Financial Analysis, Planning and Forecasting Theory and Application Chapter 23 Long-Range Financial Planning – A Linear-Programming Modeling Approach By Cheng F. Lee Rutgers University, USA John Lee Center for PBBEF Research, USA

Outline 23.1 Introduction 23.2 Carleton’s model 23.3 Brief discussion of data inputs 23.4 Objective-function development 23.5 The constraints 23.6 Analysis of overall results 23.7 Summary Appendix 23A. Carleton’s linear-programming model: General Mills as a case study Appendix 23B. General Mills’ actual key financial data

23.2 Carleton’s model

23.2 Carleton’s model

23.2 Carleton’s model

23.2 Carleton’s model

23.3 Brief discussion of data inputs Table 23.3

23.3 Brief discussion of data inputs Table 23.3 Cont.

23.3 Brief discussion of data inputs Table 23.4

23.3 Brief discussion of data inputs Table 23.4 Cont.

23.4 Objective-function development (23.1) where

23.4 Objective-function development (23.2) (23.3) (23.3a)

23.4 Objective-function development (23.4) (23.5)

23.4 Objective-function development (23.6) (23.7a) (23.7b)

23.5 The constraints Definitional constraints Policy constraints

23.5 The constraints Fig. 23.1 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.)

23.5 The constraints (23.8) (23.9) Because General Mills has no preferred stock or extraordinary items, AFC = ATP:

23.5 The constraints

23.5 The constraints , ,

23.5 The constraints Table 23.5 (a)

23.5 The constraints .

23.5 The constraints Table 23.5 (b)

23.5 The constraints To get the interest payment on long-term debt

23.5 The constraints

23.5 The constraints AFC1+0.00441DL1=149.17 (23.10a) AFC2+0.00441DL2=173.45 (23.10b) AFC3+0.00441DL3=198.22 (23.10c) AFC4+0.00441DL4=226.05 (23.10d)

23.5 The constraints (23.11) where

23.5 The constraints (23.12a) (23.12b)

23.5 The constraints (23.13) where

23.5 The constraints

23.5 The constraints

23.5 The constraints

23.5 The constraints

23.5 The constraints

23.5 The constraints (23.10e) (23.10f) (23.10g) (23.10h) (23.10i)

23.5 The constraints (23.14)

23.5 The constraints .

23.5 The constraints

23.5 The constraints (23.15a) (23.15b) (23.15c) (23.15d)

23.5 The constraints (23.16) (23.17a) (23.17b)

23.5 The constraints (23.17c) (23.17d) (23.18a)

23.5 The constraints (23.18b) (23.18c)

23.5 The constraints

23.5 The constraints (23.17f)

23.5 The constraints

23.5 The constraints

22.5 The constraints

23.5 The constraints (23.17o)

23.5 The constraints Table 23.6

23.5 The constraints

23.5 The constraints (23.17t)

23.5 The constraints Table 23.7

23.5 The constraints Table 23.7 Cont.

23.5 The constraints Table 23.7 Cont.

23.5 The constraints Table 23.7 Cont.

23.6 Analysis of overall results Table 23.8

23.6 Analysis of overall results Table 23.9

23.7 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 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.

Appendix 23A. 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

Appendix 23A. Carleton’s linear-programming model: General Mills as a case study PROBLEM SPECIFICATION (Cont.) 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

Appendix 23A. Carleton’s linear-programming model: General Mills as a case study PROBLEM SPECIFICATION (Cont.) 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

MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY Appendix 23A. 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-BASIC ACTIVITY LEVEL OPPORTUNITY COST ROW NO. 1 Dl B 51.0920000 -- 2 D2 54.1575200 3 D3 57.4069712 4 D4 60.8513895 5 El NB .0015408 6 E2 69.6152957 7 E3 82.4681751 8 E4 65.3689022 9 E5 77.4902713 10 AFC1 143.3761420 11 AFC2 163.5195372 12 AFC3 185.0936187

Appendix 23A. Carleton’s linear-programming model: General Mills as a case study SOLUTION (Cont.) VARIABLE NO. VARIABLE NAME BASIC NON-BASIC ACTIVITY LEVEL OPPORTUNITY COST ROW NO. 13 AFC4 B 208.1059384 -- 14 DL1 131.3800000 15 DL2 225.1805623 16 DL3 297.6503700 17 DL4 406.8948203 18 --SLACK 153.0400000 ( 10) 19 148.9194377 ( 11) 20 162.3496300 ( 12) 21 151.8051797 ( 13) 22 112.2200000 ( 14) 23 209.3494377 ( 15) 24 256.6301923 ( 16) 25 255.8555497 ( 17) 26 305.7448203 ( 18) 27 69.1612264 ( 19) 28 NB .0002527 ( 20) 29 .0018351 ( 21) 30 .0018840 ( 22)

Appendix 23A. Carleton’s linear-programming model: General Mills as a case study SOLUTION (Cont.) VARIABLE NO. VARIABLE NAME BASIC NON-BASIC ACTIVITY LEVEL OPPORTUNITY COST ROW NO. 31 --SLACK B 41.5594098 -- ( 23) 32 NB -.0087826 ( 24) 33 -.0089493 ( 25) 34 -.0069790 ( 26) 35 -.0039896 ( 27) 36 18.6686105 ( 28) 37 56.4401065 ( 29) 38 68.4821329 ( 30) 39 8l.4132428 ( 31) 40 95.2280643 ( 32) 41 29.5855787 ( 33) 42 29.6295894 ( 34) 43 29.6429284 ( 35)

Appendix 23A. Carleton’s linear-programming model: General Mills as a case study SOLUTION (Cont.) VARIABLE NO. VARIABLE NAME BASIC NON-BASIC ACTIVITY LEVEL OPPORTUNITY COST ROW NO. 44 --SLACK B 29.6354987 -- ( 36) 45 65.8902139 ( 37) 46 - -ARTIF NB .0172964 ( 1) 47 --ARTIF .0165658 ( 2) 48 .0158661 ( 3) 49 .0151960 ( 4) 50 -.0180592 ( 5) 51 -.0172964 ( 6) 52 -.0165658 ( 7) 53 --APTIF -.0158661 ( 8) 54 ( 9) MAXIMUM VALUE OF THE OBJECTIVE FUNCTION = -1,202792 CALCULATION TIME WAS .0670 SECONDS FOR 21 ITERATIONS.

Appendix 23B. General Mills’ actual key financial data Table 23.B.1

Appendix 23B. General Mills’ actual key financial data Table 23.B.2