Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.

Financial Analysis, Planning and Forecasting

Theory and Application

ByAlice C. Lee

San Francisco State UniversityJohn C. Lee

J.P. Morgan ChaseCheng F. Lee

Rutgers University

Chapter 22

Long-Range Financial Planning – A Linear-Programming Modeling Approach

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

22.2Carleton’s model




22.2 Carleton’s model

22.2 Carleton’s model

22.3 Brief discussion of data inputs




(Cont.)

22.4 Objective-function development

(22.1)

where

,)1()1(

1

1 00

0

T

tt

T

Tt

t

KN

P

KN

D

N

P


(22.2)

(22.3)

(22.3a)

),(''

t

tt N

PNE

,

~

1

1

1

1

j

nj

j

j

P

E

N

N

1 1 1

1 1 1 1

1 or .n n

j j j j j

j j j j

N E N P E

N P N P


(22.4)

(22.5)

1 1

1 1

or .(1 ) 1

j j j j jj j

j j j j

P D P N PP D

N N N K N K

.)1(

)~

( 11

K

EPDP

njj

jj

.)1(

~...

)1(

~

)1(

~

2

2211

jT

nTT

njj

njj

jj K

EP

K

ED

K

EDDP

.)1(

...)1(1

1

0

0

0

0j

j

j

KN

P

KN

D

N

D

N

P


(22.6)

(22.7)

(22.7a)

.)1(

~

...)1(

~

)1(...

)1(11

1

1

0

0

0

0

jT

nTT

njj

jj

j

K

EP

K

ED

KN

D

KN

D

N

D

N

P

)1()1()1(

)1()1()1(

)1()1()1()1()1(

)1()1)(1()1(

50

''5

50

3

40

''4

40

4

30

''3

30

32

0

''2

20

2

0

''1

1

1

0

0

0

0

CKN

E

KN

P

CKN

E

KN

D

CKN

E

KN

D

CKN

E

KN

D

CKN

E

KN

D

N

D

N

PMax

5015.040125.04011.030144.0

3013.02017,02015.010196.01018.0

EEDE

DEDEDMax

22.5 The constraints

Definitional constraints

Policy constraints

22.5 The constraintsFig. 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.)


(22.8)

(22.9)

Because General Mills has no preferred stock or extraordinary items,

AFC = ATP:

.tttt SAPfdivATPAFC

).)(1()(

)()1(

1121

1

'

1,0,

ttt

t

sst

Z

ztzzztttt

eAaAaeAIBB

DLiCLiaAaeAATP


22.5 The constraints01 i 085.02 i

2.651

8.570

7.497

9.431

32.371

1L

2.117

7.102

6.89

7.77

8.66

2L

0

0

0

0

0

~121 LiP

,

,

962.9

7295.8

616.7

6045.6

678.5

~222 LiP



1.731.781.837.887.93

1.531.581.631.681.73

1.135.149.153.177.18

6.43.63.88.93.11

2020303030

00000

8382818079

3

,30,3

L

CL t

%8%875.8%875.4%8%25.4%73 R

.


22.5 The constraintsTo get the interest payment on long-term debt


].~~

[~

'~~)1( 121

3

1

L

ii AeIBBLDiPAFC

2854

5.2488

4.2159

6.1856

1613

)033.0(

15.383

1.365

1.329

15.303

6.243

)36.0()07.0(

~~5

4

3

2

1

)09.0(

24475.12

46525.13

96225.14

04225.16

04425.17

962.9

7295.8

616.7

6045.6

678.5

34.519

53.460

53.406

9.357

9.311

)51.01(

~~~~ '32

LAI

DL

DL

DL

DL

DL

AFC

LDPP


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)

62.255

05.226

22.198

45.173

17.149

5

4

3

2

1

0441.0

5

4

3

2

1

DL

DL

DL

DL

DL

AFC

AFC

AFC

AFC

AFC


(22.11)

where

t

ssstt I

1

',0 )(


(22.12a)

(22.12b)

0

1

1

0

1

0 1 AC

C

C

CI

t

t

01

01 AC

CA

t

t


(22.13)

where

1 1 , 11

Zn

t t t z t t t tz

I AFC D CL DL DTL E

ntE


1

ZL L L L

t zz

I AFC D CL DL DL DTL E

4

3

2

1

0 79.105

AFC

AFC

AFC

AFC

AFC

AFC L

Z

zzt CLIEDLDAFC

11100


].)[1( 0,00 zzLiAFC

,2.2450

.3.29][ 0,zzLi

.2.480 D

.~~ LTT LLCL


5.953

0.872

2.809

4.744

82.696

~TL

0.872

2.809

4.744

82.696

63.641

.~LTL


.

50.81

80.62

80.64

58.47

19.55

.

CL

.79.105]3.292.254)[51.01(0 AFC

82.130

,19.556.2432.4879.105

11

11

EDL

EDL


1

,Z

L L L Lz

z

I AFC D CL DL DL DTL E

5

4

3

2

1

4

3

2

1

4

3

2

1

0

4.488

4

3

2

1

50.81

80.62

80.64

58.47

19.552.48

4

3

2

1

79.105

15.383

1.365

1.329

15.303

6.243

E

E

E

E

E

DL

DL

DL

DL

DL

DL

DL

DL

D

D

D

D

AFC

AFC

AFC

AFC


(22.10e)

(22.10f)

(22.10g)

(22.10h)

(22.10i)

.38.13111 EDL

1 1 22 1 255.7AFC D DL DL E

3.26423 322 EDLDLDAFC

3.30234 433 EDLDLDAFC

15.1824 544 EDLDAFC


(22.14) ,

)(1

'

1 ,0,

XDLiCLi

t

s st

Z

z tzzz

t

24.12

47.13

96.14

04.16

04.17

962.9

7295.8

616.7

6045.6

678.5

~~32 PP

4.488

4

3

2

1

)09.0(

DL

DL

DL

DL


34.519

53.460

53.406

9.357

9.311

~

].~

09.0~~

[~

32 LDPPX

.


].~

09.0~~

[35.6~

32 LDPP

,~

5715.0]~~

[35.6~

32 LDPP

311.9 5.678 17.04 1

357.9 6.6045 16.04 26.35 0.5715 .

406.53 7.616 14.96 3

460.53 8.7295 13.47 4

DL

DL

DL

DL


(22.15a)

(22.15b)

(22.15c)

(22.15d)

1. .293.33,*DL LE

2. .374.64,DL LE

3. .460.49,DL LE

4. .559.17,DL LE


(22.16)

(22.17a)

(22.17b)

,)(11

,0, t

Z

zs

Z

ztzz ADLCL

,0 , 0( ) ;z z t tL C Liabilities DL

)"".(.6.243..1 LELEDL

)"".(.15.303..12 GELEDLDL


(22.17c)

(22.17d)

(22.19)

1.329..23 LEDLDL

15.101..4 GEDL

.01 ttt DD


(22.19a)

(22.19b)

.1~

ttntt PEP

,1

t

t

N

N

.1

11 1

t

t

N

N

.1

1

t

t

N

N


.087.234

)]2854)(033.0(15.383)[36.0)(07.0(

)49.0)(96.4320.2234.519(

)()()1( 4521

5

1

'5

15055

eIBBDLiCLiAFCs

s

Z

zzzz

.)1)(1()1)(1(

)1)(1()1)(1()1()1(

2340

)1()1()1(

45

34

2321

4

34

232

11

kc

E

kc

E

kc

E

kc

E

c

E

k

k

D

k

D

K

DDP

nn

nnn


(22.17f)

,01

)11

( 11

c

EP

9.7106.1

11

)165.01(

2340

034.00387.00463.00539.0174.1

0358.00417.00486.00566.0

4

54321

4321

EEEEE

DDDD


2 3 4 2

3 4 5

2 3 2 4 5

2 4 5

5

0.0566 0.0486 0.0417 1.17280.0539 0.0463 0.0387 . .83.8.0.0566 0.0486 1.1728 0.0539 0.0463 . .97.6.0.0566 1.728 0.0539 . .113.69.

1.1728 . .132.44.

D D D EE E E LED D E E E LED E E LE

E LE

1 0

2 1

3 2

4 3

. .51.092 ( is given)1.06 . .0,1.06 . .0,1.06 . .0.

D GE DD D GED D GED D GE


;36.05

5 AFC

D

5'

5 5 0 5 51 1

1 2 5 4

(1 ) ( )

( )

Z

z z z sz s

AFC i L C i DL

B B I e


.24.84)36.0(

,99.23303.1296.221

)2854)(033.0(15.383)36.0)(07.0(

)41.488)(09.0(44125.12962.934.519)49.0(

4.488

44125.12

886.57.7308.0

712625.41.5308875.0

638625.01.1304875.0

344.03.408.0

085.0200425.0

962.92.117085.0

55

5

5

33

3333

2222

AFCD

AFC

DL

bi

bibi

bibi


(22.17o) 74.79.4 D



1 0 ( 0, ,5),t tD AFC t

2 0 ( 0, ,5),t tD AFC t

;0..115.00..75.0 111 GEAFCDLEAFCD

;0..215.00..75.0 222 GEAFCDLEAFCD

;0..315.00..75.0 333 GEAFCDLEAFCD

.0..415.00..75.0 444 GEAFCDLEAFCD


(22.17f)

0505404

303202101

AFCDAFCD

AFCDAFCDAFCD

.36.9..4.0

4.04.04.0

44

332211

LEAFCD

AFCDAFCDAFCD





22.6 Analysis of overall results

22.6 Analysis of overall results

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.

NOTES

4.

1 n

n

D

AFC

1 n n n

n

D AFC AFCg

E

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)

Appendix 22A. Carleton’s linear-programming

model: General Mills as a case study PROBLEM SPECIFICATION

MPOS VERSION 4.0 NORTHWESTERN UNIVERSITY

M P 0 SVERSION 4.0

MULTI-PURPOSE OPTIMIZATION SYSTEM

***** PROBLEM NUMBER 1 *****

MINIT VARIABLESDl D2 D3 D4 El E2 E3 E4 E5 AFC1 AFC2 AFC3 AFC4 DL1 DL2 DL3 DL4MAXIMIZE.018Dl － .0196El ＋ .015D2 － .017E2 ＋ .013D3 － .0144E3 ＋ .011D4 － .0125E4 － .015E5CONSTRAINTS

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 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.)


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.)


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 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 --


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)

SOLUTION (Cont.)


VARIABLE NO.

VARIABLE NAME

BASIC NON-BASIC ACTIVITY LEVEL OPPORTUNITY COSTROW 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)

SOLUTION (Cont.)


VARIABLE NO.

VARIABLE NAME

BASIC NON-BASIC ACTIVITY LEVEL OPPORTUNITY COSTROW 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

CALCULATION TIME WAS .0670 SECONDS FOR 21 ITERATIONS.

SOLUTION (Cont.)

Appendix 22B. General Mills’ actual key financial data

Appendix 22B. General Mills’ actual key financial data

Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.

Documents

b slide

f slide

d slide

o slide

carletons model slide

longterm debt slide

firm policy constraints

financial analysis