SEEM2440
Engineering Economic
Lecture 01 – Cost Concepts and Design Economics
The correct solution to any
problem depends primarily
on a true understanding of
what the problem really is.
Arthur M. Wellington (1887)
Copyright (c) 2015. Gabriel Fung. All rights reserved.
2
Terminologies
Cash cost / Book cost
Fixed cost / Variable cost
Sunk cost
Opportunity cost
Indirect cost / Overhead cost / Burden
Life-cycle cost
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Cash Cost / Book Cost
Cash cost
A cost that involves payment of cash (i.e., directly related to cash
flow)
Book cost
A cost does not involve cash transaction (i.e., not related to cash
flow). A typical example is “depreciation”.
In engineering economics, we are interested in costs which are
related to cash flows only.
Note: although it is not related to cash flows, it will affect
incoming tax, which is cash flows.
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Fixed Cost / Variable Cost
Fixed Cost
Tends to remain constant. (i.e., unaffected by business activities).
Examples: salary, insurance, license fees, …
Of course, any cost is subject to change, but it tends to remain
constant.
It will be affected mainly when there are large changes in business
structure.
Variable Cost
Changes according to business activities or level of service.
Examples: cost of materials.
Those associated with an operation that vary in total with the
quantity of output or other measures of business activity.
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Example – Fixed / Variable Cost
Question:
To surface a new highway, we need 50,000 yard3 of paving
material, 4 months (17 weeks and 5 working days/week) and a
workspace on one of the following two sites:
Cost Factor
Site A
Site B
Monthly rental fee
$2,000
$7,000
Cost to set up
$15,000
$50,000
Transportation fee
$2.75/yd3
$2.75/yd3
Distance to the highway
4 miles
3 miles
Extra labor cost
--
$150/day
Which site should we choose?
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Example – Fixed / Variable Cost (cont’d)
Answer:
Site B!
Total Cost of Site A: $573,000 / Total Cost of Site B: $503,250
Another question:
If we have surfaced 1 yard3, we would be get $12. How many
yard should we surfaced before we can make a profit (i.e., the
break even point)?
Answer:
Let x be the number of yard3.
$90,750 + $8.25x = $12x
x = 24,200
i.e., after we have surfaced 24,200 yard3, we will make a profit!
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Example – Make Versus Buy
A manufacturing plant has 3 departments. One of the
departments has the following features:
Produces 576 pieces of Chip X everyday. Chip X is one of the
several products being produced in this department.
1 full-time operator working 4 hours/day at $22.5/hour.
1 part-time foreman working at $30/day.
Direct material cost: $86.4. Indirect cost: $82.
The foreman recently saw an advertisement on newspapge:
“We sell Chip X for $0.35”
Question:
Should we buy Chip X (i.e., outsource) or produce by ourselves?
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Sunk Cost
Cost already spent, and has no relevance to the estimation of
future costs and revenues.
Example
John spent $6K to buy a bad second hand car. He predicts that
he needs $4K to repair it. Unfortunately, even after he spent
$10K, he found that he still need an additional of $10K to
finish the repairing. Meanwhile, another good condition second
had car costs $20K. Shall he continue to repair?
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Opportunity Cost
The cost of the best rejected (foregone) opportunity.
Incurred because of the user of limited resources.
One of the most important concepts in studying economics.
Question:
Assume that you can earn $8,000/month now (without
University Degree). Yet, you choose studying at CUHK instead
of working. What is the opportunity cost of your study?
Another question:
How about Master? PhD?
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Indirect cost / Overhead cost / Burden
Indirect costs, overhead costs and burden costs usually means
the same thing.
E.g. Electricity, Property Taxes, …
Consists of plant operating costs that are not direct labor or
direct material costs.
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Example – Which One is Correct?
You have a car!
Gasoline
Your friends ask you to drive
Oil and lubrication
them home, and pay you back. Tires
You based on last year driving Depreciation
Insurance
record (top), then draw a
Repairs
charge table.
Garage
Your friends disagree with you, Total
arguing “Depreciation” and
“Insurance” are already “paid” Cost Element
and should be ignored (bottom). Gasoline
Cost Element
Cost per km
Oil and lubrication
0.021
Tires
0.027
Repairs
0.030
Garage
0.012
Question: Who is correct?
Total
Copyright (c) 2015. Gabriel Fung. All rights reserved.
$0.120
0.021
0.027
0.150
0.024
0.030
0.012
$0.384
Cost per km
$0.120
$0.198
Example – CAD System
Consider we want to create a Computer-Aided System. The
costs are:
Lease a tel. line for communication
$1,100/month
Lease CAD software
550/month
Purchase hardware
20,000
Purchase a high speed modem
250
Purchase a laser printer
1,500
Purchase a four-color plotter
10,000
Shipping cost
500
In-house training cost
6,000
Question: What is the investment cost?
Copyright (c) 2015. Gabriel Fung. All rights reserved.
General Economic Environment
In general, when the selling price (p) of a product/service
increased, there will be less demand (D) for it.
Hence, the relationship between price and demand can be
expressed as the following linear function:
a
p = a − bD, for 0 ≤ D ≤ , a > 0, b > 0
b
p
Price
a
p = a − bD
Demand
Copyright (c) 2015. Gabriel Fung. All rights reserved.
D
General Economic Environment (cont’d)
p
Since
Revenue = price × demand
a
p = a − bD
= ( a − bD) × D
Price
= p×D
= aD − bD2
Hence (by calculus), the optimal
a
Dˆ =
2b
R
R = aD − bD 2
Revenue
Note: the cost is not included yet!
D
Demand
demand will be:
D
Quantity
Copyright (c) 2015. Gabriel Fung. All rights reserved.
General Economic Environment (cont’d)
Suppose the cost function is:
Cost = Fix Cost + Variable Cost × Demand
CT = CF + c v D
Profit
Max. Profit
= aD − bD 2 − C F − cv D
= −C F + (a − cv )D − bD 2
To maximum the profit, we get
an optimal demand size:
a − cv
D =
2b
CT
Cost and Revenue
Then,
Profit = Revenue − Cost
R = aD − bD 2
CF
D1'
D*
D2'
Break even points
*
Note: a must larger than cv in order to get a real profit.
Copyright (c) 2015. Gabriel Fung. All rights reserved.
D
General Economic Environment (cont’d)
In order to obtain the two break even points, we may need to
solve the following equation:
Profit
Cost = Revenue
Max. Profit
aD − bD = CF − c v D
2
0 = −bD + ( a − c v ) D − CF
CT
D' =
−(a − c v ) ±
(a − c )
2
v
− 4bCF
Cost and Revenue
2
R = aD − bD 2
CF
2b
D1'
D*
D2'
D
Break even points
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Example – Watch
Given a company produces watches:
The rental cost is $73,000/month. The cost for producing each
watch is $83. The selling price is “$180 – 0.02 x demand”.
Question:
What should be the maximum production size? Optimal Profit?
Break even points?
Solution:
D* =
a − c v 180 − 83
=
= 2,425
2b
2(0.02)
D1' = 932
D2' = 3,918
profit = 180(2,425) − 0.02(2,425)2 − 73,000 − 83(2,425) = 44,612
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Example – Airplane
The cost of operating a jet-powered airplane is:
COperate = knv 2/3
where n is the trip length, k is a constant of proportionality
and v is the velocity. It is known that at 400 miles/hour, the
average cost of operation is $300/miles. Furthermore, for each
hour of flight there is a cost of $300,000.
Now the company wants to minimize the cost of operation.
What should be the velocity?
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Example – Airplane
By using the previous technique (not the equations)
The total cost is:
CTotal = knv 3/2 + 300,000
n
v
The constant k can be solved as follows:
COperate = knv 3/2
300 = k (1) ( 400 )
3/2
k = 0.0375
Thus,
dCTotal
=0
dv
v* = 490.68
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Example – Hair Cut
A Salon, which may serve up to $160,000 customers per year,
has the following records based on last year operation:
A customer spent $85.56 on average.
The company spent $62 on each customer on average.
Fixed cost is $2,024,000.
Question:
What is the breakeven point in for the unit of customer and for
the unit of max capacity?
What is the percentage drop in breakeven point if…
The fixed cost is reduced by 10%?
The cost per customer is reduced by 10%?
The charge is increased by 10%?
Copyright (c) 2015. Gabriel Fung. All rights reserved.
How Often Should You Drive?
In Hong Kong, whenever you drive motor cycle, you have to
turn on the headlights (no matter day time or night time).
Is turn on the headlights during day time is “cost-effective”?
Copyright (c) 2015. Gabriel Fung. All rights reserved.
How Often Should You Drive? (cont’d)
Some assumptions:
75% of driving takes place during the daytime.
2% of fuel consumption is due to accessories (radio, headlights,
etc)
Cost of fuel = $4/gallon
Average distance traveled per year = 15,000 miles
Average cost of an accident = $2,800
$25 for headlight
The motor cycle is operated 350 hours per year
A headlight can operate 200 hours
Each 30 miles use 1 gallon of gasoline
Copyright (c) 2015. Gabriel Fung. All rights reserved.
How Often Should You Drive? (cont’d)
Annual fuel cost:
(15,000 mi / yr) (1 gal / 30 mi) ($4 / gal) = $2,000 / yr
Fuel cost due to night use of headlights:
($2,000 / yr) (0.02) = $40 / yr (Worse case. Assume that 2% of fuel are
all consumed by the headlights at night.)
Fuel cost due to continuous use:
(4) ($40 / yr) = $160 / yr
Headlight cost for night use:
0.25 (350 / 200) ($25) = $10.94
Headlight cost for continuous use:
(350 / 200) ($25) = $43.75
Total cost associated with daytime use:
($160 - $40) + ($43.75 - $10.94) = $152.81 / yr
Copyright (c) 2015. Gabriel Fung. All rights reserved.
Remember…
Make sure that you have understood the problem before you
try to solve it!
The most important thing is: You know the techniques and
how to you them, but not simply memorizing and applying the
equations!
You are a human beings, but not a machine!
Copyright (c) 2015. Gabriel Fung. All rights reserved.
How Important is Cost Estimation?
So far, we assume that the information related to the cost and
revenue are readily available.
However, this may not be the case in reality.
We need to estimate them! ! Discuss in next lecture.
Copyright (c) 2015. Gabriel Fung. All rights reserved.