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Transcript of Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco...
![Page 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.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/1.jpg)
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
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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
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22.2Carleton’s model
![Page 4: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/4.jpg)
22.2Carleton’s model
![Page 5: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/5.jpg)
22.2Carleton’s model
![Page 6: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/6.jpg)
22.2Carleton’s model
![Page 7: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/7.jpg)
22.2 Carleton’s model
![Page 8: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/8.jpg)
22.2 Carleton’s model
![Page 9: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/9.jpg)
22.3 Brief discussion of data inputs
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22.3 Brief discussion of data inputs
![Page 11: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/11.jpg)
22.3 Brief discussion of data inputs
![Page 12: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/12.jpg)
22.3 Brief discussion of data inputs
(Cont.)
![Page 13: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/13.jpg)
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
![Page 14: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/14.jpg)
22.4 Objective-function development
(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
![Page 15: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/15.jpg)
22.4 Objective-function development
(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(
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jj K
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1
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P
![Page 16: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/16.jpg)
22.4 Objective-function development
(22.6)
(22.7)
(22.7a)
.)1(
~
...)1(
~
)1(...
)1(11
1
1
0
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njj
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)1()1()1(
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50
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3
40
''4
40
4
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''3
30
32
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20
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PMax
5015.040125.04011.030144.0
3013.02017,02015.010196.01018.0
EEDE
DEDEDMax
![Page 17: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/17.jpg)
22.5 The constraints
Definitional constraints
Policy constraints
![Page 18: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/18.jpg)
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.)
![Page 19: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/19.jpg)
22.5 The constraints
(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
![Page 20: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/20.jpg)
22.5 The constraints
![Page 21: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/21.jpg)
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
![Page 22: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/22.jpg)
22.5 The constraints
![Page 23: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/23.jpg)
22.5 The constraints
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
.
![Page 24: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/24.jpg)
22.5 The constraints
![Page 25: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/25.jpg)
22.5 The constraintsTo get the interest payment on long-term debt
![Page 26: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/26.jpg)
22.5 The constraints
].~~
[~
'~~)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
![Page 27: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/27.jpg)
22.5 The constraints
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
![Page 28: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/28.jpg)
22.5 The constraints
(22.11)
where
t
ssstt I
1
',0 )(
![Page 29: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/29.jpg)
22.5 The constraints
(22.12a)
(22.12b)
0
1
1
0
1
0 1 AC
C
C
CI
t
t
01
01 AC
CA
t
t
![Page 30: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/30.jpg)
22.5 The constraints
(22.13)
where
1 1 , 11
Zn
t t t z t t t tz
I AFC D CL DL DTL E
ntE
![Page 31: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/31.jpg)
22.5 The constraints
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
![Page 32: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/32.jpg)
22.5 The constraints
].)[1( 0,00 zzLiAFC
,2.2450
.3.29][ 0,zzLi
.2.480 D
.~~ LTT LLCL
![Page 33: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/33.jpg)
22.5 The constraints
5.953
0.872
2.809
4.744
82.696
~TL
0.872
2.809
4.744
82.696
63.641
.~LTL
![Page 34: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/34.jpg)
22.5 The constraints
.
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
![Page 35: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/35.jpg)
22.5 The constraints
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
![Page 36: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/36.jpg)
22.5 The constraints
(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
![Page 37: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/37.jpg)
22.5 The constraints
(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
![Page 38: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/38.jpg)
22.5 The constraints
34.519
53.460
53.406
9.357
9.311
~
].~
09.0~~
[~
32 LDPPX
.
![Page 39: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/39.jpg)
22.5 The constraints
].~
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
![Page 40: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/40.jpg)
22.5 The constraints
(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
![Page 41: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/41.jpg)
22.5 The constraints
(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
![Page 42: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/42.jpg)
22.5 The constraints
(22.17c)
(22.17d)
(22.19)
1.329..23 LEDLDL
15.101..4 GEDL
.01 ttt DD
![Page 43: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/43.jpg)
22.5 The constraints
(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
![Page 44: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/44.jpg)
22.5 The constraints
.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
![Page 45: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/45.jpg)
22.5 The constraints
(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
![Page 46: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/46.jpg)
22.5 The constraints
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
![Page 47: Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng.](https://reader035.fdocuments.in/reader035/viewer/2022062320/56649cac5503460f9496dcd8/html5/thumbnails/47.jpg)
22.5 The constraints
;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
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22.5 The constraints
.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
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22.5 The constraints
(22.17o) 74.79.4 D
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22.5 The constraints
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22.5 The constraints
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
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22.5 The constraints
(22.17f)
0505404
303202101
AFCDAFCD
AFCDAFCDAFCD
.36.9..4.0
4.04.04.0
44
332211
LEAFCD
AFCDAFCDAFCD
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22.5 The constraints
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22.5 The constraints
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22.5 The constraints
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22.5 The constraints
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22.6 Analysis of overall results
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22.6 Analysis of overall results
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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.
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NOTES
4.
1 n
n
D
AFC
1 n n n
n
D AFC AFCg
E
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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)
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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
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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.)
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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.)
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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-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 --
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Appendix 22A. Carleton’s linear-programming model: General Mills as a case study
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.)
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Appendix 22A. Carleton’s linear-programming model: General Mills as a case study
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.)
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Appendix 22A. Carleton’s linear-programming model: General Mills as a case study
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.)
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Appendix 22B. General Mills’ actual key financial data
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Appendix 22B. General Mills’ actual key financial data