row Combine on the Optimum Replacement Patterna Number of Years "Keep" Interest rate No increase $1,000b 5% per yearC 0.00% 4 4 4 5.00% 4 4 4 7.50% 4 4 4 10.00% 4 4 5 12.50% 4 5 5 20.00% 5 5 5 Average yearly cost (dol.) 3036 3111 3638 aUses the first set of data with three per cent per year of new cost charged for obsolescence. bIncrease is assumed to be the year after purchase with no further increases expected. C$600 per year for the $12,000 two—row combine. 136 Table 49. The Optimum Replacement Policy for the Two-Row and Four—Row Combine Used in the Corn Harvest Simulator for 200 and 500 Acresa Number of Years "Keep” Interest rate 2-row 200 A. 2—row 500 A. 4-row 200 A. 4-row 500 A. 0.00% 6 6 6 6 5.00% 6 6 6 6 7.50% 7 7 7 7 10.00% 7 7 7 7 12.50% 7 7 7 7 20.00% 7 7 7 7 Average yearly cost 2376 2982 2936 3304 a Based on the actual hours used for base values. 137 new cost of $12,000 and the four—row costs $16,000. As the results previously showed, the number of hours of use does not affect the replacement using this set of data. The size Of the machine has no effect either since the same values are multiplied with a different initial cost. Footnotes 1. The function is 2 3 ARC = NC [(-.0197Xl + .OO87X1 — .00053X1 ) + (.02 + .00025X2)] where: ARC = annual repair costs NC = new cost of machinery being considered X1 = age of machine X2 = hours of annual use. The source is: An unpublished working paper written by Dr. David L. Armstrong for the corn simulation model. The working paper is based upon the following work: Armstrong, David L. and J. Edwin Faris, Farm Machinery Costs, Performance Costs, and Combination, California Agricultural Experiment Station and the Giannini Foundation of Agricultural Economics, Giannini Research Report 273, March 1964, pp. 13—14. and Huber, S. J., "Depreciation and Repair Cost of Self—Propelled Combines," Transactions of the ASAE. 2. The function is: y = (60.7 - 3.7X1) NC where: y = the estimated "market value" of the used machine X1 age of the machine NC = new cost of the machine. The source is: Peacock, David L. and John R. Brake. What is Used Farm Machinery Worth? Research Report 109, Michigan State University Agricul- tural Experiment Station, East Lansing, March 1970, p. 7. 3. Bowers, Wendell. MOdern Concepts Of Farm Machinery Manage- ment, Stipes Publishing Co., Champaign, Illinois, 1970, pp. 18, 35. CHAPTER VII ANALYSIS OF THE REPLACEMENT RESULTS AND INTEGRATION OF THE SHORT-RUN AND LONG-RUN ANALYSIS The analysis in this chapter is divided into two parts. The first part is concerned exclusively with the long-run replacement decision. In this first part each of the selected seven variables is analyzed to determine the importance of its effect on the replace- ment decision. In the second part of the chapter the short-run and the long-run analysis are integrated. Particular attention is placed on determining the effect on the optimum replacement decision of changes in variables affecting the harvesting period. The effect on income from the individual harvesting period of changes in the vari- ables affecting the replacement decision is also considered. Analysis Of the Long—run Replacement Results Due to the nature of the selected variables and the nature of the data required, a ranking of the variables similar to the one used for the harvesting period is impossible for two reasons. The first reason is that changes equivalent to those used with the short-run variables would be impossible. By its nature repair cost data must be situation—specific. This means that replacement decisions must be based on the individual situation rather than general conclusions. 138 139 With this situation—Specific data, rankings would be accurate only for that situation. Although specific rankings cannot be attained, important con- clusions can be reached. An indication of the potential importance of each of the seven selected variables can be found. A determination as to which variables always have an effect and which ones only have an effect under certain circumstances can be made. Finally, a distinction can be made concerning the changes that increase the frequency of replacement and those that decrease this frequency. On the pages that follow, each of the seven selected variables is considered. Conclusions based on the ideas expressed in the previous paragraph are reached. The reader should keep in mind that although a large part of the analysis concerned the replacement frequency, the ultimate objective is to minimize cost over time. Repair Function The discrepancy between the two sources of repair cost data used is rather large. Assuming a 7.5 per cent interest rate, the optimum replacement period is seven and six years for the two sets of data used. The average yearly cost with no discounting also has no consistency with values of $2359.00 and $2090.00. Since neither of these sources of data or any other source is recognized as being accurate, replacement decisions must be situation specific. Not only can the farm manager provide his own data on repair costs, trade-in values and obsolescence charges, he can include any other pertinent charges for either keeping or trading. These additional costs become 140 particularly important when the farm manager trades for a non-identical machine. Shape of the Repair Cost Function Although it is not very apparent, a distinct pattern is present between the shape of the function and the frequency of replacement. With the very unrealistic uniform function the machine is not replaced until it cannot survive for another year. There is no reason to re— place since the cost of keeping is unchanged the following year. As the Slope of the function becomes steeper, the frequency of replacement increases since the increased cost the following year must be averted. This relationship is true up to a certain steepness. Beyond this point the repair costs become so weighted to the last year or two that the optimum replacement frequency increases again. The relationship between the shape of the repair costs and the average cost is much more direct. As the curve increases in steepness, the average cost declines since more of the fixed total amount can be averted. The shape of the repair cost function certainly has an impor- tant effect on the replacement frequency. To the farm manager its importance is only through the effect on his replacement policy. It is not important to him in the sense that he can affect the shape. If he could affect the shape, he would delay as much of the repair costs as long as possible and then trade before the repairs were made. Number of Hours of Machine Use As was indicated previously, the effect of the number of hours of machine use on optimum replacement frequency depends on the source Port With but Le \T e The “hie all 141 of the data. Two further points require analysis. The first is the effect on the ownership cost while the second is the relative impor- tance of hours of use and age of the machine in determining the magnitude of the repair cost. The first point is simple that in- creased hours of use increase the average cost. The relative importance of hours of use and age of the machine on repair costs also depends upon the source of the data. Table 50 illustrates this fact. With the data from the Armstrong function the age is of much greater importance; with the Bowers data the hours of use have a greater effect on repair costs. Once again the answer must be determined by the specific data used. Previously the difference between the two sources of data was described as rather large. Based on Table 50, the reasons for this difference can be determined. The first difference is that the Armstrong function in general has a higher level of repair costs when the machine is new. Secondly, with the Armstrong function the major portion of the increase in repair costs comes from increasing age. With the Bowers data, there is some increase in repair costs with age, but the cost increases much more rapidly by expanding the hours of use especially with older machines. Level of Machinery Management The level of machinery management has a large effect on both the optimum replacement frequency and the corresponding average cost. The effect on the frequency depends upon the assumption regarding which costs management affects. The conclusion can be made that under all circumstances management has an effect on the optimum frequency. 142 Table 50. The Effect on Cost of an Additional 100 Hours of Use Versus an Additional Year of Age on Repair Costs for a Two—Row Combine Armstrong Dataa Bowers Datab Age of machine c d c (years) One year 100 hours One year 100 hours (dol.) (dol.) (dol.) (dol.) l 122 300 168 208 2 165 300 252 426 3 259 300 336 732 4 315 300 432 1110 5 333 300 536 1578 6 313 300 592 2118 7 255 300 696 -- aSee footnotes 1 and 2, Chapter V1, p. 137. bSee footnote 3, Chapter VI, p. 137. c . . . Repair costs at age given minus repair costs preVIOus year with no obsolescence charge for 200 hours. dAverage of difference in repair costs between 100 and 200, and 200 and 300 hours. The 01 to af new m. value trade other avera; ment 1 tradir REEpir This 1 affect trade. tradi: manage this 5 VBIUe n0t. 143 The only way for the effect to be non—existent would be for management to affect the repair costs, obsolescence charges and price paid for a new machine in exactly the same way. Management may affect trade-in value in that manner but not the difference between new cost and trade-in value. The effect of management on average cost, on the other hand, is consistent. Poorer management always produces increased average cost. The effect of the level of management on the optimum replace- ment frequency depends on whether the cost of keeping or the cost of trading is affected more. If the management level affects the cost of keeping more, the frequency decreases as the management level declines. This is the case with the first assumption that machinery management affects repair costs but does not affect obsolescence charges or trade-in value. When the management level effects the cost of trading more than the cost of keeping, the frequency increases as the management level declines. The use of the second assumption creates this situation since the cost of trading changes more as the trade-in value and repair costs are affected but the obsolescence charge is not. With assumption three where all three costs are changing no conclusion can be reached since the cost of trading is affected more if the machine is one or two years old and the cost of keeping is affected more if the machine is three or more years old. For a three year old machine which is the critical age the cost Of keeping is affected only slightly more than the cost of trading. Table 51 shows the optimum frequency with 7.5 per cent interest and the average yearly cost with no discounting for each of the management levels under each of the assumptions. uSOEUi:C...Z fine-...... MOO OIQU HOKEMO>< “.HC—C.COLIOMMOU USO. NUCODUOME OCOEOUQCQOM EJECOQO ~25“ .Hh OCQOH. 144 .COHOOOOOOHC ozn .OOOMOOOH OOOO MOO m.N OOHBO NCN« « NCoC m CN«C « Cm.H mCCC « CCmC m «mNC « mN.H NCCC « o«NC « «NHC « CH.H CCCC « CCCC « CCCC « CC.H N«NN « CoNN « o«oN « Co. CCNN « CoNN C CHCN « mN. H.HOCV OOOO NOOOOUOMC H.HOCV OOOO NOOOOUOMH mHH.HOCV OOOO ONOOOOUOMC NHMOON .O>< EOEHOOC NHMOON .O>< EOEHOOC NHMOON .O>< OOOHOOC HO>OH OOOaOCOOOz C OOHOOOOOOO N OOHOOEOOOO H OOHOOOOOOO oOHnaou BOMIOBH O Mom OOOOC COHCOMH COO COHOOOM Oo OOOeOCOOOz NMOOHCOOZ mo OOOHCM OOO COHOMOoOOo OOHOOOOOOO OOOC COO HO>OH OOOEOCOOOZ OOOC Mom OOOC OCOMO>O COHCOOOOOMMOC COO NoOOOvOMm OOOOOOOHOOM OOOHOOC OOH .Hm OHCOH Obsc tree and dete prob talc extr and tiOn 145 Obsolescence Charges Since obsolescence charges increase the cost of keeping, in— creases in these charges increase the frequency of optimum replacement and the average cost. Although the effect of these charges is easily recognized, the actual value is extremely difficult to determine for two reasons. First, the charge depends on the type of machine, improve— ments in that type of machine since the one being used was purchased, age of the machine, hours of use of the machine and characteristics of the machine Operator. These numerous variables make imperative the determination of obsolescence charges for each situation. The second problem is now encountered. Even in this individual situation, the calculation of the actual loss from not having the newest machine is extremely difficult. This loss will vary from one machine to another and depending upon the field conditions. Even though this determina— tion is difficult and may have to be estimated in many instances, obsolescence changes must be included when determining Optimum replace- ment costs because its effect is great. A cost per acre or per hour may be more accurate than the percentage of new cost used in this study. Increasing Cost With increasing costs for the new machine to be traded for, the cost of trading increases so the optimum replacement frequency should decrease. Although this relationship is true for the two cases studied, it does not necessarily hold. In situations where a lump sum increase occurs immediately after purchase as in the first case studied, the relationship holds; however, when the increase is greater eac? tra- ten upo Of In It the Proj of t does in C inc: Gene easi reple 146 each year, two forces are at work. The first is the increased cost of trading tending to decrease the frequency. The second force is the tendency to trade sooner to avoid the upcoming increases. Depending upon which force is stronger, the frequency can increase or decrease. Of course, the second force increases in strength as the yearly in- creases become larger. Information concerning price increases that will apply to all farms is easier to acquire than the types of information discussed previously. The general inflation rate and/or average price increases for farm machinery could be used. Once again, however, using figures for individual farms is more accurate since the farm manager knows or can determine what price increases are likely in his locality for that particular machine. Interest Rate As explained previously, increases in the interest rate decrease the optimum replacement frequency by making the delay of trade-in profitable. This interest increase does not decrease the actual cost of the machine unless the money is borrowed; however, the increase does improve the opportunity of added profit from the use of the funds in other investments. As shown in the results presented previously, increases in the interest rate often delay purchase for one year. General Conclusions From the above analysis of each variable the conclusion is easily reached that any of the variables studied can change the Optimum replacement frequency and that all of the variables affect the average in: th: thI teI 147 cost. Any ranking of the variables seems impossible because their importance depends on the situation before the change and the source of the data used. Emphasis must once again be placed on the importance of using data from the actual situation being studied. Although the effect of each variable cannot be ranked, the effects can be separated into those that increase the optimum replace- ment frequency and those that decrease this frequency. In general, the optimum replacement frequency increases when the cost of keeping is increased relative to the cost of trading. The following changes in the variables tend to increase this frequency: 1. Increases in the slope of the repair cost function until the slope becomes so steep that nearly all of the repair costs are in the last year or two. 2. Additional hours of use. 3. Declining levels of machinery management when the assump- tions are such that the cost of trading is affected more. 4. Increases in obsolescence charges. 5. Increasing cost for the new machine when the yearly increases are large. When the cost of trading increases relative to the cost of keeping, the optimum replacement frequency decreases. The following conditions tend to decrease this frequency: 1. Increases in steepness of the repair cost function when it is already very steep. 2. Declining levels of machinery management when the assump— tions are such that the cost of keeping is affected more. fa CO the and con com are 148 3. Increasing cost for the new machine unless the yearly increases are large. 4. Increases in the interest rate. The reader may be wondering how these conclusions can help a farm manager. The number of variables the farm manager must be cognizant of when he considers his replacement decision can be reduced. Assuming that the farm manager has already calculated his own repair costs and trade-in value, the variables "source of the cost data" and "shape of the cost function" are no longer variables. The number of variables to be considered is thus reduced to five--number of hours the machine is used, level of machinery management, rate of obsolescence, cost of the new machine and the interest rate. Since the situation being considered is for a specific farm manager, the level of machinery management can be considered constant leaving only four variables. Of these four, the farm manager must consider the cost of the new machine and the interest rate. The number of hours of use only has to be considered if it will change significantly in the relevant future. A common method of considering obsolescence charges is to assume they are reflected in the decreasing value of the used machine. Integration of the Short—run and Long-run Analysis Since a new machine is used in the first year and only three years are used, the conclusions of the previous section would not affect the simulator as it was used in this study. If a longer period had been used, however, this conclusion would not be correct. The optimum replacement period is seven years using the repair cost [D 3t Ea de 149 function in the simulator and no obsolescence charge. If, for example, eight years of corn harvest are simulated with a four-row combine har— vesting 500 acres, the decision as to whether to keep or trade the seven year-old combine depends on the length of run being considered. For this production period the cost to repair the combine is $3164.00 while the cost of trading is $9252.00. The average yearly cost of the policy of trading every seven years is $3036.00 while the average yearly cost if the manager kept one additional year and then traded would be greater. Therefore, in the seventh year the farm manager would trade for a new combine to minimize his costs over time even though keeping would be much less expensive for the present harvest season. Changes in many of the variables that have been studied for one length of run have an effect when the other length of run is con— sidered. The effect of the variables affecting the optimum replacement frequency on the short-run model is simply that a machine may be traded more or less frequently. The effect on costs in the individual harvesting period may be substantial; however, the long-run effect on cost will be the change in average yearly cost. The effect of each long-run variable on the short—run is simply the effect presented in the first section of this chapter applied to the individual harvest period. The effect on the optimum replacement frequency of the variables studied for the harvest period is not nearly as simple. The effect of each of these variables on the costs of keeping and trading must be determined. The effect of these changes in costs on the optimum pr a1 tc qu le th As se 0f 1'10 de 150 replacement frequency is then determined. On the following pages each of the nine variables studied for the short-run is considered. Size of the Enterprise In general increases in size increase the hours of use. The effect would be the same as with changes in hours of use. One further condition must be considered, however. When the size of enterprise changes enough so that the present machine is inefficient, complica- tion results. For example, if the size of enterprise increases, the probability of loss from failure to harvest may increase to an alarming point. Some amount should be added to the cost of keeping to cover this possibility of loss. Of course, the cost of trading would also increase since a larger machine would be traded for. Price The effect of the price of corn on the optimum replacement fre- quency works through the obsolescence charge. The result of obso- lescence usually is increased field losses. With changes in the price the loss from obsolescence changes thus altering the cost of keeping. With changes in the cost of keeping the optimum frequency may change. As prices increase, replacement tends to occur sooner. Since the price seldom changes more than a few cents a bushel, the effect of the price of corn on the Optimum replacement frequency is very small. Many if not most farm managers put too much emphasis on the crop price when determining their machinery replacement policy. r11 ‘4‘. ['X' 'C‘l r13 ’7'! He is Ca lSl Yield The effect of yield is similar to the effect of price. As yield changes, the obsolescence loss will change thus altering the cost of keeping relative to the cost of trading. This effect may become more important as yield increases since an older machine may be more inefficient with large yields than with lesser ones. Also, with higher seed and fertilizer investments and greater yields, the potential loss from not completing harvest increases, creating the possibility that a larger machine may be more profitable. Conse- quently the potential on replacement policy with changes in yield is greater than the effect of changes in price. Once again though many farm managers overestimate the importance of this effect. Opportunity Cost The labor cost has an effect on the optimum replacement fre- quency only when the new machine requires less labor because of improvement in design or increased size. Even in these two cases there would be no effect using the cost structure of this study. The needed costs could, however, be easily included. In this case in- creased cost for labor would tend to increase replacement frequency. The above effect is a part of the process of mechanization continuing today. Hours As with the labor cost, the effect of the hours in the work day is only relevant when the manager is trading for a machine with greater capacity. In this case increasing the work day would decrease the pro day tra wit hou Gra moi to the dec inc me: UR; Va] 152 profitability of trading for a new combine. Any decrease in the work- day would have the Opposite effect of increasing the profitability of trading. This variable and the previous labor cost often go together with labor costs increasing and labor becoming unavailable for long- hours of work. Grain Moisture and Loss As with the two previous variables, the effect of the grain moisture criterion for commencing harvest and of the loss from failure to complete harvest during the harvest period is nonexistant unless the new machine has more capacity. When the new machine is larger, decreases in the grain moisture criterion causing a later harvest and increases in the loss tend to increase the optimal frequency. Move- ment in the opposite direction creates the Opposite effects. Since changes in the average temperature and rainfall are so unpredictable and so limited to the short-run, the effect of these two variables on the Optimum replacement frequency can easily be considered nonexistent unless the manager is trading for a larger machine. In general, the effect of the short-run variables on replacement policy is not great. Changes in size easily have the greatest effect. Rather small effects are felt from changes in several other variables especially if the machine to be purchased is nonidentical. CHAPTER VIII SUMMARY AND CONCLUSIONS Since all previous efforts are lost if the crop is not har- vested, harvesting is the most critical phase in a crop production system. Many variables must be considered by the farm manager. When making harvesting decisions, the farm manager must be cognizant of two views of the harvesting system. The first view is of the individual harvesting period, and the second considers the purchase of a major machine. In light of the importance of correct decision-making during harvest, the objective of this study was to determine and evaluate the effects of nine variables on the individual harvest period and seven variables on machinery replacement decisions. The computer model used to determine the effect of these vari- ables included a simulator of a corn harvesting system to determine the effect on the individual harvest and a dynamic programming re- placement model to consider the purchase of a major machine. Using actual harvest conditions for 1966-1968 as a base, a wide variety of weather, yield, and price conditions were simulated for various sizes of enterprise with a two-row and a four-row combine. The replacement routine was then used to determine the optimum time to purchase a new machine using the two-row combine in a variety of situations. 153 f0 31' du ha 154 The effect of nine variables on management income from the individual harvest period-~loss due to failure to complete harvest during the harvest season, size of enterprise, hours in the work day, grain moisture criteria for starting harvest, Opportunity cost of labor, average temperature, additional rainfall, price and yield—-was considered. When these variables are ranked according to their effect on management income from the individual years; size of enterprise, temperature, price and yield appeared to change average income by 20 per cent or more. The rankings, however, are very dependent upon the individual situation. Different weather conditions are found to have a great effect on the rankings. The rankings of the effect of the variables on management income acquired consistency when the harvesting situations were divided into those situations in which the harvest is completed and those in which it is not. Four variables-~size of enterprise, hours in the work day, grain moisture criterion, and additional rainfall--actually had opposite effects on the farm manager's income depending upon whether harvest is completed during the harvesting period. When harvest is completed during the harvesting period, four variables have an effect on management income in excess of 20 per cent (of average income) while the effect of the other five variables is less than 10 per cent. The four variables having a major effect in decreasing order of importance are: size of enterprise, price, temperature and yield. In the less frequent situation where harvest is not completed during the harvesting period, more variables occupy a major role since harvesting time is now of the essence. The four variables of prime 155 importance when harvest is completed--size of enterprise, price, temperature and yield--retain their important effect. Loss from failure to complete harvest and hours in the work day also create changes in management income in excess of 20 per cent (of average income). Changes in the grain moisture criterion and rainfall also created changes in income in excess of 20 per cent (of average income) under certain circumstances. In general the variables size and loss had the greatest effect on management income with effects in excess of 100 per cent under certain circumstances. The importance of the selected variables in "good" and "bad" years is of interest to the farm manager. "Good" and "bad" years are looked at first in terms of price and/or yield and then in terms of the weather during harvest. In terms of relative importance of the variables, "good" and "bad” price-yield conditions have the same effect. The effect goes back to the question of completion of harvest. In terms of the actual dollar value of the change, the effect is greater during a "good" year because the same change now affect more bushels and/or has a larger value per bushel. In terms of weather conditions, the "good" year is represented by the conditions when har— vest is completed during the harvest season and the "bad" year by conditions when harvest is not completed. Changes in these nine variables also have an effect on the relative income positions of the two-row and the four-row combines. In order to get consistent results, the situations must be divided into three categories: those in which both combines finish harvest, those in which only the four-row completes harvest and those in which 156 neither combine completes harvest during the harvest period. Only in the second category where only the four-row completes harvest did any of the variables affect the relative income positions. In this category the size Of enterprise, hours and loss variable were extremely important (greater than 70 per cent change in income), and rainfall (22 per cent) and grain moisture (17 per cent) variables had an important effect. Of the nine variables studied, three--size of enterprise, hours in the work day and grain moisture criterion--can be largely controlled by the farm manager. The profit maximizing value for each of these variables could be determined using the gain (in dollars) from in- creases in the values for the three variables with completion of harvest during the harvesting period, the loss (in dollars) from increases if harvest is not completed and the probability (in per cent) of completing harvest during the harvest season. The maximizing length of the harvest day can be updated periodically throughout the harvest period. The effect on the timing of the purchase of a major machine of seven variables—-the farm situation from which the repair data is derived, the shape of the repair cost function, the number of hours the machine is used, the level of machinery management, the rate of obsolescence, the cost of the new machine being considered and the interest rate--was considered. Each of the variables studied was found to have a potential effect large enough to alter the year in which the farm.manager would trade if he were minimizing costs over time. Changes in the variables resulted in Optimum policies of 157 keeping the combine from three to seven years. The farm situation from which the data came was found to have the greatest effect on the replacement decision. Since no set of repair data has been found that is representative of all farms or even of a class of farms, the effect of the other variables depends upon the farm situation being considered. Because of the above situation, replacement decisions must be based on the individual situation rather than general policies. Even though few conclusions can be reached relative to the magnitude of the effect of the selected variables, conclusion can be reached regarding the direction of the effect. Additional hours of use and increase in the obsolescence charges increase the likelihood of purchasing the new machine. Increases in the interest rate delay the Optimum time to trade for the new machine. Increases in the cost Of the new machine tend to delay the time to trade unless the trade can be made the year prior to a large price increase. The situation for the individual farm manager is not as complex as it initially appears. Assuming that the farm manager has calcu— lated his own repair cost date, the variables source of the cost data, shape of the cost function and the level of machinery management are constant. Only four variables remain. If the farm manager does not plan to change the hours of use of the machine, that variable can be disregarded. Furthermore, many farm managers let the declining value of the used machine (with age) represent the obsolescence charge. The farm manager must now consider (beside the age of his present machine) a maximum of four variables and a minimum of two--cost of the new machine and the interest rate. 158 Changes in eight of the nine variables affecting the individual harvest had almost no effect on the replacement decision. The only exception was the size of the enterprise which affected the replace— ment decision as a change in the hours of use of the machine. Changes in the seven variables affecting the decision to purchase machinery have an effect on the income from the individual year through the average minimum cost. For changes in the seven variables in the relevant range, this affect amounts to only a few dollars a year. The above findings have important implications on how and when the farm manager makes decisions concerning harvest. The first of these decisions must be made in the winter months prior to the new harvesting season. Taking into account a number of years, the farm manager must decide whether to purchase any new machinery. The major decision for the harvesting system concerns a combine. At the same time, the manager must use his potential gains, losses and prob- abilities Of completing harvest with the combine he owns to determine his profit maximizing size of enterprise. The acreage thus determined is the maximum possible for that enterprise. This maximum may be reduced by limitation during the planting or growing seasons, by acreage limitations within the firm or by the profitability of the enterprise relative to other enterprises. Throughout this decision- making process, the farm manager must keep in mind possible changes in the variables found to have an important effect on income. As the harvesting season approaches, the farm manager must determine the profit maximizing date to start harvesting using the gain from delaying the harvest if it is completed, the loss if it is 159 not completed, and the probability of completion. The manager can use the expected hours in the work-day to determine when to start harvesting. During the harvest the hours worked can be adjusted according to the success of harvest to date. Although few farm managers explicitly follow this process, the process is implicit in the actions of many farm managers. Realizing the above, a number of conclusions concerning the actions of farm managers can be reached: 1. Farm managers may be justified in maintaining overcapacity of 20 to 30 per cent. The relatively small cost of this overcapacity may prevent losses in income of 20 per cent or more. 2. Farm managers, particularly those with large acreages, may be justified in trading their equipment, especially harvesting equip- ment, every two or three years. 3. In years that the grain moisture content is high, farm managers may be justified in starting corn harvest even though the moisture content is abnormally high. 4. The optimum size of enterprise for each farm manager may depend significantly upon whether he is a profit maximizer, a risk averter, or a risk taker. CHAPTER IX IMPLICATIONS FOR FUTURE RESEARCH The early stage of development of the simulator and the limited scope of this study produced a number of limitations. Probably the most important was that harvest is an important subsystem of a much larger production system. Studying this subsystem by assuming the remainder of the system essentially constant ignores many important relationships. The impact of planting date and the effect of an extremely unfavorable growing season on the harvesting system are two examples of these relationships. Many of these relationships could be partially studied by altering the initial conditions facing the harvesting system. Many aspects of the harvesting system were not fully developed in the model used for this study. The criterion for determining when to start harvest was not fully developed. Also, the harvesting of all corn remaining in the field on December 1 at one time was an un- supportable assumption. The greatest Obstacle to studying the bar- vesting system was the lack of any drying and storage facilities. Given these initial limitations in the simulation model used, a number of limitations are evident in the study itself. In addition to the nine variables studied, others could have been added. Two of the most important additions could have been the efficiency Of the 160 161 combine Operator and field losses due to lodging and harvest. In ranking the nine variables relative to their effect on income, the assumption that all of the changes were equal is questionable. The changes in size of enterprise (100 acres) and temperature (five degrees) seem particularly large. In studying the effects of changing variables, little attention was paid to simultaneous changes in more than one variable. Although the replacement routine was much smaller and therefore more easily developed, limitations are evident. The most important was the restriction to two alternatives and seven states. This re- striction ruled out any consideration of trading for a used combine. The use of only seven variables and the assumption that only identical machines are purchased limits the value of the conclusions concerning machinery replacement. The analysis of each of the models suffers from the lack of sufficient valid data. Although the data used in the simulator had never been used in that manner previously, the greatest deficiency was the lack of tractability data for December. The replacement routine suffers from a lack of consistent repair data. Based upon these limitations and the conclusion of the study, a number of implications for future research in this area can be made. From the results of this study and of others using the harvesting model, the conclusion seems to be clear that the simulation of agricultural production systems should continue. The short-run objectives should be two. The first is to refine the harvesting model by adding drying and storage facilities and by adjusting specific 162 criteria. The most important criteria concern when to start harvest and how to handle the corn not harvested during the harvesting period. The second objective should be to add the other subsystem necessary to complete the corn production system. These subsystems include tillage, planting, and growing. The longer—run objective should be to extend the simulation to other crops. The analysis of results from the replacement routine indicate a potential for a dynamic programming replacement routine of this type. In order to conform more with the real world, the routine should be adjusted to include the alternative of trading for a used machine. At this point the routine could be used to evaluate individual farm decisions by adding an apprOpriate matrix generator. A final exten- sion could be to consider replacement of additional item, such as buildings, dairy cattle and/or livestock. One last implication that is not limited to studies of this type is that researchers must be cognizant of the time period they are considering. In this study replacement decisions had to be separated from the other decisions to insure that the necessary long- run considerations would be made. BIBLIOGRAPHY BIBLIOGRAPHY Ackoff, Russel L. and Rivett, Patrick. A Manager's Guide to Operations Research, New York, London: John Wiley and Sons, 1963. Ackoff, Russell L. (ed.). Progress in Operations Research, Volume 1, New York: John Wiley and Sons, Inc., 1961. Armstrong, David L. and Faris, J. Edwin, Farm Machinery Costs, Per- formance Costs and Combination, Giannini Research Report 273, California Agricultural Experiment Station and the Giannini Foundation Of Agricultural Economics, March 1964. Babo, E. M. and French, C. E., Use of Simulation Procedures, Journal of Farm Economics, VL (November 1963), 876-877. Baumol, W. J., Economic Theory and Operations Analysis, Englewood Cliffs, New Jersey: Prentice-Hall Publishing Co., 1961. Bellman, Richard E. and Stuart E. Dreylus. Applied Dynamic Programming, Princeton, New Jersey: Princeton University Press, 1962. Bowers, Wendell. Modern Concepts of Farm Machinery Management, Champaign, Illinois: Stipes Publishing Co., 1970. Brown, L. H. and Speicher, John, TelFarm Business Analysis Summary for Specialized Southern Dairy Farms, 1968, Agricultural Economics Report 137, East Lansing, Michigan State University Department of Agricultural Economics, June 1969. Burt, Oscar R. "Economic Replacement," SIAM Review, Vol. 5, NO. 3, July 1963. Burt, Oscar R. "Optimal Replacement Under Risk," Journal of Farm Economics, VLII (May 1965), 324-346. Carter, H. O. and G. W. Dean. "Cost-Size Relationships for Cash CrOp Farms in a Highly Commercialized Agriculture, Journal of Farm Management, XLIII (May 1961), 264-277. Churchman, C. West, Achoff, Russel and Arnoff, E. Leonard. Introduc- tion to OperatiOns Research, New York: John Wiley and Sons, Inc., 1966. 163 De He He Hc H1 164 Connor, L. J., Benjamin, C. L., Brake, J. R. and Lee, W. F., Michigan Farm Management HandbOok, Agricultural Economics Report 36, East Lansing: Michigan State University, Department of Agricultural Economics, October 1967. Department of Agricultural Economics. Simulation in Agricultural Economics: Proceedings of Joint Conference of North Central Regional Farm Management Extension and Research, Report NO. 157, East Lansing, Michigan State University Department of Agricul- tural Economics, February 1970. Deutsch, Ralph, Systems Analysis Techniques, Englewood Cliffs, New Jersey: Prentice—Hall, Inc., 1969. Faris, J. Edwin, "Analytical Techniques used in Determining the Optimum Replacement Pattern," Journal of Farm Economics, XLII (November 1960), 755-766. Goetz, Billy E., Quantitative Methods: A Survey and Guide for Managers, New York: McGraw Hill Book Company, 1965. Halter, A. N. and Dean, G. W., "Use of Simulation in Evaluating Management Policies under Uncertainty," Journal of Farm Economics, VLII (August 1965), 557—573. Harsh, Stephen B., TelFarm Business Analysis Summary for Cash Grain Farms, 1968, Agricultural Economics Report 133, East Lansing: Michigan State University, Department of Agricultural Economics, August 1969. Hepp, Ralph E., Michigan Farm Business Analysis Summary -- 1968 Data, Research Report 95, East Lansing: Michigan State University, Agricultural Experiment Station, October 1969. Holtman, J. B., Pickett, L. K., Armstrong, D. L. and Connor, L. J., "Modelinggof Corn Production - A New Approach," For presentation at the 1970 annual meeting, American Society of Agricultural Engineers, Minneapolis, Minnesota, June 7-10, 1970. Howard, Ronald A.,_Dynamic Programming and Markov Processes, New York: John Wiley and Sons, Inc. and the Technology Press of the Massachusetts Institute of Technology, 1960. Huber, S. J., "Depreciation and Repair Cost of Self-Propelled Combines," Transactions Of the ASAE. Jenkins, Keith B. and Albert N. Halter, A.Mu1ti-Stage Stocastic Replacement Decision Model (Application to Replacement of Dairy Cows), Technical Bulletin 67, Agricultural Experiment Station, Oregon State University, Corvallis, April 1963. 165 Kletke, Darrel D. ”Farm Replacement Problems in a Dynamic Environ- ment," For Presentation at the 1969 Annual Meetings, American Society of Agricultural Engineers, Purdue University, June 22-25, 1969. Kyle, Leonard R., TelFarm Business Analysis Summary for Cattle Feeding Farms, 1968, Agricultural Economics Report 137, East Lansing: Michigan State University Department of Agricultural Economics, June 1969. Kyle, Leonard F., TelFarm Business Analysis Summary for Saginaw Vallgy Cash Crop_Farms, 1968, Agricultural Economics Report 122, East Lansing: Michigan State University Department of Agricultural Economics, June 1969. Peacock, David L. and Brake, John R., What is Used Machinery Worth, Research Report 109, East Lansing: Michigan State University, Agricultural Experiment Station, March 1970. Smith, Vernon L., "The Theory of Investment and Production," Quarterly Journal of Economics, February 1969, 61-87. Stictland, Roger P., Combining Simulation and Linear Programming in StudyingyFarm Firm Growth, Unpublished Ph.D. thesis; Michigan State University, East Lansing, 1970. Sutton, R. E. and Crom, R. J., "Computer Models and Simulation," Journal of Farm Economics, VLI (December 1964), 1341-50. Tyner, F. H. and Tweeten, "Simulation as a Method of Appraising Farm Programs," Journal of Farm Economics, L (February 1968), 66-81. White, Cleland W. "The Determination of an Optimal Replacement Policy for a Continually Operating Egg Production Enterprise," Journal of Farm Economics, XLI (December 1959), 1535—1542. Zusman, P. and Amiada, A., "Simulation: A Tool of Farm Planning under Conditions of Weather Uncertainty," Journal of Farm Economics, VLII (August 1965), 574-594. APPENDICES APPENDIX A INPUT VALUES FOR CORN HARVEST SIMULATOR APPENDIX A INPUT VALUES FOR CORN HARVEST SIMULATOR Appendix Table A. 1. Simulation Input Data The following values are used as exogenous coefficients for the corn harvest simulator: 1. Coefficients for the combines. New Cost two-row $12,000 four-row: $16,000 Type of depreciation Straight line with 20 per cent additional first year Years to be depreciated over: eight Salvage value: 10 per cent Fuel cost: two-row: $1.775 per hour four-row: $3.50 per hour Width: two-row: 2 rows four row: 4 rows Harvester row spacing: 40 inches Hours used per day: eight 166 167 Appendix Table A. 1 (cont'd.) Efficiency of Operator: two-row: 1.0 four-row: 0.9 Repair function: ARC = NC [(-.Ol97Xl + .0087Xi - .00053Xi,) + 1.02 + .00025X2)] ARC = annual repair cost NC = new cost for the machine X1 = age of machine X2 = hours of annual use 2. Fixed coefficients Hired wage rate: First 600 hours: $2.00 per hour. Second 600 hours: $2.25 per hour. Third 600 hours: $2.50 per hour. Fourth 600 hours: $2.75 per hour. A11 in excess of 2400: $3.00 per hour. Tax rate: 20 per cent Interest rate: 7.5 per cent Housing charge: .0075 x depreciated value Insurance charge: .0075 x depreciated value Drying charge: $.01 per point to .155 Hauling charge: $ .06 per bushel (wet) Land value: $600.00 per acre Hours of operator's labor available: 320 Charge for Operator's labor: $960.00 Appendix Table A. 1 (cont'd.) 3. State of system on October 1 Grain moisture content 168 First year: 0.367 Second year: 0.409 Third year: 0.278 Potential yield First year: 150 bu. Second year: 100 bu. Third year: 125 bu. 4. Date of physiological death First year: 10/30 Second year: 11/06 Third year: 10/11 5. 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NN«.«I omo.o| m«H.mH mwm.«H mNm mNN Nm m «N mH\OH wo\HH mN\OH om. oom.«u NHa.o- m-.afi mo~.oH HNm o«m No a NN mH\oH oo\HH HM\oH om. H.Howv A.Howv H.Hopv H.Hovv Ammuomv Amouomv umou now» How» ummh umm> Hmo% 3oul« 3OHIN Boul« 3ouIN aou|« aouIN bum ch umH mum poN umH A.o>mv A.o>mv A.o>mv OOHuom‘ Apouumum mpmuumum OOHuoano OEOOOH ooEoocH umm>umz onusp umm>um£ Houmm uwm>ums mama w uaosommcmz sumo uwz vmumm>ums mouo¢ mkmw OHnmuomuH uaoucoo ousumHoz :Hmuw Ono wcHaumoaou «HuouHuo O>HumapmuH< :uH3 mouo< oo« :0 ocHnEoo nomm waHmD wo>Hooom oeoocH mwmho>< umow mounH .HN .m mHan prooma< 190 mucomo oH . .mH umnfio>oz ouommn «m. .mN Hogam>oz .HH Hmnam>oz ouomon Nm. .« Hoaam>oz ouommn om. .mN Honouoo ouowon mN. .HN nonouoo ouowmn oN. BOHon HHom unauooo annumHoe aHmuw NH uumum vHaoo umo>ummo .OOHumuHHO Os» cmnu umHuv mH cuoo cmn3 vosoHHm mH umm>Hmm p .uwo>um£ ou HOHHQ umoo whom you oo.m«m OSu mowOHoaHO .mHnmuomuu mma vamH Ono uwzu wouumum umo>umn noumm mzmw vo nonasz a .mHnmuOmnu mmB HHom m:u vow nod mma OOHuouHuO unaumHoE man unfiu mop umuHmm omo.oH- ooa.amu on.aHn moo.o~- No~.oH- Hoo.a~- moa.mH| MON.wNI Hma.om oHH.oN mHH.Hm ~m~.HN Hao.om on.o~ ooo.o~ «HH.oH no« moN mom omN mm« MNN m«« mmN Hm o mm oH\oH oo\HH om\oH mmoHoHHm mm o om mH\oH oo\HH «~\oH mm. mm o om mH\oH oo\HH om\oH om. mm o NH mH\oH oo\oH HM\oH oN. H.Hoov H.Hoov 3OHI« BOHIN H.Howv A.Hopv 30HI« BOHIN Ammuomv Amouomv 3OHI« BOHIN poo» “mom Hawk Homm HMO% um0% ppm ch umH mum vaN umH A.m>mv A.o>mv A.o>mv OOHumml Abouumum abouHMum OOHHOHHHU ooEoocH ooEOOOH umo>um£ onunw umo>ums Houmm umo>um£ moon w oomsowmcmz ammo umz vOumo>um£ mouo< mzmv OHnmuomnH uoouooo unsumHoz :Hmuw map mcHouoocoo mHuouHuo O>HquHouH< nuHB mmpo< OOOH so maHnEoo Loam maHmD wo>Hooom oeoocH owmuo>< Hum» OOHSH .NN .m mHan vacmma< APPENDIX C SUPPORTING DATA ON RANKING OF VARIABLES 191 .EOEHKOE OOu wOHOOOpoOH Sopm OEooOH pOmOOpOOp OuOOHpOH OOOHO> O>HquOO mpOHHpOO OHwOn OOO me>pOO om pOmOOpOOH OH BOEHOOE Onu OO£3 anoOH pOmOOpoOH OmeHpOH OOOHO> O>HuHmom OpOMOn OpOuOHoe OHOpw EOEHxOE pom OOHpOquO Onu OH OOwOmso ou OpOMOp OHnOHpO> OHOHp .OUQOEEOU GNU um .QEOUGH @Omm mOpOmHm O>HpmwOO .mpOOO pmeOpoOH OOHS OEOOOH OH OmmOpoOH Om 305m mOpOme O>HuHmomo O>pmn OpOOp .OOOH anoOH Om OuOOHpOH OOpOwHw O>HquOO mmOpOO oom Op OON Eopm pOpOmOxO OH OmeOpOpOO OOH mm mOmmOpoOH OEOOOH OuOOHpOH OpOOoaO O>HpHmom n .uOOH On On pOEOmmO OH pOOO pOO oN OOOB pOLmHO Lose umnu OH anoOH OOH mOpOOHpOH pOOoEO O>HpHmomO Now «mm omo «Nu «on «No Nmm who HpHOHw ooHH oHHH NoHH NoHH moo moH oHoH NHHH HOUHOO 0mm Nmm mom «0N m«HH mum «NNH ommH wOpOquOOSOH mm: NOHI ooHI 00H: m HI mNH: m«HI wHHOHOHOp HOOOHqup< HHN oNH How mHm HHN ooo OHN mom oumoo suHosupoooo mmHI «NHI o o on mON mow: Nmml pOpOpmHoa OHOpw mm mHH meI nmml o«« cum NoHI onI ompsom mm«| NNmI onI HNmI N«le mHmmI Nom« m~o« OONHm mm ONm o o HoN NmmH o o OOOOH H.Hooo H.Hooo H.Hoov H.Hooo H.Hooo H.Hoov H.Hooo H.Hooo Bopl« BopIN 30p|« BopIN Bopl« zopIN 30pI« SoplN OOHanpO> OmOpO>< pr% ppm pOOh pON pOOh pmH pOOw 30mm OH OmeOpOuOm Opo< ooN O :pH3 OOHanpm> OOp OH mOwOOOU mo OOOmmm OOH .H .o OHQOH prOOOOO 192 .AH pOOOuOOV pOHpOO wOHumO>pOO mo wOHOOHwOO um pHOHH HOHuOOpOO OH OmmOpOOH Om OpH3 OEOOOH OH OmOOpoOH mo uOOoBO O3OOmH .mmUflHQ fiQQNQHUfifl £ua3 QEOUGH SH OWNMHUGH 05H m30£m£ .mmeQHUGH GHDUMHQQEMU mwmhm>m mm QEOUGH CH QmNQHUGfi 05H mOUGUHUCHw .HHOHOHmp HOOOHqupO OOHB anoOH pOOOOpOOH 30OO OOOHO> O>HpOmOO ”HHOHOHOp HOOoHqupO OuH3 pOmOOpOOp OEOOOH uOOu OpOOHpOH OOpOwHH O>HpHmomm .OOOOOpOOH OOHO>_OHOu OOOB umoo pOmOOpo IOH OOp OuOOmOpOOp OpOme OOH .OEHp m.p0quan OOHOBOO OOp mo OOHO> OOp OH OHOOHpO> OHOHO 193 .OOpOO oon ou oo« 50pm OH OOHO3 ONHO OHOOHpO> OOu OH OmOOOO OOu meoxO OOHOOHpO> OOp OH OOwOOOO mo OOOHpOOOHONO pom HmH OwOO .H .o OHOOH OOmm mmmH NOOH H«mH mwOH mm«H mmmH mm«N mHmH pHOHH mmmN «o«N «HON mmnN NHNH HomH mNmm mHmN OOHpm HmON mNHN «m« moH nmoN «mON omom mmo« OpOquOOaOH HmNH ommH «m«| me o o HwH« mNHm HHOHOHOp HOOOHppr< mom woo NNH ooo mam moo mam NNoH Hmoo HuHooupoooo mOH won N 0 mm« mNN le mNoN OpOuOHoa OHOpu m ommN moon mHON meH mmm CHH: mem OpOOO NmH: OHmmI moH: mNomu Ho«m| HHmmI OHHm «HOHI ONHm moHH No«« 0 powH HNHm mN«p o NHNO OOOH A.Hopv A.Hopv H.Hopv H.Hopv A.Hopv H.Hopv H.Hopv H.Hopv 30p|« BopIN 3OpI« BopIN BOpI« sopIN sop|« 3Op|N OOHOOHpO> OwOpO>< pOOm ppm pOOH pON pOOm,uOH O pOOH Oomm OH OOHpOpOpOm Opoo OpoO oom O OOHB OOHOOHpm> OOp OH OOmOOOo mo OOOmmm OOH .N .o mHomp xHoamao< Appendix Table C. 3. 194 Economic Ranking of Variables in Each Year-- 200 Acres 2—row 4-row Rank Variable Change Variable Change (dol.) (dol.) First Year 1 Size 4673 Size 4562 2 Temperature 1556 Price 1413 3 Price 1412 Temperature 1274 4 Yield 975 Yield 952 5 Grain moisture -582 Grain moisture -803 6 Opportunity cost 392 Opportunity cost 216 7 Hours —168 Hours -162 8 Rainfall —145 Rainfall -128 9 Loss 0 Loss 0 Second Year 1 Size -5317 Size —5242 2 Loss 1562 Temperature 1149 3 Temperature 975 Price 903 4 Hours 876 Yield 764 5 Price 745 Hours 440 6 Yield 624 Grain moisture 326 7 Opportunity cost 496 Loss 261 8 Grain moisture 209 Opportunity cost 211 9 Rainfall -1 Rainfall 3 195 Appendix Table C. 3 (cont'd.) 2-row 4-row Rank Variable Change Variable Change (dol.) (dol.) Third Year 1 Price 1192 Price 1192 2 Yield 724 Size -816 3 Opportunity cost 373 Yield 690 4 Hours —357 Temperature 505 5 Size 321 Opportunity cost 207 6 Temperature 264 Hours -183 7 Rainfall -l60 Rainfall -160 8 Grain moisture 0 Loss 0 9 Loss 0 Grain moisture 0 Average 1 Price 1116 Price 1169 2 Temperature 932 Temperature 976 3 Yield 774 Yield 802 4 Loss 520 Size -499 5 Opportunity cost 420 Opportunity cost 211 6 Size —332 Grain moisture -159 7 Hours 117 Hours 95 8 Grain moisture -124 Rainfall 95 9 Rainfall 102 Loss 87 Appendix Table C. 4. 196 Economic Ranking of Variables in Each Year-- 500 Acres 2-row 4-row Rank Variable Change Variable Change (dol.) (dol.) First Year 1 Loss 6212 Size 5110 2 Temperature 4085 Rain 4187 3 Hours 3981 Temperature 3650 4 Rainfall 3123 Price 3525 5 Price 2915 Yield 2487 6 Grain moisture 2075 Hours -710 7 Yield 1914 Opportunity cost 548 8 Opportunity cost 1022 Grain moisture —72 9 Size -1014 Loss 0 Second Year 1 Loss 6429 Size —5401 2 Size -5311 Loss 5127 3 Temperature 2094 Temperature 2087 4 Price 1561 Price 1717 5 Yield 1383 Hours 1698 6 Opportunity cost 983 Yield 1488 7 Hours 839 Opportunity cost 545 8 Grain moisture 229 Grain moisture 458 9 Rainfall 0 Rainfall 0 Appendix Table C. 4 (cont'd.) 197 2-row 4-row Rank Variable Change Variable Change (dol.) (dol.) Third Year 1 Size -3623 Price 2974 2 Price 2735 Yield 1841 3 Hours 2919 Hours -908 4 Loss 1866 Temperature 434 5 Yield 1688 Rainfall -434 6 Opportunity cost 960 Opportunity cost 422 7 Rainfall 926 Size -195 8 Temperature 195 Grain moisture 2 9 Grain moisture 0 Loss 0 Average 1 Loss 4402 Price 2739 2 Size -3316 Temperature 2057 3 Hours 2580 Yield 1939 4 Price 2404 Loss 1709 5 Temperature 2125 Rainfall 1351 6 Yield 1662 Opportunity cost 505 7 Rainfall 1350 Grain moisture 193 8 Opportunity cost 988 Size -162 9 Grain moisture 768 Hours 27 Appendix Table C. 5. 198 Effect Of Changes in the Variables With and Without Completion of Harvest--200 Acresa 2—row 4-row Variable Not Not Completed completedC Completed completedc (dol.) (dol.) (dol.) (dol.) Loss 0 1562 0 261 Sizee 2176 —5317 1874 -5424 Hoursf —262 876 -172 440 Grain moistureg —191 209 -402 326 Opportunity costh 382 496 211 211 Additional rainfalli -152 o -94 o Temperaturej 910 975 872 1149 Pricek 1302 745 1158 903 Yieldl 850 624 821 764 8Harvest completed means completed by NOvember 30. A11 corn not harvested by then is assumed to be harvested at December 31 con— ditions with a 40 per cent loss. bThis column contains figures from the first and the third year. CThis column contains dSee e See fSee gSee hSee 1 See Table jSee kSee 1See Table C. Table C. Table C. Table C. Table C. Table C. Table C. Table C. Page Page page Page Page Page Page page Page figures from the second year. 191, footnote one. 191, footnote two. three. 191, footnote 191, footnote four. 191, footnote five. 191, footnote six. 191, footnote seven. 191, footnote eight. 191, footnote nine. 199 Appendix Table C. 6. Effect of Change in the Variables With and Without Completion of Harvest--500 Acresa 2-row 4-row Variable Not Not Completed completedC Completed completede (dol.) (dol.) (dol.) (dol.) Lossf -- 4836 o 5127 Sizeg -- —3316 2458 -5401 Hoursh -- 2580 -809 1698 Grain moisturei -- 768 -35 458 Opportunity costj -— 988 484 545 Additional rainfallk -- 1350 -434 2094 Temperature1 -- 2125 2042 2087 Pricem -- 2404 3250 1717 Yieldn -- 1662 2164 1488 aHarvest completed means completed by November 30. A11 corn not harvested by then is assumed to be harvested at December 31 con- ditions with a 40 per cent loss. bHarvest is never completed with the two-row. CThis column contains figures from all three years. dThis column contains figures from the first and third year. e I This column contains fSee gSee hSee 1See jSee kSee lSee m See n See Table Table Table Table Table Table Table Table Table C. Page Page Page Page Page Page Page page Page figures from the second year. 191, 191, 191, 191, 191, 191, 191, 191, 191, footnote footnote footnote footnote footnote footnote footnote footnote footnote one. two. three. four. five. six. seven. eight. nine. Appendix Table C. 7. 200 Completion of Harvest—-200 Acres Economic Ranking of Variables Depending upon Completed Not completed Rank Variable Change Variable Change (dol.) (dol.) Two-Row 1 Size 2176 Size -5317 2 Price 1302 Loss 1562 3 Temperature 910 Temperature 975 4 Yield 850 Hours 876 5 Opportunity cost 382 Price 745 6 Hours -262 Yield 624 7 Grain moisture —19l Opportunity cost 496 8 Rainfall -152 Grain moisture 209 9 Loss 0 Rainfall 0 Four-Row 1 Size 1874 Size -5424 2 Price 1158 Temperature 1149 3 Temperature 872 Price 903 4 Yield 821 Yield 764 5 Grain moisture —402 Hours 440 6 Opportunity cost 211 Grain moisture 326 7 Hours -172 Loss 261 8 Rainfall -94 Opportunity cost 211 9 Loss 0 Rainfall O 201 Appendix Table C. 8. Economic Ranking of Variables Depending upon Completion of Harvest--500 Acres Completed Not completed Rank Variable Change Variable Change (dol.) (dol.) Two-Row 1 Loss 4836 2 Size —3316 3 Hours 2580 4 Price 2404 5 Temperature 2125 6 Yield 1662 7 Rainfall 1350 8 Opportunity cost 988 9 Grain moisture 768 Four-Row 1 Price 3250 Loss 5127 2 Size 2458 Size -5401 3 Yield 2164 Rainfall 2094 4 Temperature 2042 Temperature 2087 5 Hours —809 Price 1717 6 Opportunity cost 484 Hours 1698 7 Rainfall -434 Yield 1488 8 Grain moisture -35 Opportunity cost 545 9 Loss 0 Grain moisture 458 202 Appendix Table C. 9. Effect of Changes in Variables on the Choice of a Combine with a 200 Acre Corn Enterprise Variable lst yeara 2nd yeara 3rd year3 Averagea (dol.) (dol.) (dol.) (dol.) Lossb o 1301 o 434 Sizec 110 74 495 226 Hoursd 38 -436 -175 -191 Grain moisturee 218 110 0 109 Opportunity costf 176 172 166 171 Rainfallg -17 o o -6 Temperatureh —282 174 241 44 Price1 1 158 o 53 Yieldj -23 140 -34 28 aThe values represent the change for a 4-row combine minus the change for a 2-row combine. bAs loss increases from 20 per cent to 40 per cent the 4-row be- comes the given amount more profitable than the 2-row. C200 to 300 acre increase. d8 hour day increases to 10 hours day. Negative figure indicates 2—row increased in relative profitability with the increased hours. e2 per cent increase in maximum grain moisture. f$3.00 increase in labor cost. 8Reduction of 1" rainfall. Negative figures indicate 2—row increased in relative profitability with increased rainfall. h85 per cent increase in average temperature. i$.05 increase in price. j5 bushel increase in potential yield. Negative figures indi- cate 2-row increased in relative profitability. Appendix Table C. 10. 203 Effect of Changes in Variables on the Choice of 3 Combine with a 500 Acre Corn Enterprise Variable lst yeara 2nd year8 3rd year8 Averagea (dol.) (dol.) (dol.) (dol.) Loss 6512 1302 1866 3327 Sizec 6124 -90 3428 3154 Hoursd -4691 829 -3827 -2563 Grain moisturee -1807 228 o -526 Opportunity costf -474 439 438 450 Rainfallg -1064 o —1360 -808 Temperature -435 7 239 -63 Price 610 156 239 335 Yieldj 573 105 153 277 3The values represent the change for a 4-row combine minus the change for a 2-row combine. bAs loss increases from 20 per cent to 40 per cent the 4-row becomes the given amount more profitable than the 2-row. C400 to 500 acre increase. d8 hour day increases to 10 hour day. Negative figure indicates 2-row increased in relative profitability with the increased hours. 82 per cent increase in maximum grain moisture. f$3.00 increase in labor cost. 8Reduction of 1" rainfall. Negative figures indicate 2-row increased in relative profitability with increased rainfall. 85 per cent increase in average temperature. 1$.05 increase in price. j5 bushel increase in potential yield. Negative figures indi- cate 2—row increased in relative profitability. Appendix Table C. 11. 204 Ranking of Variables According to Their Effect on the Choice Between the Two Combines 200 acres 500 acres Rank Variable Change Variable Change (dol.) (dol.) First Year 1 Temperature -282 Loss 6512 2 Grain moisture 218 Size 6124 3 Opportunity cost 176 Hours -4691 4 Size 110 Grain moisture -1807 5 Hours 38 Rainfall -1064 6 Yield -23 Price 610 7 Rainfall —17 Yield 573 8 Price 1 Opportunity cost 474 9 Loss 0 Temperature -435 Second Year 1 Loss 1301 Loss 1302 2 Hours —463 Hours 829 3 Temperature 174 Opportunity cost 439 4 Opportunity cost 172 Grain moisture 228 5 Price 158 Price 156 6 Yield 140 Yield 105 7 Grain moisture 110 Size -90 8 Size 74 Temperature 7 9 Rainfall 0 Rainfall 0 Appendix Table C. 11 (cont'd.) 205 200 acres 500 acres Rank Variable Change Variable Change (dol.) (dol.) Third Year 1 Size 495 Hours -3827 2 Temperature 241 Size 3428 3 Hours —175 Loss 1866 4 Opportunity cost 166 Rainfall -1360 5 Yield -34 Opportunity cost 438 6 Rainfall 0 Temperature 239 7 Price 0 Price 239 8 Grain moisture 0 Yield 153 9 Loss 0 Grain moisture 0 Average 1 Loss 434 Loss 3227 2 Size 226 Size 3154 3 Hours -191 Hours -2563 4 Opportunity cost 171 Rainfall -808 5 Grain moisture 109 Grain moisture —526 6 Price 53 Opportunity cost 450 7 Temperature 44 Price 335 8 Yield 28 Yield 277 9 Rainfall —6 Temperature -63 206 Appendix Table C. 12. Ranking of the Effect of Changing Variables on the Choice of Machine by Categories Concerning Completion of Harvesta Rank Variable Change (dol.) Both Combines Complete Harvest 1 Size 302 2 Opportunity cost 171 3 Grain moisture 109 4 Hours 68 5 Yield 28 6 Temperature 20 7 Rainfall -8 8 Price 0 9 Loss 0 Only 4-Row Completes Harvest 1 Size 4776 2 Hours —4259 3 Loss 4189 4 Rainfall 1212 5 Grain moisture -904 6 Opportunity cost 456 7 Price 424 8 Yield 363 9 Temperature -98 207 Appendix Table C. 12 (cont'd.) Rank Variable Change (dol.) Neither Combine Completes Harvest 1 Loss 1302 2 Opportunity cost 305 3 Hours 198 4 Grain moisture 169 5 Price 157 6 Yield 122 7 Temperature 90 8 Size -8 9 Rainfall 0 aPositive numbers indicate the four-row combine's relative income improved with the changes outlined in Table APPENDIX D SUPPORTING DATA ON REPLACEMENT ROUTINE APPENDIX D SUPPORTING DATA ON REPLACEMENT ROUTINE Appendix Table D. 1. Additional Input and Output Using Armstrong Data with 200 Hours of Use Ave. cost or Cost to Cost to Interest discounted present State keep trade rate Optimum policy value 1 734 5862 0.00 Keep 6 years 2359 2 899 6306 .05 Keep 6 years 56096 3 1158 6750 .075 Keep 7 years 36886 4 1473 7194 .10 Keep 7 years 27043 5 1806 7638 .125 Keep 7 years 21456 6 2119 8082 .20 Keep 7 years 14134 7 2374 8526 208 209 Appendix Table D. 2. Additional Output Using Bower's Data for 200 Hours Ave. cost or Cost to Cost to Interest discounted present State keep trade rate Optimum policy value 1 228 5244 0.00 Keep 5 years 2090 2 480 5952 .05 Keep 5 years 46491 3 816 6600 .075 Keep 6 years 32978 4 1248 7176 .10 Keep 6 years 26003 5 1784 7680 .125 Keep 6 years 21850 6 2376 8148 .20 Keep 6 years 15,730 7 3072 8556 "11111111111111