Financial Analysis, Planning and Forecasting Theory and Application

1
Financial Analysis, Planning and
ForecastingTheory and Application
Chapter 22
Long-Range Financial Planning A
Linear-Programming Modeling Approach

• By
• Alice C. Lee
• San Francisco State University
• John C. Lee
• J.P. Morgan Chase
• Cheng F. Lee
• Rutgers University

2
Outline

• 22.1 Introduction
• 22.2 Carletons 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. Carletons linear-programming
  model General Mills as a case study
• Appendix 22B. General Mills actual key financial
  data

3
22.2 Carletons model
4
22.2 Carletons model
5
22.2 Carletons model
6
22.2 Carletons model
7
22.2 Carletons model
8
22.2 Carletons model
9
22.3 Brief discussion of data inputs
10
22.3 Brief discussion of data inputs
11
22.3 Brief discussion of data inputs
12
22.3 Brief discussion of data inputs
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
22.5 The constraints
,
,
22
22.5 The constraints
23
22.5 The constraints
.
24
22.5 The constraints
25
22.5 The constraints

• To get the interest payment on long-term debt

26
22.5 The constraints
27
22.5 The constraints

• AFC10.00441DL1149.17 (22.10a)
• AFC20.00441DL2173.45 (22.10b)
• AFC30.00441DL3198.22 (22.10c)
• AFC40.00441DL4226.05 (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
32
22.5 The constraints
33
22.5 The constraints
34
22.5 The constraints
35
22.5 The constraints
36
22.5 The constraints

• (22.10e)
• (22.10f)
• (22.10g)
• (22.10h)
• (22.10i)

37
22.5 The constraints

• (22.14)

38
22.5 The constraints
.
39
22.5 The constraints
40
22.5 The constraints

• (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
22.5 The constraints

• (22.17f)

46
22.5 The constraints
47
22.5 The constraints
48
22.5 The constraints
49
22.5 The constraints

• (22.17o)

50
22.5 The constraints
51
22.5 The constraints
52
22.5 The constraints

• (22.17f)

53
22.5 The constraints
54
22.5 The constraints
55
22.5 The constraints
56
22.5 The constraints
57
22.6 Analysis of overall results
58
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. Carletons linear-programming
model General Mills as a case study

• PROBLEM SPECIFICATION

MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY
M P 0 S VERSION 4.0 MULTI-PURPOSE OPTIMIZATION SYSTEM M P 0 S VERSION 4.0 MULTI-PURPOSE OPTIMIZATION SYSTEM
PROBLEM NUMBER 1 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 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. DL1E1 .EQ. 131.38
6. AFC1-D1DL2-DL1E2 .EQ. 255.7
7. AFC2-D2DL3-DL2E3 .EQ. 264.3
8. AFC3-D3DL4-DL3E4 .EQ. 302.3
9. -AFC4D4DL4-E5 .EQ. 182.15
10. DL1 .LE. 284 .42
63
Appendix 22A. Carletons 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-.0358D41.1740El.0539E2.0463E3.0387E4 .034E5 .LE. 71.8
20. -.0566D2-.0486D3-.04 17D4.1728E2.0539E3.0463E4.0397E55 .LE. 83.8
21. -.0566D3-.0486D41.1728E3.0533E4.046E5 .LE. 97.6
22. -.0566D41.7280E4.0539E5 .LE. 113.69
23. 1.1728E5 .LE. 132.44
24. Dl .GE. 51.092
25. D2-1.06D1 .GE. 0
64
Appendix 22A. Carletons 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-.4AFClD2-.4AFC2D3-.4AFC3D4-.4AFC4 .LE. 9.36
65
Appendix 22A. Carletons linear-programming
model General Mills as a case study

• SOLUTION

MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY
PROBLEM NUMBER PROBLEM NUMBER PROBLEM NUMBER PROBLEM NUMBER PROBLEM NUMBER PROBLEM NUMBER
USING MINIT USING MINIT USING MINIT USING MINIT USING MINIT USING MINIT
SUMMARY OF RESULTS SUMMARY OF RESULTS SUMMARY OF RESULTS SUMMARY OF RESULTS SUMMARY OF RESULTS SUMMARY OF RESULTS
VARIABLE NO. VARIABLE NAME BASIC NON-BASIC ACTIVITY LEVEL OPPORTUNITY COST ROW NO.
1 Dl B 51.0920000 --
2 D2 B 54.1575200 --
3 D3 B 57.4069712 --
4 D4 B 60.8513895 --
5 El NB -- .0015408
6 E2 B 69.6152957 --
7 E3 B 82.4681751 --
8 E4 B 65.3689022 --
9 E5 B 77.4902713 --
10 AFC1 B 143.3761420 --
11 AFC2 B 163.5195372 --
12 AFC3 B 185.0936187 --
66
Appendix 22A. Carletons 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 B 131.3800000 --
15 DL2 B 225.1805623 --
16 DL3 B 297.6503700 --
17 DL4 B 406.8948203 --
18 --SLACK B 153.0400000 -- ( 10)
19 --SLACK B 148.9194377 -- ( 11)
20 --SLACK B 162.3496300 -- ( 12)
21 --SLACK B 151.8051797 -- ( 13)
22 --SLACK B 112.2200000 -- ( 14)
23 --SLACK B 209.3494377 -- ( 15)
24 --SLACK B 256.6301923 -- ( 16)
25 --SLACK B 255.8555497 -- ( 17)
26 --SLACK B 305.7448203 -- ( 18)
27 --SLACK B 69.1612264 -- ( 19)
28 --SLACK NB -- .0002527 ( 20)
29 --SLACK NB -- .0018351 ( 21)
30 --SLACK NB -- .0018840 ( 22)
67
Appendix 22A. Carletons 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 --SLACK NB -- -.0087826 ( 24)
33 --SLACK NB -- -.0089493 ( 25)
34 --SLACK NB -- -.0069790 ( 26)
35 --SLACK NB -- -.0039896 ( 27)
36 --SLACK B 18.6686105 -- ( 28)
37 --SLACK B 56.4401065 -- ( 29)
38 --SLACK B 68.4821329 -- ( 30)
39 --SLACK B 8l.4132428 -- ( 31)
40 --SLACK B 95.2280643 -- ( 32)
41 --SLACK B 29.5855787 -- ( 33)
42 --SLACK B 29.6295894 -- ( 34)
43 --SLACK B 29.6429284 -- ( 35)
68
Appendix 22A. Carletons 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 --SLACK B 65.8902139 -- ( 37)
46 - -ARTIF NB -- .0172964 ( 1)
47 --ARTIF NB -- .0165658 ( 2)
48 --ARTIF NB -- .0158661 ( 3)
49 --ARTIF NB -- .0151960 ( 4)
50 --ARTIF NB -- -.0180592 ( 5)
51 --ARTIF NB -- -.0172964 ( 6)
52 --ARTIF NB -- -.0165658 ( 7)
53 --APTIF NB -- -.0158661 ( 8)
54 --ARTIF NB -- .0151960 ( 9)

MAXIMUM VALUE OF THE OBJECTIVE FUNCTION -1,202792 MAXIMUM VALUE OF THE OBJECTIVE FUNCTION -1,202792 MAXIMUM VALUE OF THE OBJECTIVE FUNCTION -1,202792 MAXIMUM VALUE OF THE OBJECTIVE FUNCTION -1,202792 MAXIMUM VALUE OF THE OBJECTIVE FUNCTION -1,202792 MAXIMUM VALUE OF THE OBJECTIVE FUNCTION -1,202792
CALCULATION TIME WAS .0670 SECONDS FOR 21 ITERATIONS. CALCULATION TIME WAS .0670 SECONDS FOR 21 ITERATIONS. CALCULATION TIME WAS .0670 SECONDS FOR 21 ITERATIONS. CALCULATION TIME WAS .0670 SECONDS FOR 21 ITERATIONS. CALCULATION TIME WAS .0670 SECONDS FOR 21 ITERATIONS. CALCULATION TIME WAS .0670 SECONDS FOR 21 ITERATIONS.
69
Appendix 22B. General Mills actual key
financial data
70
Appendix 22B. General Mills actual key
financial data