Jose A. Briones, Ph.D.
SpyroTek Performance Solutions, LLC
Palisade’s Risk Analysis Conference, October 2009
Introduction
Model description
Financial modeling inputs
Scenario modeling
Results analysis
Profitability projections in a manufacturing environment are
directly tied to how the sales forecast fits with the capability
of the operation.
When a company has a large portfolio of products with very
different operational production rates, the manufacturing
capacity of the plant will be significantly impacted by the
product mix to be produced. This in turn will have a radical
effect on the output of the plant and the allocation of the
fixed cost of production.
There is a need to integrate the financial model with the
production forecast and production capabilities
In this case we present an example where a
company is trying to meet the following
objectives
Balance sales and production of certain families of
products to maximize profit
Maintain a diverse product line
Properly price each individual product based on
the impact to the manufacturing schedule and
fixed cost allocation
Model uses @Risk probabilistic decision analysis software
Monte Carlo simulation
Risk and opportunity analysis
Designed for complex projects with high levels of
uncertainty
Inputs contain high number of variables, either technical or financial
with a high degree of uncertainty, assumptions and dependencies
▪
▪
▪
▪
New product development assessment
Capital spending decisions
Value chain analysis
Production and sales forecasting analysis
Eliminates use of “one at a time” cases
Analyzes thousands of cases simultaneously
Generates a range of outcomes
Outcome charts are analyzed to make decisions on direction
Input values are entered in range format – Width and shape
of range are critical inputs
Definition of the input ranges is the most critical step
Do not start with the typical value, start with the range, define the
shape of the function (10%, 50%, 90% probability).
There are multiple choices for the shape of the input range:
Triangular: Most common for initial assumptions
Normal distribution: Used when more accurate input data
is available
PERT: When data is in form of probabilities
Gamma distribution: Good to model pricing distributions
in B-B cases
Multiline product portfolio
4 Product families – A, B, C, D
A, C and D are existing products
B is a new product family that is meant to replace
product A
▪ B has higher margins than A but lower production rates
▪ C and D have higher margins than B but even lower
production rates
4 Production lines – 1, 2, 3, 4
Products A and B can be made in all production
lines
▪ Products A and B have different production rates
Products C and D can only be made in lines 3 and 4
▪ Products C and D have different production rates
Post-treatment facility after production lines
limits total production rate
Product Family A
Line 1
125 Kg/hr/line
Product Family B
Line 2
87.5 Kg/hr/line
Product Family C
Post-Treatment
Facility
Line 3
62.5 Kg/hr/line
Product Family D
37.5 Kg/hr/line
Line 4
350 Kg/hr
Manufacturing facility was being upgraded
and debottlenecked.
Production rates for all products were expected to
change as the project progresses throughout the
year.
Variable margins are different for all product
families and cannot be known with absolute
certainty
Sales forecast is not exact, has variability
Fixed costs billed in foreign exchange
Business manager wants to forecast total
business profitability and profit by product
under 2 scenarios:
1. Maintain forecast for Product C and D fixed and
evaluate if Product A should be discontinued
and replaced by better performing Product B
2. Maximize sales of Product C, maintain D
forecast fixed, again evaluate Product B vs. A
Typical
Production Target of product C, Kg/mo
Production Target of product D, Kg/mo
Production Rate of Product A, lines 1 and 2, Kg/hr
Production Rate of Product B, lines 1 and 2, Kg/hr
Rate of Production product C, lines 3 and 4 Kg/hr
Rate of Production product D, lines 3 and 4 Kg/hr
Maximum Production Rate 4 lines running, Kg/hr
Var Margin Product A US$/kg
Var Margin Product B US$/kg
Var Margin Product C US$/kg
Var Margin Product D US$/kg
Plant fixed cost Euros/month
Selling & Admin costs Euros/month
Projected fixed cost savings Euros/month
US Dollar/ Euro Exchange Rate
15,000
10,000
Range
Min
10,000
5,000
Range
Max
20,000
15,000
250
175
125
75
350
240
165
90
60
330
260
200
140
80
370
$2.50
$2.75
$4.00
$5.00
$2.30
$2.60
$3.50
$4.50
$2.70
$3.00
$4.50
$5.50
500,000 €
50,000 €
75,000 €
0.8
450,000 € 550,000 €
45,000 € 55,000 €
65,000 € 90,000 €
0.7
0.95
Plant will be run at full capacity to maximize
profit.
Production capacity of products A or B is
dependent on the free time left after meeting
production targets for C and D.
Common method of dividing total fixed cost by
the total production is not acceptable when
products have widely different production rates.
In order to calculate profitability by product, we
need to allocate fixed costs based on projected
run time for each product family
This allows us to make the right decisions as to
which product to promote or stop promoting.
Do not subsidize slow running products.
Calculate % manufacturing time used to
meet forecast of C & D
Calculate % manufacturing time available to
manufacture A or B
Calculate maximum production of A or B
subject to treatment line constraints
Estimate total profitability and gross profit by
product
Run sensitivity analysis
0.772 0.829
% of treatment line time
devoted to A + B Grades /
Column
5.0%
100.0%
60
Minimum
Maximum
Mean
Std Dev
Values
50
40
D
% of treatment line time
devoted to Product D /
Column
30
20
C
Minimum
Maximum
Mean
Std Dev
Values
A or B
10
0.0854
0.1304
0.1031
0.00761
1000
9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.0
0.7431
0.8577
0.8027
0.0176
1000
20% of Production time is allocated to C & D
Values
1000
0.
% of treatment line time devoted to A or B, C & D
% of treatment line time
devoted to Product C /
Column
Minimum
Maximum
Mean
Std Dev
0.0549
0.1432
0.0941
0.0155
Total theoretical capacity, Product A plus Products C & D, kg/yr
2.699
5.0%
92.3%
7
2.906
90.0%
7.7%
Values x 10^-6
6
5.0%
0.0%
Total theoretical capacity,
Product A plus Products C &
D, kg/yr
Minimum
Maximum
Mean
Std Dev
Values
A
5
B
4
3
2633085.3298
3018607.7688
2803346.2034
63912.9226
1000
Total theoretical capacity,
Product B plus products C &
D, kg/yr
2
1
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
2.3
0
Minimum
Maximum
Mean
Std Dev
Values
2357095.8177
2788160.2845
2604929.4916
65567.7702
1000
Values in Millions
Substituting Product A with Product B Results in Lower Total Plant Capacity
Profitability, Product A vs. Product B US$/yr
0.000
17.3%
11.3%
8
75.9%
75.8%
6.8%
12.9%
Profitability, Product A Case
US$/yr / Column
A
7
Values x 10^-7
7
1.450
6
A
5
Minimum
Maximum
Mean
Std Dev
Values
B
-1219775.4188
2289688.1319
596061.7364
598929.0090
1000
4
Profitability, Product B Case
US$/yr / Column
3
2
1
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
Minimum
Maximum
Mean
Std Dev
Values
Values in Millions
Product B has a lower probability of losses than product A
-1091259.4015
2484366.8328
752663.4930
597144.6785
1000
Fixed cost US$/kg Products A, B, C, D
5.45
5.0%
99.8%
2.5
2.0
7.40
90.0%
0.2%
Fixed cost US$/kg Product
D
5.0%
0.0%
Minimum
Maximum
Mean
Std Dev
Values
B
Fixed cost US$/kg Product
C
1.5
A
1.0
C
Minimum
Maximum
Mean
Std Dev
Values
D
0.5
Values in $
Slower production rates result in much higher
fixed costs for Products C and D
9
8
7
6
5
4
3
2
0.0
1
$4.9476
$8.3905
$6.3397
$0.6112
1000
$2.8058
$5.5362
$3.8559
$0.4473
1000
Fixed cost US$/kg Product
A
Minimum
Maximum
Mean
Std Dev
Values
$1.8656
$2.9132
$2.3665
$0.1899
1000
Fixed cost US$/kg Product
B
Minimum
Maximum
Mean
Std Dev
Values
$2.0664
$3.1881
$2.5700
$0.1997
1000
Gross Profit Products A, B, C, D US$/Kg
-0.22 0.48
5.0%
2.9%
2.5
Profit Product A US$/Kg /
Column
5.0%
12.1%
Minimum
Maximum
Mean
Std Dev
Values
2.0
A
1.5
Profit Product B US$/Kg /
Column
B
1.0
D
Minimum
Maximum
Mean
Std Dev
Values
C
0.5
2
1
Values in $ Profit Product D US$/Kg /
Minimum
Maximum
Mean
Std Dev
-$0.4348
$0.8052
$0.2133
$0.2216
1000
Profit Product C US$/Kg /
0
-1
-2
-3
-4
-5
0.0
Product D has a Negative Gross
Profit Due to Long Production
Cycles
-$0.5836
$0.7011
$0.1335
$0.2097
1000
-$4.5032
-$0.7534
-$2.3397
$0.6452
Minimum
Maximum
Mean
Std Dev
Values
-$1.5576
$1.4447
$0.1441
$0.4867
1000
% of treatment line time devoted to A/B, C & D Grades
0.448
5.0%
100.0%
60
0.575
90.0%
0.0%
% of treatment line time
devoted to A + B Grades /
Column
5.0%
0.0%
Minimum
Maximum
Mean
Std Dev
Values
D
50
40
0.3699
0.6080
0.5203
0.0384
5000
% of treatment line time
devoted to Product D /
Column
30
20
C
Minimum
Maximum
Mean
Std Dev
Values
A or B
10
~50% of time devoted to C & D
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
0.0849
0.1304
0.1032
0.00770
5000
% of treatment line time
devoted to Product C /
Column
Minimum
Maximum
Mean
Std Dev
Values
0.2963
0.5094
0.3766
0.0374
5000
Total theoretical capacity, Product A vs. B plus Products C & D, kg/yr
2.700
5.0%
100.0%
7
2.906
90.0%
0.0%
Total theoretical capacity,
Product A plus Products C &
D, kg/yr
A
6
Values x 10^-6
5.0%
0.0%
Minimum
Maximum
Mean
Std Dev
Values
5
4
2596788.1735
3001093.4875
2803246.3861
62557.3764
5000
B
3
Total theoretical capacity,
Product B plus products C &
D, kg/yr
2
1
3.2
3.0
2.8
2.6
2.4
2.2
2.0
1.8
0
Minimum
Maximum
Mean
Std Dev
Values
1942146.1959
2697819.5994
2362657.7945
120704.1615
5000
Values in Millions
Production of B v.s A results in a more significant loss of capacity compared to Scenario 1
Profitability, Product A vs B Case US$/yr
0.00
1.45
1.2%
51.1%
47.7%
13.2%
72.0%
14.8%
Profitability, Product A Case
7
US$/yr / Column
6
V a lu e s x 1 0 ^ -7
B
A
5
Minimum
-852160.3638
Maximum
3287264.9694
Mean
1405082.2802
Std Dev
608985.6034
Values
4
3
5000
Profitability, Product B Case
US$/yr / Column
2
1
0
Minimum
-2021651.9911
Maximum
3250368.3280
Mean
735213.2672
Std Dev
665321.2558
5000
4
3
2
1
0
-1
-2
-3
Values
Values in Millions
Production of A has less than 2% probability of losses, 48% probability of profit >1.5 MM $
Fixed cost US$/kg Products A, B, C & D
5.40
5.0%
99.8%
2.0
1.8
7.43
90.0%
0.2%
Fixed cost US$/kg Product
D / Column
5.0%
0.0%
Minimum
Maximum
Mean
Std Dev
Values
A
1.6
B
1.4
$4.6730
$8.7315
$6.3410
$0.6228
5000
Fixed cost US$/kg Product
C / Column
1.2
1.0
C
0.8
D
Minimum
Maximum
Mean
Std Dev
Values
0.6
0.4
0.2
Values in $
Fixed cost US$/kg Product
A / Column
9
8
7
6
5
4
3
2
1
0.0
$2.6522
$5.8660
$3.8579
$0.4645
5000
Minimum
Maximum
Mean
Std Dev
Values
Fixed Cost of Product A drops in this scenario
$1.2306
$2.6219
$1.9559
$0.2068
5000
Fixed cost US$/kg Product
B. / Column
Minimum
Maximum
Mean
Std Dev
Values
$1.8782
$3.2967
$2.5241
$0.2136
5000
Profit Products A, B C & D US$/Kg
0.00
0.91
0.7%
94.3%
5.0%
13.2%
86.7%
0.1%
B
1.4
-$0.1944
Minimum
-$4.8411
Maximum
$1.2512
Maximum
-$0.3715
Mean
$0.5441
Mean
-$2.3410
$0.2233
Std Dev
Minimum
1.8
1.6
Profit Product D US$/Kg /
Column
Profit Product A US$/Kg /
Column
A
Std Dev
Values
5000
1.2
Profit Product B US$/Kg /
Column
1.0
0.8
D
0.6
C
Minimum
-$0.6366
Maximum
$1.0344
Mean
$0.2593
0.4
Std Dev
$0.2276
0.2
Values
Profit Product C US$/Kg /
Column
2
1
0
-1
-2
-3
-4
-5
0.0
Values in $
Minimum
-$2.0249
Maximum
$1.5637
Mean
$0.1421
Std Dev
$0.5091
Values
Profit of Product A increases in this scenario
5000
5000
Values
$0.6569
5000
Scenario 1 - A
Scenario 1 - B
Scenario 2 - A
Scenario 2 - B
% time devoted
to C & D
20%
20%
48%
48%
Production of C
0.2 MM kg/yr
0.2 MM kg/yr
0.7 MM kg/yr
0.7 MM kg/yr
Total Plant
Capacity
2.8 MM kg/yr
2.6 MM kg/yr
2.8 MM kg/yr
2.4 MM kg/yr
Profitability
0.6 MM$/yr
0.75 MM$/yr
1.4 MM $/yr
0.7 MM $/yr
17%
11%
1%
13%
Probability of
Losses
Scenario 2 with sales of Product A has the best probability for higher profits
Scenario 1 –
Fixed Cost/Kg
Scenario 1 –
Gross Profit/Kg
Scenario 2 –
Fixed Cost/Kg
Scenario 2 –
Gross Profit/Kg
Product A
$2.37
$0.13
$1.96
$0.54
Product B
$2.57
$0.21
$2.52
$0.26
Product C
$3.86
$0.14
$3.85
$0.14
Product D
$6.34
-$2.34
$6.34
-$2.34
Fixed cost for Product A drops in Scenario 2, gross profit increases
Product D has negative gross profit under both scenarios
Profitability, Product A Case US$/yr / Column
Regression Coefficients
US Dollar/ Euro Exchange Rate
0.73
-0.51
Plant fixed cost Euros/month
0.34
Var Margin Product A US$/kg
0.22
Maximum Production Rate 4 lines running, kg/hr
0.13
Projected fixed cost savings Euros/month
0.10
Operational Efficiency
Days of the week operating
0.07
Production of product C, Kg/mo
0.06
0.06
Var Margin Product C US$/kg
-0.05
Selling & Admin costs Euros/month
0.05
Rate of Production product D, Kg/mo
0.04
Var Margin Product D US$/kg
Production Rate of Product A, lines 1 and 2, kg/hr
0.03
Hours/day operating
0.02
Coefficient Value
0.8
0.6
0.4
0.0
-0.2
-0.4
-0.6
0.2
0.01
Production of product D, Kg/mo
Maximum Production Rate for the 4 lines is a critical factor for profitability of A
Product D was discontinued
Emphasis was placed on Product C sales
Product B sales were not emphasized but
sold based on market demands
Product A had been overpriced relative to
fixed costs.
Findings allowed pricing flexibility and an increase
in market share
Jose A. Briones, Ph.D.
SpyroTek Performance Solutions, Irving, TX
Brioneja@Spyrotek.com
(469) 737-0421
Theoretical capacity Products A & B Kg/mo
154.4
5.0%
100.0%
8
172.8
90.0%
0.0%
5.0%
0.0%
Theoretical capacity Product
A Kg/mo / Column
Minimum
Maximum
Mean
Std Dev
Values
6
5
143825.4377
182165.7345
163603.8872
5589.9594
5000
4
Theoretical capacity Product
B kg/mo / Column
3
2
1
Values in Thousands
190
180
170
160
150
140
130
120
110
100
90
0
80
Values x 10^-5
7
Minimum
Maximum
Mean
Std Dev
Values
89846.9886
157539.8296
126888.1712
10465.5035
5000
Lines 3 and 4 fully devoted to Products C and D
Production of product C & D, Kg/mo
Comparison with Triang(55000,60000,65000)
56.6 63.4
5.0%
5.0%
0.0010
0.0009
0.0008
0.0007
0.0006
0.0005
0.0004
0.0003
0.0002
0.0001
0.0000
Production of product C,
Kg/mo / Column
5.0%
5.0% Minimum
Maximum
Mean
Std Dev
Values
55075.1959
64901.1442
59999.9773
2041.4514
5000
Triang(55000,60000,65000)
70
60
50
40
30
20
10
0
Minimum
Maximum
Mean
Std Dev
Values in Thousands
Production of C goes from 15 M to 60 M Kg/mo
55000.0000
65000.0000
60000.0000
2041.2415
Production of product D,
Kg/mo / Column
Minimum
Maximum
Mean
Std Dev
Values
9008.7846
10992.7913
10000.0010
408.2882
5000