Capacity Planning
Break-Even Point
Ardavan Asef-Vaziri
Systems and Operations Management
College of Business and Economics
California State University, Northridge
Capacity Planning: Break-Even Analysis
Operation costs are divided into 2 main groups:
 Fixed costs – Costs of Human and Capital Resources
wages, depreciation, rent, property tax, property insurance.
the total fixed cost is fixed throughout the year. No matter if
we produce one unit or one million units. It does not depend
on the production level.
 fixed cost per unit of production is variable.
Variable costs – Costs of Inputs
 raw material, packaging material, supplies, production water
and power.
 The total variable costs depend on the volume of production.
The higher the production level, the higher the total variable
costs.
 variable cost per unit of production is fixed.



Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
2
Five Elements of the Process View
Information
structure
Inputs
(natural or
processed
resources, parts
and components,
energy, data,
customers, cash,
etc.)
Variable
Break-Even Analysis
Process
Management
Network of
Activities and Buffers
Outputs
Goods
Services
Flow Unit
Human & Capital
Resources
Ardavan Asef-Vaziri
March, 2015
Fixed
3
Total Fixed Cost and Fixed Cost per Unit of Product
Total fixed cost
(F)
Fixed cost per unit of product
Production volume (Q)
Production volume (Q)
Break-Even Analysis
(F/Q)
Ardavan Asef-Vaziri
March, 2015
4
Variable Cost per Unit and Total Variable Costs
Variable costs
Per unit of product
(V)
Total Variable costs
(VQ)
Production volume (Q)
Production volume (Q)
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
5
Total Costs in $ (TC)
Total Costs TC = F+VQ
0
Break-Even Analysis
Total Fixed cost (F)
Volume of Production and Sales in units (Q)
Ardavan Asef-Vaziri
March, 2015
6
Total Revenue
It is assumed that the price of the product is fixed,
and we sell whatever we produce.
Total sales revenue depends on the production level.
The higher the production, the higher the total sales revenue.
Price per unit
(P)
Production (and sales) (Q)
Break-Even Analysis
Total revenue
(TR)
Production (and sales ) (Q)
Ardavan Asef-Vaziri
March, 2015
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Total Costs or Revenue in $ (TC)
Break-Even Computations
TC=TR
F+VQ=PQ
QBEP = F/ (P-V)
Break-Even Point
Volume of Production and Sales in units (Q)
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
8
Example 1
$1000,000 total yearly fixed costs.
$200 per unit variable costs
$400 per unit sale price
TR = TC
400Q= 1000,000+200Q
(400-200)Q= 1000,000
Q= 5000
QBEP=5000
If our market research indicates that the present demand is >
5,000, then this manufacturing system is economically feasible.
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
9
BEA for Multiple Alternatives
Break-even analysis for multiple alternatives:
Such an analysis is implemented to compare cases such as
A Simple technology
An Intermediate technology
An Advanced technology
General purpose machines
Multi-purpose machines
Special purpose machines
Low F high V
In between
High F Low V
In general, when we move from a simple technology to an
advanced technology; F  V
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
10
BEA for Multiple Alternatives
Flow-Shop
Batch
Job-Shop
Q1
Break-Even Analysis
Q2
Ardavan Asef-Vaziri
March, 2015
11
Example 2
Management should decide whether to make a part at house or
outsource it. Outsource at $10 per unit.
To make it at house; two processes: Advanced and Intermediate
(1) At house with intermediate process
Fixed Cost:
$10,000/year
Variable Cost: $8 per unit
(2) At house with advanced process.
Fixed Cost:
$34,000/year
Variable Cost: $5 per unit
Prepare a table to summarize your recommendations.
Demand
Recommendation
R≤?
?
?≤R≤?
?
?≤R
?
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
12
Example 2. BEA for Multiple Alternatives
Manufacture II
Manufacture I
Outsource
Q1
Break-Even Analysis
Q2
Ardavan Asef-Vaziri
March, 2015
13
Example 2. Outsource vs. Manufacturing I
100000
90000
80000
70000
60000
10000+8Q=10Q
2Q=10000
50000
40000
30000
20000
10000
1000
Break-Even Analysis
2000
3000
4000
5000
6000
Q=5000
7000
8000
Ardavan Asef-Vaziri
9000
10000
March, 2015
14
Example 2. Manufacturing I vs. Manufacturing II
100000
90000
80000
70000
60000
10000+8Q=34000+5Q
3Q=24000
50000
40000
30000
20000
10000
1000
Break-Even Analysis
2000
3000
4000
5000
6000
7000
8000
9000
Q=8000
Ardavan Asef-Vaziri
10000
March, 2015
15
Example 2. Executive Summary
We summarize our recommendations as
Demand
Recommendation
R ≤ 5000
Buy
5000 ≤ R ≤ 8000
Manufacture Alternative I
8000 ≤ R
Manufacture Alternative II
On the boundary points, in practice, we need more information
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
16
Example 3. BEA for Multiple Alternatives
Three alternatives
1) Job-Shop
Total Fixed Cost
Variable cost
F = $10,000,
V = $10 per unit
2) Group-Shop
Total Fixed Cost
Variable cost
F = $60,000,
V = $5 per unit
3) Flow-Shop
Total Fixed Cost
F = $150,000,
Variable cost
V = $2 per unit
Tell me what to do: In terms of the range of demand and the
preferred choice…
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
17
Example 3. BEA for Multiple Alternatives
Q1
Break-Even Analysis
Q2
Ardavan Asef-Vaziri
March, 2015
18
Example 3. BEA, Job-Shop vs. Batch Processing
Group-Shop
Job-Shop
Q1
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
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Example 3. BEA, Job-Shop vs. Batch Processing
F1=10000
F2=60000
V1=10
V2=5
Break-even of 1 and 2
F1+ V1 Q = F2+ V2 Q
10000+10Q = 60000 + 5Q
Q = 60000  10000  10000
10  5
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
20
Example 3. Batch Processing vs. Flow Shop
Flow-Shop
Group-Shop
Q2
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
21
Example 3. Batch Processing vs. Flow Shop
F2=60000
F3=150000
V2=5
V3=2
Break-even of 2 and 3
F2+ V2 Q = F3+ V3 Q
60000 + 5Q = 150000+2Q
Q = 150000  60000  30000
52
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
22
Recommendations to Management and Marketing
Demand
Recommended Alternative
D ≤ 10000
Job-Shop
10000 ≤ D ≤ 30000
Group-Shop
30000 ≤ D
Flow-Shop
We also need to know Price and Revenue!
Suppose sales price is $8 per unit. Revise the table
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
23
Recommendations to Management and Marketing
Alternative 1 has a variable cost of $10>$8 will never use it
Alternative 2 has a variable cost of $5<$8
Alternative 3 has a variable cost of $2<$8
As we saw before, Alternatives 2 and 3 break even at 30,000
If demand is greater than 30,000, we use alternative 3.
Now we can compute the break-even point of Alternative 2.
Can you analyze the situation before solving the problem?
If the break-even point for alternative 2 is X and is greater than
30,000, then we never use Alternative 2 since beyond a demand of
30,000, Alternative 3 is always preferred to Alternative 2.
D<X
Do nothing
D> X
Alternative 3
Lets see where is the BEP of alternative 2
F+VQ = PQ
60,000+5Q=8Q  Q= 20,000.
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
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Recommendations to Management and Marketing
D < 20,000
20,000 < D < 30,000
30,000 < D
Do nothing
Alternative 2
Alternative 3
If sales price was $6.5 instead of $8, then
F+VQ = PQ
60,000+5Q=6.5Q
Q= 40,000.
But for Q> 30,000 you never use Alternative 2, but Alternative 3
Where Alternative 3 breaks even?
150000+2Q = 6.5Q
150000 = 4.5 Q  Q = 33333
D ≤ 33333
Do nothing
D ≥ 30,000
Alternative 3
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
25
Example 4. BEP for the Three Global Locations
You’re considering a new manufacturing plant in the sites at the
suburb of one of the three candidate locations of:
Bristol (England), Taranto (Italy), or Essen (Germany).
Total Fixed costs (costs of human and capital resources) per year
and variable costs (costs of inputs) per case of product is given
below
Bristol (England)
Essen (Germany):
Taranto (Italy):
Break-Even Analysis
F = $300000, V = $18
F = $600000, V = $12
F = $900000, V = $9
Ardavan Asef-Vaziri
March, 2015
26
Example 3. BEA for Multiple Alternatives
Taranto
Essen
Bristol
Q1
Break-Even Analysis
Q2
Ardavan Asef-Vaziri
March, 2015
27
Example 3. BEA for Multiple Alternatives
Taranto
Essen
Bristol
Q1
Break-Even Analysis
Q2
Ardavan Asef-Vaziri
March, 2015
28
Example 4. BEP for the Three Global Locations
1. At what level of demand a site at Bristol suburb is preferred?
Bristol Total Costs = 300000+18Q
Essen Total Costs = 600000+12Q
300000+18Q = 600000+12Q
6Q = 300,000
Q = 50,000
2. At what level of demand is a site at Essen suburb preferred?
Essen Total Costs = 600000+12Q
Taranto Total Costs = 900000+9Q
600000+12Q = 900000+9Q
3Q = 300,000
Q = 100,0000
Essen is preferred for 100,000≥ Q ≥ 50,000
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
29
Example 3. BEA for Multiple Alternatives
Taranto
Essen
Bristol
50000
Break-Even Analysis
100000
Ardavan Asef-Vaziri
March, 2015
30
Example 4. BEP for the Three Global Locations
3. At what level of demand a site at Taranto suburb is preferred?
More than 100,000
4. Suppose sales price is equal to the average of the variable costs
at Bristol and Essen. At what level of demand is a site at Bristol
suburb preferred?
Never
6. Given the same assumption as (4). At what level of demand a
site at Essen suburb is preferred?
P = (18+12)/2 = 15
Total Essen cost = 600,000 + 12Q
PQ = F + VQ
15Q = 600,000 + 12Q
3Q = 600,000
Q = 200,000
Never. Why???
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
31
Example 5. BEP for the Three Global Locations
Why
At Q = 100,000 Taranto dominates Essen
5. Given the same assumption as (4). At what level of demand is a
site at Taranto suburb preferred?
P = (18+12)/2 = 15
Taranto Total cost = 900,000 + 9Q
PQ = F + VQ
15Q = 900,000 + 9Q
6Q = 900,000
Q = 150,000
P =15
D ≤ 150000
No Where
D ≥ 150,000
Taranto
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
32
Example 5. BEP for the Three Global Locations
7. Suppose sales price is $20. At what level of demand a site at
Essen suburb is preferred?
Essen Total cost = 600,000 + 12Q
20Q = 600,000+12Q
Q = 75000
From 75000 to ??
At what level of demand a site at Essen is preferred?
At 100,000 Essen and Taranto Break Even – After that Taranto
denominates
From 75,000 to 100,000
P= 20
75,000 ≤ D ≤ 100000
D ≥ 100,000
Break-Even Analysis
Essen
Taranto
Ardavan Asef-Vaziri
March, 2015
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Financial Throughput and Fixed Operating Costs
We define financial throughput as the rate at which the
enterprise generates money. By selling one unit of product we
generate P dollars, at the same time we incur V dollars pure
variable cost. Pure variable cost is the cost directly related to
the production of one additional unit - such as raw material. It
does not include sunk costs such as salary, rent, and
depreciation. Since we produce and sell Q units per unit of
time. The financial throughput is Q(P-V).
Fixed Operating Expenses (F) include all costs not directly related
to production of one additional unit. That includes costs such
as human and capital resources.
Throughput Profit Multiplier = % Changes in Profit divided by %
Changes in Throughput
1% change in the throughput leads to TPM% change in the profit
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
34
Financial Throughput and Fixed Operating Costs
Suppose fixed cost F = $180,000 per month. Sales price per unit P
= 22, and variable cost per unit V = 2. In July, the process
throughput was 10,000 units. A process improvement
increased throughput in August by 2% to 10,200 units without
any increase in the fixed cost. Compute throughput profit
multiplier.
July: Financial Throughput = 10000(22-2) = 200000
Fixed cost F = 180,000
Profit = 200000-180000 = $20,000
In August throughput increased by 2% to 10200
August: Financial Throughput of the additional 200 units =
200(22-2) = 4,000
We have already covered our fixed costs, the $4000 directly goes
to profit.
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
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Throughput Profit Multiplier (TPM)
% Change in Throughput = 2%
% change in profit = 4000/20000 = 20%
Throughput Profit Multiplier (TPM) = 20%/2% = 10
1% throughput improvement  10% profit improvement
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
36
A Viable Vision – Eliyahu Goldratt
A Viable Vision (Goldratt): What if we decide to have todays
total revenue as tomorrows total profit.
In our example, Financial Throughput in July was Q1(P-V) =
10,000(22-2). In order to have your profit equal this amount we
need to produce Q2 units such that:
Q2(P-V) – F = Q1(P)
Q2(20) -180,000 = 10,000(22)
Q2(20) = 40,000
Q2 = 20,000
In order to have your todays total revenue as tomorrows total
profit. We only need to double our throughput. Our sales, our
current revenue becomes our tomorrows profit.
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
37
Example 5
A manager has the option of purchasing 1, 2 or 3 machines.
The capacity of each machine is 300 units.
Fixed costs are as follows:
Number of Machines
1
2
3
Fixed cost
$9,600
$15,000
$20,000
Total Capacity
1-300
301-600
601-900
Variable cost is $10 per unit, and the sales price of product is
$40 per unit.
Tell management what to do!
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
38
Example 5. BEP Recommendations
Prepare an executive summary similar the following:
R<= ?
?<R<=?
R>?
?
?
?
Now it is up to the Marketing Department to provide an
Executive Summary regarding the demand.
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
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BEP: One Machine
The beak-even point for 1 machine is 320
But one machine can not produce more than 300
Demand <= 300  No Production
Otherwise  Consider two machines
40000
35000
30000
25000
20000
15000
9600 + 10Q = 40Q
9600= 30Q
10000
5000
320
100
200
Break-Even Analysis
300
400
500
600
700
800
900
Ardavan Asef-Vaziri
1000
March, 2015
40
BEP: Two Machine
The beak-even point for 2 machine is 500
Demand <= 500  No Production
Otherwise  Two machines and consider 3 machines
40000
35000
30000
25000
20000
15000
15000 + 10Q = 40Q
15000= 30Q
10000
5000
500
100
200
Break-Even Analysis
300
400
500
600
700
800
900
Ardavan Asef-Vaziri
1000
March, 2015
41
BEP: Three Machine
The beak-even point for 3 machine is 667
Demand <= 667  Produce up to 600 using 2 machine
Otherwise  3 machines
40000
35000
30000
25000
20000
15000
20000 + 10Q = 40Q
20000= 30Q
10000
5000
667
100
200
Break-Even Analysis
300
400
500
600
700
800
900
Ardavan Asef-Vaziri
1000
March, 2015
42
BEP for the Three Alternatives and Recommendations
Prepare an executive summary similar the following:
R<= 500
 Do nothing
500 <R<=667  Buy two machines and produce 500< Q<= 600
Q>667
 Buy three machines and produce
667<R<=900
Now it is up to the Marketing Department to provide an
Executive Summary regarding the demand.
Please Think again!.
We have made a mistake.
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
43
BEP: Two Machine- Revisited
TC = 15000 + 10(600)
TC = 21000
TR = 40(600) = 24000
Profit = 24000-21000 = 3000
40000
35000
30000
25000
}
20000
You do not switch to 3
machines unless you make
3000 profit
15000
10000
5000
600
100
200
Break-Even Analysis
300
400
500
600
700
800
900
Ardavan Asef-Vaziri
1000
March, 2015
44
From Wrong to Right Recommendations
Q<= 500  Do-Nothing
500<Q<=667  Buy two machines and produce 500<Q<= 600
Q>667  Buy three machines and produce 667<Q<=900
At Q = 667 you make 0 profit with 3 machines
20000 + 10Q = 40Q
20000= 30Q
Q = 667
Break-Even Analysis
20000 + 10Q +3000= 40Q
23000= 30Q
Q = 767
Ardavan Asef-Vaziri
March, 2015
45
Executive Summary
Q<= 500  Do-Nothing
500<Q<=767  Buy two machines and produce 500<Q<= 600
Q>767  Buy three machines and produce 767<Q<=900
Now it is to Marketing Department to provide executive
summary regarding the demand
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
46
Example 5- At Your Own Will
You are the production manager and are given the option to
purchase either 1, 2 or 3 machines. Each machine has a
capacity of 500 units. Fixed costs are as follows:
Number of Machines
1
2
3
Fixed cost
$19,200
$30,000
$40,000
Total Capacity
1- 500
501-1000
1001-1500
Variable cost is $35 per unit, and the sales price of product is
$69 per unit.
Determine the best option!
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
47
BEP for the Three Alternatives and Recommendations
Prepare an executive summary similar the following:
R<= ?
?<R<=?
R>?
Break-Even Analysis
?
?
?
Ardavan Asef-Vaziri
March, 2015
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Variable Cost Per Unit is Not Fixed – Diminishing Marginal Return
Variable costs
Per unit of product
(V)
Total Variable costs
(VQ)
Output
Production volume (Q)
Production volume (Q)
Input
Variable costs
Per unit of product
(V)
Output
Input
Break-Even Analysis
Production volume (Q)
Ardavan Asef-Vaziri
March, 2015
49
Average Total Costs
Economy of Scale- Dis-economy of Scale
ATC-1
ATC-5
ATC-2
ATC-3
ATC-4
Long-Run
ATC
Output
Break-Even
Analysis
LO4
Ardavan Asef-Vaziri
March, 2015
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7-50
Total Production
Note on the Basic MEP Model
30
TP
20
10
0
Marginal and Average
Production
1
Break-Even
Analysis
LO2
20
2
3
Increasing
Marginal
Returns
4
5
6
7
8
9
Negative
Marginal
Returns
Diminishing
Marginal
Returns
10
AP
1
2
3
4
5
6
7
8
9
MP
Ardavan Asef-Vaziri
March, 2015
51
7-51
A Viable Vision – Eliyahu Goldrat
Economies of scale
Labor specialization
Managerial specialization
Efficient capital
------------Diseconomies of scale
Control and coordination problems
Communication problems
Worker alienation
Shirking
Dinosaur Effect
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
52
Stop Here
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
53
Back to Example1 - Simulation
$1000,000 average total yearly fixed costs ($800,000-$1,200,000).
$200 average per unit variable costs ($180-$220).
$400 average per unit sale price ($350-$450)
Sales 4000-6000
.
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
54
180
350
220
450
Variable Cost Sales Price
185
448
207
405
215
426
183
400
188
427
205
434
208
439
188
422
209
387
182
442
220
423
213
369
215
382
194
447
180
438
188
374
180
352
220
410
206
435
208
350
4000
6000
Sales Total Cost Total Revenue
4457
1780941
1996736
4071
1818543
1648755
4812
2008625
2049912
4183
1668455
1673200
5200
1783752
2220400
5386
2048308
2337524
4594
1817549
2016766
5541
1941992
2338302
4155
1706063
1607985
4327
1747484
1912534
4229
1883842
1788867
4401
1890272
1623969
5611
2069902
2143402
5233
1973607
2339151
4093
1542329
1792734
4134
1647911
1546116
4051
1605308
1425952
5779
2170288
2369390
5017
1899201
2182395
5034
1959326
1761900
Break-Even Analysis
Profit
215795
-169788
41287
4745
436648
289216
199217
396310
-98078
165050
-94975
-266303
73500
365544
250405
-101795
-179356
199102
283194
-197426
Max
772024
Min
-467941
Range
1239965 4194304 K 22
1 -467941 -439759 -467941 to -439758.5
2 -439759 -411576 -439758.5 to -411576
3 -411576 -383394 -411576 to -383393.5
4 -383394 -355211 -383393.5 to -355211
5 -355211 -327029 -355211 to -327028.5
6 -327029 -298846 -327028.5 to -298846
7 -298846 -270664 -298846 to -270663.5
8 -270664 -242481 -270663.5 to -242481
9 -242481 -214299 -242481 to -214298.5
10 -214299 -186116 -214298.5 to -186116
11 -186116 -157934 -186116 to -157933.5
12 -157934 -129751 -157933.5 to -129751
13 -129751 -101569 -129751 to -101568.5
14 -101569
-73386 -101568.5 to -73386
15
-73386 -45203.5 -73386 to -45203.5
16 -45203.5
-17021 -45203.5 to -17021
17
-17021 11161.5 -17021 to 11161.5
18 11161.5
39344 11161.5 to 39344
19
39344 67526.5 39344 to 67526.5
Ardavan Asef-Vaziri
2
2
4
20
36
58
102
137
205
227
266
316
344
429
444
484
491
512
515
0.0002
0.0002
0.0004
0.002
0.0036
0.0058
0.0102
0.0137
0.0205
0.0227
0.0266
0.0316
0.0344
0.0429
0.0444
0.0484
0.0491
0.0512
0.0515
March, 2015
TRUE Width
56365
CumulativeLoss
28182.5
0.0002
0.0002
0.3363
0.0004
0.0002 Probability of Loss is: 0
0.0008
0.0004
0.0028
0.002
0.0064
0.0036
0.0122
0.0058
0.0224
0.0102
0.0361
0.0137
0.0566
0.0205
0.0793
0.0227
0.1059
0.0266
0.1375
0.0316
0.1719
0.0344
0.2148
0.0429
0.2592
0.0444
0.3076
0.0484
0.3567
0.4079
0.4594
55
Break-Even Analysis
Ardavan Asef-Vaziri
March, 2015
56