1. Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng F. Lee Rutgers University Chapter 22 Long-Range Financial Planning – A Linear-Programming Modeling Approach

2. Outline  22.1 Introduction  22.2 Carleton’s model  22.3 Brief discussion of data inputs  22.4 Objective-function development  22.5 The constraints  22.6 Analysis of overall results  22.7 Summary and conclusion  Appendix 22A. Carleton’s linear-programming model: General Mills as a case study  Appendix 22B. General Mills’ actual key financial data

3. 22.2 Carleton’s model

9. 22.3Brief discussion of data inputs

12. (Cont.)

13. 22.4 Objective-function development (22.1) where

14. 22.4 Objective-function development (22.2) (22.3) (22.3a)

15. 22.4 Objective-function development (22.4) (22.5)

16. 22.4 Objective-function development (22.6) (22.7) (22.7a)

17. 22.5 The constraints  Definitional constraints  Policy constraints

18. 22.5 The constraints Fig. 22.1 Structure of the optimizing financial planning model. (From Carleton, W. T., C. L. Dick, Jr., and D. H. Downes, "Financial policy models: Theory and Practice," Journal of Financial and Quantitative Analysis (December 1973). Reprinted by permission.)

19. 22.5 The constraints (22.8) (22.9) Because General Mills has no preferred stock or extraordinary items, AFC = ATP:

20. 22.5 The constraints

21. ,,

23. .

25. To get the interest payment on long-term debt

26. 22.5 The constraints

27. AFC1+0.00441DL1=149.17 (22.10a) AFC2+0.00441DL2=173.45 (22.10b) AFC3+0.00441DL3=198.22 (22.10c) AFC4+0.00441DL4=226.05 (22.10d)

28. 22.5 The constraints (22.11) where

29. 22.5 The constraints (22.12a) (22.12b)

30. 22.5 The constraints (22.13) where

31. 22.5 The constraints

36. (22.10e) (22.10f) (22.10g) (22.10h) (22.10i)

37. 22.5 The constraints (22.14)

38. 22.5 The constraints.

40. (22.15a) (22.15b) (22.15c) (22.15d)

41. 22.5 The constraints (22.16) (22.17a) (22.17b)

42. 22.5 The constraints (22.17c) (22.17d) (22.19)

43. 22.5 The constraints (22.19a) (22.19b)

44. 22.5 The constraints

45. (22.17f)

46. 22.5 The constraints

49. (22.17o)

50. 22.5 The constraints

52. (22.17f)

53. 22.5 The constraints

57. 22.6 Analysis of overall results

59. 22.7 Summary and conclusion In this chapter, we have considered Carleton's linear- programming model for financial planning. We have also reviewed some concepts of basic finance and accounting. Carleton's model obtains an optimal solution to the wealth- maximization problem and derives an appropriate financing policy. The driving force behind the Carleton model is a series of accounting constraints and firm policy constraints. We have seen that the model relies on a series of estimates of future factors. In making these estimates we have reviewed our growth-estimation skills from Chapter 6. In the next chapter, we will consider another type of financial-planning model, the simultaneous-equation models. Many of the concepts and goals of this chapter will carryover to the next chapter. We will, of course, continue to expand our horizons of knowledge and valuable tools.

60. NOTES  4.

61. NOTES  6. 5.678 + 17.04 + (131.38)(0.09) = 34.542 (1979) 6.605 + 16.04 + (225.18)(0.09) = 42.911 (1980) 7.616 + 14.96 + (297.65)(0.09) = 49.365 (1981) 8.730 + 13.47 + (406.89)(0.09) = 58.820 (1982) 9.962 + 12.24 + (488.40)(0.09) = 66.158 (1983)

62. Appendix 22A. Carleton’s linear-programming model: General Mills as a case study PROBLEM SPECIFICATION MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY M P 0 S VERSION 4.0 MULTI-PURPOSE OPTIMIZATION SYSTEM ***** PROBLEM NUMBER 1 ***** MINIT VARIABLES Dl D2 D3 D4 El E2 E3 E4 E5 AFC1 AFC2 AFC3 AFC4 DL1 DL2 DL3 DL4 MAXIMIZE.018Dl －.0196El ＋.015D2 －.017E2 ＋.013D3 －.0144E3 ＋.011D4 －.0125E4 －.015E5 CONSTRAINTS 1. AFC1 ＋.0441DLl.EQ. 149.17 2. AFC2 ＋.0441DL2.EQ. 173.45 3. AFC3 ＋.0441DL3.EQ. 198.22 4. AFC4 ＋.0441DL4. EQ. 226.05 5. DL1 ＋ E1.EQ. 131.38 6. AFC1 － D1 ＋ DL2 － DL1 ＋ E2.EQ. 255.7 7. AFC2 － D2 ＋ DL3 － DL2 ＋ E3.EQ. 264.3 8. AFC3 － D3 ＋ DL4 － DL3 ＋ E4.EQ. 302.3 9. － AFC4 ＋ D4 ＋ DL4 － E5.EQ. 182.15 10.DL1.LE. 284.42

63. Appendix 22A. Carleton’s linear-programming model: General Mills as a case study 11.DL2.LE. 374.1 12.DL3.LE. 460 13.DL4.LE. 558.7 14.DL1.LE. 243. 6 15. DL2 － DL1.LE. 303.15 16. DL3 － DL2.LE. 329.1 17. DL4 － DL3.LE. 365.1 18.DL4.GE. 101.15 19. －.0566D1 －.0486D2 －.0417D3 －.0358D4 ＋ 1.1740El ＋.0539E2 ＋.0463E3 ＋.0387E4 ＋.034E5.LE. 71.8 20. －.0566D2 －.0486D3 －.04 17D4 ＋.1728E2 ＋.0539E3 ＋.0463E4 ＋.0397E55.LE. 83.8 21. －.0566D3 －.0486D4 ＋ 1.1728E3 ＋.0533E4 ＋.046E5.LE. 97.6 22. －.0566D4 ＋ 1.7280E4 ＋.0539E5.LE. 113.69 23.1.1728E5.LE. 132.44 24.Dl.GE. 51.092 25. D2 － 1.06D1.GE. 0 PROBLEM SPECIFICATION (Cont.)

64. Appendix 22A. Carleton’s linear-programming model: General Mills as a case study 26. D3 － 1.06D2.CE. 0 27. D3 － 1.06D3.GE. 0 28.D4.LE. 79.47 29. D1 －.75AFC1.LE. 0 30. D2 －.75AFC2.LE. 0 31. D3 －.75AFC3.LE. 0 32. D4 －.75AFC4.LE. 0 33. Dl －. 15AFC1.GE. 0 34. D2 －.15AFC2.GE. 0, 35. D3 －.15AFC3.GE. 0 36. D4 －.15AFC4.GE. 0 37. Dl －.4AFCl ＋ D2 －.4AFC2 ＋ D3 －.4AFC3 ＋ D4 －.4AFC4.LE. 9.36 PROBLEM SPECIFICATION (Cont.)

65. Appendix 22A. Carleton’s linear-programming model: General Mills as a case study SOLUTION MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY PROBLEM NUMBER USING MINIT SUMMARY OF RESULTS VARIABLE NO.VARIABLE NAME BASIC NON-BASICACTIVITY LEVELOPPORTUNITY COSTROW NO. 1DlB51.0920000-- 2D2B54.1575200-- 3D3B57.4069712-- 4D4B60.8513895-- 5ElNB--.0015408 6E2B69.6152957-- 7E3B82.4681751-- 8E4B65.3689022-- 9E5B77.4902713-- 10AFC1B143.3761420-- 11AFC2B163.5195372-- 12AFC3B185.0936187--

66. Appendix 22A. Carleton’s linear-programming model: General Mills as a case study VARIABLE NO.VARIABLE NAME BASIC NON-BASICACTIVITY LEVELOPPORTUNITY COSTROW NO. 13AFC4B208.1059384-- 14DL1B131.3800000-- 15DL2B225.1805623-- 16DL3B297.6503700-- 17DL4B406.8948203-- 18--SLACKB153.0400000-- ( 10) 19--SLACKB148.9194377-- ( 11) 20--SLACKB162.3496300-- ( 12) 21--SLACKB151.8051797-- ( 13) 22--SLACKB112.2200000-- ( 14) 23--SLACKB209.3494377-- ( 15) 24--SLACKB256.6301923-- ( 16) 25--SLACKB255.8555497-- ( 17) 26--SLACKB305.7448203-- ( 18) 27--SLACKB69.1612264-- ( 19) 28--SLACKNB--.0002527 ( 20) 29--SLACKNB--.0018351 ( 21) 30--SLACKNB--.0018840 ( 22) SOLUTION (Cont.)

67. Appendix 22A. Carleton’s linear-programming model: General Mills as a case study VARIABLE NO.VARIABLE NAME BASIC NON-BASICACTIVITY LEVELOPPORTUNITY COST ROW NO. 31--SLACKB41.5594098-- ( 23) 32--SLACKNB---.0087826 ( 24) 33--SLACKNB---.0089493 ( 25) 34--SLACKNB---.0069790 ( 26) 35--SLACKNB---.0039896 ( 27) 36--SLACKB18.6686105-- ( 28) 37--SLACKB56.4401065-- ( 29) 38--SLACKB68.4821329-- ( 30) 39--SLACK B 8l.4132428-- ( 31) 40--SLACKB95.2280643-- ( 32) 41--SLACKB29.5855787-- ( 33) 42--SLACKB29.6295894-- ( 34) 43--SLACKB29.6429284-- ( 35) SOLUTION (Cont.)

68. Appendix 22A. Carleton’s linear-programming model: General Mills as a case study VARIABLE NO.VARIABLE NAME BASIC NON-BASICACTIVITY LEVELOPPORTUNITY COST ROW NO. 44--SLACKB29.6354987-- ( 36) 45--SLACKB 65.8902139 -- ( 37) 46- -ARTIFNB--.0172964 ( 1) 47--ARTIFNB--.0165658 ( 2) 48--ARTIFNB--.0158661 ( 3) 49--ARTIFNB--.0151960 ( 4) 50--ARTIFNB---.0180592 ( 5) 51--ARTIFNB---.0172964 ( 6) 52--ARTIFNB---.0165658 ( 7) 53--APTIFNB---.0158661 ( 8) 54--ARTIFNB--.0151960 ( 9) MAXIMUM VALUE OF THE OBJECTIVE FUNCTION = -1,202792 CALCULATION TIME WAS.0670 SECONDS FOR 21 ITERATIONS. SOLUTION (Cont.)

69. Appendix 22B. General Mills’ actual key financial data