ENGR 345
Engineering Economy
Breakeven Analysis
Dr. Lotfi Gaafar
The American University in Cairo
Engineering Economy
Breakeven Analysis
Gaafar 2007
Introduction to Breakeven Analysis
• Breakeven Analysis in the context of Production planning
addresses the decision of whether to make or buy a
product.
• Making the product involves two cost elements:
– Fixed costs such as machine renting cost and operation expenses
– Variable costs such as raw material cost
• Buying the product involves only one cost element, the
selling price. However, the price may either be constant or
variable based on the quantity.
Engineering Economy
Breakeven Analysis
Gaafar 2007
Linear Breakeven Analysis
Assumptions: (1) Price is constant (p); (2) We have fixed costs; (3) We
have constant variable cost.
Buy Cost (BC) = pQ
Making is better
Cost
Make Cost (MC) = FC + vQ
Buying is better
Variable cost: vQ
Fixed Cost: FC
Savings : S = BC – MC = pQ – FC – vQ
Breakeven: S = 0, pQ = FC + vQ
Quantity (Q)
Q’
Engineering Economy
Breakeven Analysis
Gaafar 2007
Linear Breakeven Analysis
A particular product sells for a price of $70. If the fixed cost are $800/month and the variable
cost per unit is $30/unit, determine the breakeven quantity. [20]
Engineering Economy
Breakeven Analysis
Gaafar 2007
Nonlinear Breakeven Analysis
Assumptions: (1) Price varies with demand; (2) We have fixed costs;
(3) We have constant variable cost.
$
Make Cost (MC) = FC + vQ
Buy Cost (BC) = pQ
Break-even
output
maximum
savings
Break-even
output
Fixed Cost: FC
p = (a – bQ)
Savings (S) = pQ – FC – vQ = (a – bQ)Q – FC – vQ
S = aQ – bQ2 – (FC+vQ)
S = (a-v)Q – bQ2 –FC ………….. (1)
•Set (1) equal to zero to determine breakeven.
•Differentiate (1) with respect to Q and set the result equal to zero to find Q that maximizes the savings.
Engineering Economy
Breakeven Analysis
Gaafar 2007
Nonlinear Breakeven Analysis
A particular product has a unit price that starts at $78 with a $0.1 discount for each unit
purchased. If the fixed cost are $800/month and the variable cost per unit is $30/unit, determine
the demand quantity that maximizes the savings of making and the breakeven quantities. [240,
17.28, 462.72]
Engineering Economy
Breakeven Analysis
Gaafar 2007
Time Value of Money
Suppose a firm is considering manufacturing a new product and the
following data have been provided:
Sales price
$12.50/unit
Equipment cost
$200,000
Overhead cost
$50,000/year
Operating and maintenance cost
$25/operating hour
Production time/1000 units
100 hours
Planning horizon
5 years
Minimum attractive rate of return
15%
Determine the sales volume that would make manufacturing this
product profitable.
[10,966]
Engineering Economy
Breakeven Analysis
Gaafar 2007
Time Value of Money
Consider a contractor who experiences a seasonal pattern of activity for
compressors. The manager currently owns eight compressors and suspects that
this number will not be adequate to meet the demand. The contractor realizes that
there will arise situations when more than eight compressors will be required, and
is considering purchasing an additional compressor for use during heavy demand
periods. Local equipment rental firm will rent compressors at a cost of $50/day.
Compressors can be purchased for $6000. The difference in operating and
maintenance costs between owned and rented compressors is estimated to be
$3000/year.
Letting X denote the number of days a year that more than eight compressors are
required, perform a breakeven analysis. Assume a planning horizon of 5 years,
zero salvage values, and 20% minimum attractive rate of return.
[100.128]
Engineering Economy
Breakeven Analysis
Gaafar 2007
Basic Definitions
• Fixed/Variable Costs - If costs change appreciably with
fluctuations in business activity, they are “variable.” Otherwise,
they are “fixed.” A widely used cost model is: Total Costs =
Fixed Costs + Variable Costs
• Price is the amount of money, goods or services that must be
given up to acquire ownership or use of a product.
• Recurring/Nonrecurring Costs are repetitive and occur when
an organization produces goods or services on a continuing
basis, they are “recurring.” Otherwise they are “nonrecurring.”
Variable costs are recurring since they repeat with each unit of
output.
• Direct/Indirect Costs - If costs can be reasonably measured
and allocated to a specific output, they are “direct.” Otherwise
they are “indirect.”
Engineering Economy
Breakeven Analysis
Gaafar 2007
Basic Definitions
• Overhead Costs - All costs of providing goods or services other
than direct labor and direct material. Indirect costs are a subset of
overhead costs. Fixed overhead relates more to plant capacity than
production volume (variable overhead). Allocation of overhead to
specific outputs may be in proportion to:
1. Direct labor hours
2. Direct material costs
3. Machine hours
• Opportunity Costs - The cost of forgoing the chance to earn
interest (or profit) on investment funds.
Engineering Economy
Breakeven Analysis
Gaafar 2007