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. In this case we present an example where a company is trying to decide how best to balance the sales of certain families of products to maximize revenue, maintain a diverse product line and properly price each individual product based on the impact to the manufacturing schedule and fixed cost allocation.

1. Jose A. Briones, Ph.D.
SpyroTek Performance Solutions, LLC
Palisade’s Risk Analysis Conference, October 2009

2.  Introduction
 Model description
 Financial modeling inputs
 Scenario modeling
 Results analysis

3.  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

4.  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

5.  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

6.  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

7.  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

8.  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

9. Product Family A Line 1
125 Kg/hr/line
Product Family B Line 2
87.5 Kg/hr/line Post-Treatment
Facility
Product Family C Line 3
350 Kg/hr
62.5 Kg/hr/line
Product Family D Line 4
37.5 Kg/hr/line

10.  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

11.  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

12. Typical Range Range
Min Max
Production Target of product C, Kg/mo 15,000 10,000 20,000
Production Target of product D, Kg/mo 10,000 5,000 15,000
Production Rate of Product A, lines 1 and 2, Kg/hr 250 240 260
Production Rate of Product B, lines 1 and 2, Kg/hr 175 165 200
Rate of Production product C, lines 3 and 4 Kg/hr 125 90 140
Rate of Production product D, lines 3 and 4 Kg/hr 75 60 80
Maximum Production Rate 4 lines running, Kg/hr 350 330 370
Var Margin Product A US$/kg $2.50 $2.30 $2.70
Var Margin Product B US$/kg $2.75 $2.60 $3.00
Var Margin Product C US$/kg $4.00 $3.50 $4.50
Var Margin Product D US$/kg $5.00 $4.50 $5.50
Plant fixed cost Euros/month 500,000 € 450,000 € 550,000 €
Selling & Admin costs Euros/month 50,000 € 45,000 € 55,000 €
Projected fixed cost savings Euros/month 75,000 € 65,000 € 90,000 €
US Dollar/ Euro Exchange Rate 0.8 0.7 0.95

13.  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.

14.  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.

15.  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

16. % of treatment line time devoted to A or B, C & D
0.772 0.829 % of treatment line time
5.0% devoted to A + B Grades / % of treatment line time
0.
Column devoted to Product C /
100.0% Column
60 Minimum 0.7431
Maximum 0.8577 Minimum 0.0549
50 Mean 0.8027 Maximum 0.1432
Std Dev 0.0176 Mean 0.0941
Values 1000 Std Dev 0.0155
40
D % of treatment line time
30 devoted to Product D /
Column
20 Minimum 0.0854
C A or B Maximum
Mean
0.1304
0.1031
10
Std Dev 0.00761
Values 1000
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
9
20% of Production time is allocated to C & D
Values 1000

17. Total theoretical capacity, Product A plus Products C & D, kg/yr
2.699 2.906
5.0% 90.0% 5.0% Total theoretical capacity,
92.3% 7.7% 0.0% Product A plus Products C &
7 D, kg/yr
6 Minimum 2633085.3298
A Maximum 3018607.7688
5 Mean 2803346.2034
Val ues x 10 ^ -6
B Std Dev 63912.9226
4 Values 1000
3 Total theoretical capacity,
Product B plus products C &
2 D, kg/yr
1 Minimum 2357095.8177
Maximum 2788160.2845
0 Mean 2604929.4916
Std Dev 65567.7702
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
Values 1000
Values in Millions
Substituting Product A with Product B Results in Lower Total Plant Capacity

18. Profitability, Product A vs. Product B US$/yr
0.000 1.450
17.3% 75.9% 6.8%
11.3% 75.8% 12.9% Profitability, Product A Case
8 US$/yr / Column
7 A Minimum -1219775.4188
Maximum 2289688.1319
6 Mean 596061.7364
A B
Values x 10 ^ -7
Std Dev 598929.0090
5
Values 1000
4
Profitability, Product B Case
3 US$/yr / Column
2 Minimum -1091259.4015
1 Maximum 2484366.8328
Mean 752663.4930
0 Std Dev 597144.6785
Values 1000
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
Values in Millions
Product B has a lower probability of losses than product A

19. Fixed cost US$/kg Products A, B, C, D
5.45 7.40 Fixed cost US$/kg Product Fixed cost US$/kg Product
5.0% 90.0% 5.0% D B
99.8% 0.2% 0.0% Minimum $4.9476 Minimum $2.0664
2.5 Maximum $8.3905 Maximum $3.1881
Mean $6.3397 Mean $2.5700
Std Dev $0.6112 Std Dev $0.1997
2.0
B Values 1000 Values 1000
1.5 Fixed cost US$/kg Product
C
A Minimum $2.8058
1.0 Maximum $5.5362
C D Mean $3.8559
Std Dev $0.4473
0.5
Values 1000
0.0 Fixed cost US$/kg Product
A
1
2
3
4
5
6
7
8
9
Values in $ Minimum $1.8656
Maximum $2.9132
Mean $2.3665
Slower production rates result in much higher Std Dev $0.1899
fixed costs for Products C and D Values 1000

20. Gross Profit Products A, B, C, D US$/Kg
-0.22 0.48 Profit Product A US$/Kg /
5.0% 5.0% Column
2.9% 12.1% Minimum -$0.5836
2.5 Maximum $0.7011
Mean $0.1335
Std Dev $0.2097
2.0
Values 1000
A
1.5 Profit Product B US$/Kg /
B Column
1.0 Minimum -$0.4348
Maximum $0.8052
D C Mean $0.2133
0.5 Std Dev $0.2216
Values 1000
0.0 Profit Product C US$/Kg /
-5
-4
-3
-2
-1
0
1
2
Values in $ Profit Product D US$/Kg / Minimum -$1.5576
Product D has a Negative Gross Maximum $1.4447
Mean $0.1441
Profit Due to Long Production Minimum -$4.5032
Std Dev $0.4867
Maximum -$0.7534
Cycles Mean -$2.3397
Values 1000
Std Dev $0.6452

21. % of treatment line time devoted to A/B, C & D Grades
0.448 0.575 % of treatment line time
5.0% 90.0% 5.0% devoted to A + B Grades /
Column
100.0% 0.0% 0.0%
60 Minimum 0.3699
D Maximum 0.6080
50 Mean 0.5203
Std Dev 0.0384
Values 5000
40
% of treatment line time
30 devoted to Product D /
Column
20 Minimum 0.0849
C A or B Maximum 0.1304
Mean 0.1032
10
Std Dev 0.00770
Values 5000
0
0.4
0.5
0.6
0.7
0.0
0.1
0.2
0.3
% of treatment line time
devoted to Product C /
Column
Minimum 0.2963
Maximum 0.5094
~50% of time devoted to C & D Mean 0.3766
Std Dev 0.0374
Values 5000

22. Total theoretical capacity, Product A vs. B plus Products C & D, kg/yr
2.700 2.906
5.0% 90.0% 5.0% Total theoretical capacity,
100.0% 0.0% 0.0% Product A plus Products C &
7 D, kg/yr
A Minimum 2596788.1735
6
Maximum 3001093.4875
5 Mean 2803246.3861
Val ues x 10 ^ -6
Std Dev 62557.3764
4 Values 5000
B
3 Total theoretical capacity,
Product B plus products C &
2 D, kg/yr
1 Minimum 1942146.1959
Maximum 2697819.5994
0 Mean 2362657.7945
Std Dev 120704.1615
2.6
2.8
3.0
3.2
1.8
2.0
2.2
2.4
Values 5000
Values in Millions
Production of B v.s A results in a more significant loss of capacity compared to Scenario 1

23. 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 Minimum -852160.3638
B A
Maximum 3287264.9694
5 Mean 1405082.2802
V al u e s x 1 0 ^ - 7
Std Dev 608985.6034
4 Values 5000
3 Profitability, Product B Case
US$/yr / Column
2
Minimum -2021651.9911
Maximum 3250368.3280
1
Mean 735213.2672
Std Dev 665321.2558
0
Values 5000
-3
-2
-1
0
1
2
3
Values in Millions 4
Production of A has less than 2% probability of losses, 48% probability of profit >1.5 MM $

24. Fixed cost US$/kg Products A, B, C & D
5.40 7.43 Fixed cost US$/kg Product Fixed cost US$/kg Product
5.0% 90.0% 5.0% D / Column B. / Column
99.8% 0.2% 0.0% Minimum $4.6730 Minimum $1.8782
2.0 Maximum $8.7315 Maximum $3.2967
1.8 Mean $6.3410 Mean $2.5241
A Std Dev $0.6228 Std Dev $0.2136
1.6 Values 5000 Values 5000
1.4 B
1.2 Fixed cost US$/kg Product
C / Column
1.0
0.8
C D Minimum $2.6522
Maximum $5.8660
0.6 Mean $3.8579
Std Dev $0.4645
0.4
Values 5000
0.2
0.0 Fixed cost US$/kg Product
A / Column
1
2
3
4
5
6
7
8
9
Values in $ Minimum $1.2306
Maximum $2.6219
Mean $1.9559
Std Dev $0.2068
Values 5000
Fixed Cost of Product A drops in this scenario

25. Profit Products A, B C & D US$/Kg
0.00 0.91 Profit Product D US$/Kg /
Profit Product A US$/Kg /
Column Column
0.7% 94.3% 5.0%
13.2% 86.7% 0.1% Minimum -$0.1944 Minimum -$4.8411
1.8 Maximum $1.2512 Maximum -$0.3715
Mean $0.5441 Mean -$2.3410
1.6
1.4
B A Std Dev $0.2233 Std Dev
Values
$0.6569
5000
Values 5000
1.2
Profit Product B US$/Kg /
1.0 Column
0.8 Minimum -$0.6366
0.6 D C Maximum $1.0344
Mean $0.2593
0.4 Std Dev $0.2276
Values 5000
0.2
0.0 Profit Product C US$/Kg /
-5
-4
-3
-2
-1
0
1
2
Column
Values in $
Minimum -$2.0249
Maximum $1.5637
Mean $0.1421
Std Dev $0.5091
Values 5000
Profit of Product A increases in this scenario

26. Scenario 1 - A Scenario 1 - B Scenario 2 - A Scenario 2 - B
% time devoted 20% 20% 48% 48%
to C & D
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 2.8 MM kg/yr 2.6 MM kg/yr 2.8 MM kg/yr 2.4 MM kg/yr
Capacity
Profitability 0.6 MM$/yr 0.75 MM$/yr 1.4 MM $/yr 0.7 MM $/yr
Probability of 17% 11% 1% 13%
Losses
Scenario 2 with sales of Product A has the best probability for higher profits

27. Scenario 1 – Scenario 1 – Scenario 2 – Scenario 2 –
Fixed Cost/Kg Gross Profit/Kg Fixed Cost/Kg 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

28. Profitability, Product A Case US$/yr / Column
Regression Coefficients
US Dollar/ Euro Exchange Rate 0.73
Plant fixed cost Euros/month -0.51
Var Margin Product A US$/kg 0.34
Maximum Production Rate 4 lines running, kg/hr 0.22
Projected fixed cost savings Euros/month 0.13
Operational Efficiency 0.10
Days of the week operating 0.07
Production of product C, Kg/mo 0.06
Var Margin Product C US$/kg 0.06
Selling & Admin costs Euros/month -0.05
Rate of Production product D, Kg/mo 0.05
Var Margin Product D US$/kg 0.04
Production Rate of Product A, lines 1 and 2, kg/hr 0.03
Hours/day operating 0.02
Production of product D, Kg/mo 0.01
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Coefficient Value
Maximum Production Rate for the 4 lines is a critical factor for profitability of A

29.  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

30.  Jose A. Briones, Ph.D.
 SpyroTek Performance Solutions, Irving, TX
 Brioneja@Spyrotek.com
 (469) 737-0421

32. Theoretical capacity Products A & B Kg/mo
154.4 172.8
5.0% 90.0% 5.0%
100.0% 0.0% 0.0% Theoretical capacity Product
8 A Kg/mo / Column
7 Minimum 143825.4377
Maximum 182165.7345
6 Mean 163603.8872
Val ues x 10 ^ -5
Std Dev 5589.9594
5
Values 5000
4
Theoretical capacity Product
3 B kg/mo / Column
2 Minimum 89846.9886
1 Maximum 157539.8296
Mean 126888.1712
0 Std Dev 10465.5035
Values 5000
140
150
160
170
180
190
80
90
100
110
120
130
Values in Thousands

33.  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 Production of product C,
5.0% 5.0% Kg/mo / Column
5.0% 5.0% Minimum 55075.1959
0.0010 Maximum 64901.1442
0.0009 Mean 59999.9773
0.0008 Std Dev 2041.4514
Values 5000
0.0007
0.0006
Triang(55000,60000,65000)
0.0005
0.0004 Minimum 55000.0000
0.0003 Maximum 65000.0000
Mean 60000.0000
0.0002
Std Dev 2041.2415
0.0001
0.0000 Production of product D,
0
10
20
30
40
50
60
70
Kg/mo / Column
Values in Thousands Minimum 9008.7846
Maximum 10992.7913
Mean 10000.0010
Std Dev 408.2882
Production of C goes from 15 M to 60 M Kg/mo Values 5000