# PRODUCTIONS/OPERATIONS MANAGEMENT ```Ch 5(B) : Capacity Planning: Break-Even Analysis
Operation costs are divided into 2 main groups:
• Fixed costs
• Variable costs
1
Fixed Costs
Include rent, property tax, property insurance, wages
of permanent employees, depreciation (except in
working hour depreciation).
The total fixed cost is fixed throughout the year.
It does not depend on the production level.
When we have a plant, then the above costs are
fixed, no matter if we produce one unit or one million
units.
2
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)
(F/Q)
3
Variable Costs
Costs of raw material, packaging material, direct
labor, production W&amp;P are the main variable costs.
Variable cost is fixed per unit of production.
The total variable costs depend on the volume of
production.
The higher the production level, the higher the total
variable costs.
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)
5
Amount (\$)
Total Costs
Total Fixed cost (F)
0
Q (volume in units)
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)
Total revenue
(TR)
Production (and sales ) (Q)
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Amount (\$)
Break-Even Point
0
BEP units
Q (volume in units)
8
Break-Even Computations
TC=TR
TC=F+VQ
TR=PQ
F+VQ=PQ
QBEP = F/ (P-V)
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Example
\$500,000 total yearly fixed costs.
\$150 per unit variable costs
\$200 per unit sale price
QBEP=500,000/(200-150) =10,000 units
If our market research indicates that the
present demand is &gt; 10,000, then this
manufacturing system is economically
feasible.
10
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
 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
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BEA for Multiple Alternatives
CIM
CNCs
Universal
Q1
Q2
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BEA for Multiple Alternatives
1) A General Purpose machine
Total Fixed Cost F = \$10,000,
Variable cost
V = \$10 per unit
2) A Multi Purpose machine
Total Fixed Cost F = \$60,000,
Variable cost
V = \$5 per unit
3) A Single Purpose machine
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…
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BEA for Alternatives (1) and (2)
2
1
Q1
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Break-Even for Alternatives (1) and (2)
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
15
BEA for Alternatives (2) and (3)
3
2
Q2
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Break-Even for Alternatives (2) and (3)
F2=60000
V2=5
F3=150000
V3=2
Break-even of 2 and 3
F2+ V2 Q = F3+ V3 Q
60000 + 5Q = 150000+2Q
Q
150000  60000
 30000
=
52
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Recommendations to Management and Marketing
Demand
Recommended Alternative
D &lt; 10000
Alternative 1
10000 &lt; D &lt; 30000
Alternative 2
30000 &lt; D
Alternative 3
We also need to know Price and Revenue!
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Assignment 3: Problem 1
A firm plans to begin production of a new small appliance.
Management should decide whether to make the small engine
for this product in-plant, or buy it from an outside source.
If management decides to make the engine, then there are 2
alternatives:
(1) Built it with a simple manufacturing system
Fixed Cost:
\$10,000/year
Variable Cost: \$8 per unit
(2) Built it with an advanced manufacturing system.
Fixed Cost:
\$30,000/year
Variable Cost: \$5 per unit
The purchase price of the engine is \$10 per unit.
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BEP for the Three Alternatives and Recommendations
Prepare a table similar to the following table, to summarize
Demand
Recommendation
Q &lt;= ?
?
?&lt;Q&lt;=?
?
?&lt;Q
?
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Assignment 3: Problem 2
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!
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BEP for the Three Alternatives and Recommendations
Prepare an executive summary similar the following:
Q&lt;= ?  ?
?&lt;Q&lt;=?  ?
Q&gt;?
?
Now it is up to the Marketing Department to provide an
Executive Summary regarding the demand.
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Assignment 3: Problem 3
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!
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BEP for the Three Alternatives and Recommendations
Prepare an executive summary similar the following:
Q&lt;= ?  ?
?&lt;Q&lt;=?  ?
Q&gt;?
?
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