1. 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

2. 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

3. 23.2 Carleton’s model

4. 23.2 Carleton’s model

5. 23.2 Carleton’s model

6. 23.2 Carleton’s model

7. 23.3 Brief discussion of data inputs
Table 23.3

8. 23.3 Brief discussion of data inputs
Table 23.3 Cont.

9. 23.3 Brief discussion of data inputs
Table 23.4

10. 23.3 Brief discussion of data inputs
Table 23.4 Cont.

11. 23.4 Objective-function development
(23.1)
where

12. 23.4 Objective-function development
(23.2)
(23.3)
(23.3a)

13. 23.4 Objective-function development
(23.4)
(23.5)

14. 23.4 Objective-function development
(23.6)
(23.7a)
(23.7b)

15. 23.5 The constraints
Definitional constraints
Policy constraints

16. 23.5 The constraints
Fig 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.)

17. 23.5 The constraints
(23.8)
(23.9)
Because General Mills has no preferred stock or extraordinary items,
AFC = ATP:

18. 23.5 The constraints

19. 23.5 The constraints , ,

20. 23.5 The constraints
Table 23.5 (a)

21. 23.5 The constraints .

22. 23.5 The constraints
Table 23.5 (b)

23. 23.5 The constraints
To get the interest payment on long-term debt

24. 23.5 The constraints

25. 23.5 The constraints AFC1+0.00441DL1=149.17 (23.10a)
AFC DL2= (23.10b)
AFC DL3= (23.10c)
AFC DL4= (23.10d)

26. 23.5 The constraints
(23.11)
where

27. 23.5 The constraints
(23.12a)
(23.12b)

28. 23.5 The constraints
(23.13)
where

29. 23.5 The constraints

30. 23.5 The constraints

31. 23.5 The constraints

32. 23.5 The constraints

33. 23.5 The constraints

34. 23.5 The constraints
(23.10e)
(23.10f)
(23.10g)
(23.10h)
(23.10i)

35. 23.5 The constraints
(23.14)

36. 23.5 The constraints .

37. 23.5 The constraints

38. 23.5 The constraints
(23.15a)
(23.15b)
(23.15c)
(23.15d)

39. 23.5 The constraints
(23.16)
(23.17a)
(23.17b)

40. 23.5 The constraints
(23.17c)
(23.17d)
(23.18a)

41. 23.5 The constraints
(23.18b)
(23.18c)

42. 23.5 The constraints

43. 23.5 The constraints
(23.17f)

44. 23.5 The constraints

45. 23.5 The constraints

46. 22.5 The constraints

47. 23.5 The constraints
(23.17o)

48. 23.5 The constraints
Table 23.6

49. 23.5 The constraints

50. 23.5 The constraints
(23.17t)

51. 23.5 The constraints
Table 23.7

52. 23.5 The constraints
Table 23.7 Cont.

53. 23.5 The constraints
Table 23.7 Cont.

54. 23.5 The constraints
Table 23.7 Cont.

55. 23.6 Analysis of overall results
Table 23.8

56. 23.6 Analysis of overall results
Table 23.9

57. 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.

58. Appendix 23A. Carleton’s linear-programming model: General Mills as a case study
PROBLEM SPECIFICATION
MPOS VERSION 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 2.
AFC2＋.0441DL2 .EQ 3.
AFC3＋.0441DL3 .EQ 4.
AFC4＋.0441DL4. EQ 5.
DL1＋E1 .EQ 6.
AFC1－D1＋DL2－DL1＋E2 .EQ 7.
AFC2－D2＋DL3－DL2＋E3 .EQ 8.
AFC3－D3＋DL4－DL3＋E4 .EQ 9.
－AFC4＋D4＋DL4－E5 .EQ
10.
DL1 .LE

59. Appendix 23A. Carleton’s linear-programming model: General Mills as a case study
PROBLEM SPECIFICATION (Cont.)
11.
DL2 .LE
12.
DL3 .LE. 460
13.
DL4 .LE
14.
DL1 .LE
15.
DL2－DL1 .LE
16.
DL3－DL2 .LE
17.
DL4－DL3 .LE
18.
DL4 .GE
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
23.
1.1728E5 .LE
24.
Dl .GE
25.
D2－1.06D1 .GE. 0

60. 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
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 ,
35.
D3－.15AFC3 .GE. 0
36.
D4－.15AFC4 .GE. 0
37.
Dl－.4AFCl＋D2－.4AFC2＋D3－.4AFC3＋D4－.4AFC4 .LE. 9.36

61. MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY
Appendix 23A. Carleton’s linear-programming model: General Mills as a case study
SOLUTION
MPOS VERSION 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 -- 2 D2 3 D3 4 D4 5 El NB 6 E2 7 E3 8 E4 9 E5 10
AFC1 11
AFC2 12
AFC3

62. 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 -- 14
DL1 15
DL2 16
DL3 17
DL4 18
--SLACK
( 10) 19
( 11) 20
( 12) 21
( 13) 22
( 14) 23
( 15) 24
( 16) 25
( 17) 26
( 18) 27
( 19) 28 NB
( 20) 29
( 21) 30
( 22)

63. 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 --
( 23) 32 NB
( 24) 33
( 25) 34
( 26) 35
( 27) 36
( 28) 37
( 29) 38
( 30) 39 8l
( 31) 40
( 32) 41
( 33) 42
( 34) 43
( 35)

64. 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 --
( 36) 45
( 37) 46
- -ARTIF NB
( 1) 47
--ARTIF
( 2) 48
( 3) 49
( 4) 50
( 5) 51
( 6) 52
( 7) 53
--APTIF
( 8) 54
( 9)
MAXIMUM VALUE OF THE OBJECTIVE FUNCTION = ,202792
CALCULATION TIME WAS SECONDS FOR 21 ITERATIONS.

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

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