Cost Concepts and
Design Economics
Lecture 2
Cost Analysis
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Cost Estimating
 A term used to describe the process by which the
present and future cost consequences of engineering
designs are forecast.
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Cost estimating used to
1. Provide information used in setting a selling price for
quoting, bidding, or evaluating contracts
2. Determine whether a proposed product can be made
and distributed at a profit (for simplicity, price = cost +
profit)
3. Evaluate how much capital can be justified for
process changes or other improvements
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Cost Classifications
 Fixed and Variable Costs
 Direct and Indirect Costs
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Cost Classifications (cont.)
 Fixed costs are those unaffected by changes in activity
level over a feasible range of operations for the
capacity or capability available.
 (e.g. insurance and taxes on facilities, general
management and administrative salaries, license fees,
and interest costs on borrowed capital).
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Cost Classifications (cont.)
 Variable costs are those associated with an operation
that vary in total with the quantity of output or other
measures of activity level.
 Example of variable costs include : costs of material
and labor used in a product or service, because they
vary in total with the number of output units -- even
though costs per unit remain the same.
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Cost Classifications (cont.)
 Direct costs can be reasonably measured and
allocated to a specific output or work activity -- labor
and material directly allocated with a product, service
or construction activity.
 Indirect costs are difficult to allocate to a specific output
or activity -- costs of common tools, general supplies,
equipment maintenance and overhead costs.
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Cost Terminology
 Investment Cost or capital investment is the capital (money)
required for most activities of the acquisition phase;
 Working Capital refers to the funds required for current
assets needed for start-up and subsequent support of
operation activities;
 Operation and Maintenance Cost includes many of the
recurring annual expense items associated with the
operation phase of the life cycle;
 Disposal Cost includes non-recurring costs of shutting down
the operation;
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Total Cost Calculation
Total Cost (TC) = Fixed Costs (CF) + Variable Costs (CV)
TC = CF + CV
TC = CF + cv * D
cost
CT
Cv
CF
Quantity (D)
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Profit Calculation
Profit = Total Revenue (TR) – Total Cost (TC)
Scenario1:
Constant Price
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Scenario2:
Variable Price
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Scenario 1: Constant Price
Profit = Total Revenue (TR) – Total Cost (TC)
TR = p * D , where p is constant
Profit = p * D – TC
Break-even point occurs when Profit = 0
TR = TC
p * D’ =CF + cv * D’
D’ = CF/ (p – cv)
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Breakeven Chart (Scenario 1)
TR
CT
cost
Cv
CF
BEP (D’)
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Quantity
(D)
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Scenario 2: Variable Price
Profit = Total Revenue (TR) – Total Cost (TC)
TR = p * D , where p is variable
p = a – b*D
Price (p)
a
-b
p
D
is the intercept at the price axis
is the slope
p=a-bD
is the selling price per unit
is the demand
Demand (D)
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The Total Revenue Function
TR
TR = Max
Total Revenue = p x D
= (a – bD) x D
=aD – bD2
QUANTITY ( OUTPUT )
D=a/2b
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Breakeven Chart (Scenario 2)
Maximum Profit
(not necessarily at max revenue)
Cost / Revenue
CT
Profit
D’1
D*
D’2
Total Revenue
Quantity ( Output )
Demand
D’1 and D’2 are breakeven points
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Finding BEP: Scenario 2
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Scenario 2:
Profit Maximization D*
 Occurs where total revenue exceeds total cost by the
greatest amount;
 Occurs at d(profit)/dD=0
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Solved Examples
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Example 1:
Finding BEP: Scenario 1

A engineering consulting firm measures its output in a
standard service hour unit, which is a function of the
personnel grade levels in the professional staff. The
variable cost is $62 per standard service hour. The
charge-out rate (i.e., selling price) is $85.56 per hour.
The maximum output of the firm is 160 000 hours per
year, and its fixed cost is $2,024,000 per year. For
this firm:
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Example 1 (cont.)
1. what is the breakeven point in standard service hours
and in % of total capacity
2. What is the % reduction in the breakeven point
a.
b.
c.
d.
if fixed cost s are reduced by 10%;
if variable cost per hour is reduced by 10%;
if both costs are reduced by 10%; and
if the selling price per unit is increased by 10%?
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Example 1: Solution
1. At BEP:
TR=TC
p D’ = CF + cvD’
D’ = CF / (p – cv)
D’=$2,024,000/($85.56 – $62)=85,908 hours per year
D’=85,908/160,000=0.537 (or 53.7% of capacity)
2. Sensitivity Analysis
a. BEP at 10 % reduction in CF:
D’= 0.9($2,024,000)/($85.56 – $62)=77,318 hours per
year
(85,908 – 77,318)/85,908=0.10 (or a reduction of 10% in D’)
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Example 1: Solution (cont.)
b. BEP at 10% reduction in cv:
D’= ($2,024,000)/($85.56 – 0.9($62))=68,011 hours per year
(85,908 – 68,011)/85,908=0.208 (or a reduction of 20.8% in D’)
c. 10 % reduction in both costs
D’=$(0.9)(2,024,000)/($85.56 – (0.9)$62)= 61,210 hours per year
(85,908 – 61,210)/85,908=0.287 (a reduction of 28.7% in D’)
d. 10% increase in p
D’=$2,024,000/((1.1)$85.56 – $62)=63,021 hours per year
(85,908-63,021)/85,908=0.266 (26.6% reduction in D’)
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Example 1: Solution Summary
Change in Factor value (s)
Decrease in BEP
10% reduction in CF
10% reduction in cv
10% reduction in CF and in cv
10.0%
20.8%
10% increase in p
26.6%
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28.7%
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Example 2:
Finding BEP: Scenario 2
A company has established that the relationship between
the sales price for one of its products and the quantity
sold per month is approximately D= 780-10 p units. (D is
the demand or quantity sold per month, and p is the price
per dollars.) The fixed cost is $800 per month, and the
variable cost is $30 per unit produced.
a. What number of units, D*, should be produced per
month and be sold to maximum net profit?
b. What is the maximum profit per month related to the
product?
c. Determine D'1 and D'2.
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Example 2: Solution
Given:
D = 780 - 10p (units/month)
Fixed Cost (CF) = $800/month
Variable Cost per Unit (cv) = $30/unit
p= (780 – D )/10
p = 78 – 0.1 * D
D* = (78 – 30)/0.2 = 240 units/month
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Example 2: Solution (cont.)
 D* = 240,
 Profit = 48D - 0.1D2 - 800
 Profit = 48(240) - 0.1(240)2 - 800 = $4,960
 Maximum Profit = $4,960/month
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Example 2: Solution (cont.)
𝐷′1,2 =
−(78−30)± (78−30)2 −4(−0.1)(−800)
2(−0.1)
D1' = 17.28 or 18 units/month
D2' = 462.71 or 462 units/month
Profitable range of demand:
18 units/month To 462 units/month
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See you next week!
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