Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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LEARNING OBJECTIVES
Purpose: Understand
the
fundamental concepts
of
engineering economy.
Questions
Decision making
Study approach
Interest rate
Equivalence
Simple and compound interest
Symbols
Spreadsheet functions
Minimum
Attractive
Rate
of Return
Cash
flows
Doubling
time
Spreadsheets
This
chapter
will
help
you:
1.
Understand
the
types
of
questions
engineering
economy
can answer.
2.
Determine
the
role
of
eng
i
neering
economy
in
the
decision-
making
process.
3.
I
dent
ify
what
is
needed
to
successfully
pe
rf
orm
an
engineering
economy
study
.
4. Pe
rf
orm
ca
lcula
ti
ons
abou
t
int
erest
ra
tes
and
rate of
re
turn.
5.
Understand
what
equ
i
va
lence means in
eco
n
omic
terms.
6.
Ca
lculate
simple
i
nterest
and
compou
nd i
nterest
for
one
or
more
inte
r
est
per
i
ods
.
7.
Identify
and
use
engineering
economy
termino
l
ogy
and
symbols.
8.
Identify
the
Excel©
spreadsheet
functions
commonly
used
to
solve
engineering
economy
problems.
9.
Understand
the
meaning
and
use
of
Minimum
Attractive
Rate
of
Return (MARR).
10.
Understand
cash flows,
their
esti
mat
ion,
and
how
to
graph
ically r
epresent
them.
11. Use
th
e rule
of
72
to
esti
mate
a
co
mp
ound i
nterest
rate
or
number
of years f
or
a present
wort
h amou
nt
to
do
ubl
e.
12. Devel
op
a spreadsheet that i
nvo
lves simple and
compound
interest, incor
porati
ng sensi
tivity
anal
ys
i
s.
6
CHAPTER I
Foundations
of
Engineering Economy
1.1
WHY
ENGINEERING
ECONOMY
IS
IMPORTANT
TO
ENGINEERS (and
other
professionals)
Decisions made by engineers, managers, corporation presidents, and individuals
are commonly the result
of
choosing one alternative over another. Decisions
often reflect a person's educated choice
of
how to best invest funds, also called
capital.
The
amount
of
capital
is
usually restricted,
just
as the cash available to
an individual
is
usually limited.
The
decision
of
how to invest capital will in-
variably change the future, hopefully for the better; that is, it will be value
adding. Engineers
playa
major role in capital investment decisions based on
their analysis, synthesis, and design efforts.
The
factors considered in making the
decision are a combination
of
economic and noneconomic factors. Additional
factors may be intangible, such as
convertience, goodwill, friendship, and others.
Fundamentally, engineering economy involves formulating, estimating,
and
evaluating the economic outcomes when alternatives to accomplish a
defined
purpose
are
available.
Another
way to define engineering econ-
omy
is
as a collection
of
mathematical techniques
that
simplify economic
comparison.
For many corporations, especially larger ones, many
of
the projects and services
are international
in
scope. They may be developed
in
one country for application
in
another. People and plants located in sites around the world routinely separate
product design and manufacturing from each other, and from the customers who
utilize the product.
The
approaches presented here are easily implemented
in
multinational settings or within a single country or location. Correct use
of
the
techniques
of
engineering economy is especially important, since virtually any
project-local,
national, or
international-will
affect costs and/or revenues.
Some
of
the typical questions that can be addressed using the material
in
this
book are posed below.
Fo
r Engineering Activities
• Should a new bonding technique be incorporated into the manufacture
of
au-
tomobile brake pads?
•
If
a computer-vision system replaces the human inspector
in
perforrrting qual-
ity tests on an automobile welding line, will operating costs decrease over a
time horizon
of
5 years?
• Is it an economically wise decision
to
upgrade the composite material pro-
duction center
of
an airplane factory
in
order to reduce costs by 20%?
• Should a highway bypass be constructed around a city
of
25,000 people, or
should the current roadway through the city be expanded?
• Will we make the required rate
of
return if we install the newly offered tech-
nology onto
our
medical laser manufacturing line?
For Public Sector Projects
an
d Gove
rnm
ent
Agencies
• How much new tax revenue does the city need to generate to pay for
an
up-
grade to the electric distribution system?
•
Do
the benefits outweigh the costs
of
a bridge over the intracoastal waterway
at this point?
SECTION 1.2 Role
of
Engineering Economy
in
Decision Making
•
Is
it cost-effective for the state
to
cost-share with a contractor to construct a
new toll road?
• Should the state university contract with a local community college
to
teach
foundation-level undergraduate courses or have university faculty teach them?
For Individuals
• Should I
payoff
my
credit card balance with borrowed money?
• What are graduate studies worth financially over my professional career?
• Are federal income tax deductions for my home mortgage a good deal, or
should I accelerate
my
mortgage payments?
• Exactly what rate
of
return did we make on our stock investments?
• Should I buy or lease my next car, or keep the one I have now and
payoff
the
loan?
EXAMPLE 1.1
\,
Two lead engineers with a mechanical design company and a structural analysis firm work
together often. They have decided that, due to their joint and frequent commercial airline
travel around the region, they should evaluate the purchase
of
a plane co-owned by the two
companies. What are some
of
the economics-based questions the engineers should answer
as
they evaluate the alternatives
to
(1) co-own a plane or (2) continue to
fly
commercially?
Solution
Some questions (and what
is
needed to respond) for each alternative are
as
follows:
• How much will it cost each year? (Cost estimates are needed.)
• How do
we
pay for it? (A financing plan is needed.)
• Are there tax advantages? (Tax law and tax rates are needed.)
• What
is
the basis for selecting an alternative? (A selection criterion
is
needed.)
•
What
is the expected rate
of
return? (Equations are needed.)
• What happens
if
we
fly
more or less than we estimate now? (Sensitivity analysis is
needed.)
1.2
ROLE
OF ENGINEERING ECONOMY
IN DECISION MAKING
People make decisions; computers, mathematics, and other tools do not. The tech-
niques and models
of
engineering economy assist people
in
making decisions.
Since decisions affect what will be done, the time frame
of
engineering economy is
primarily
the future. Therefore, numbers used in an engineering economic analysis
are
best estimates
of
what is expected to occur. These estimates often involve the
three essential elements mentioned earlier: cash flows, time
of
occurrence, and in-
terest rates. These estimates are about the future, and will be somewhat different
than what actually occurs, primarily because
of
changing circumstances and
unplanned-for events. In other words, the
stochastic nature
of
estimates will likely
make the observed value
in
the future differ from the estimate made now.
Commonly,
sensitivity analysis is performed during the engineering economic
study
to
determine how the decision might change based on varying estimates,
7
8 CHAPTER I Foundations
of
Engineering Economy
especially those that may vary widely. For example, an engineer who expects ini-
tial software development costs
to
vary
as
much as
±20%
from
an
estimated
$250,000 should perform the economic analysis for first-cost estimates
of
$200,000, $250,000, and $300,000. Other uncertain estimates about the project
can be
"tweaked" using sensitivity analysis. (Sensitivity analysis
is
quite easy
to
perform using electronic spreadsheets. Tabular and graphical displays make
analysis possible
by
simply changing the estimated values. The power
of
spread-
sheets is used to advantage throughout this text and on the supporting website.)
Engineering economy can be used equally well
to
analyze outcomes
of
the past.
Observed data are evaluated
to
determine if the outcomes have met or not met a
specified criterion, such
as
a rate
of
return requirement. For example, suppose
that 5 years ago, a United States-based engineering design company initiated a
detailed-design service in Asia for automobile chassis. Now, the company president
wants
to
know
if
the actual return on the investment has exceeded
15
% per year.
There is
an
important procedure used
to
address the development and selec-
tion
of
alternatives. Commonly referred
to
as
the problem-solving approach or
the
decision-making process, the steps in the approach follow.
1.
Understand the problem and define the objective.
2.
Collect relevant information.
3.
Define the feasible alternative solutions and make realistic estimates.
4.
Identify the criteria for decision making using one or more attributes.
5.
Evaluate each alternative, using sensitivity analysis to enhance the
evaluation.
6.
Select the best alternative.
7. Implement the solution.
8.
Monitor the results.
Engineering economy has a major role in all steps and is primary
to
steps 2
through
6.
Steps 2 and 3 establish the alternatives and make the estimates for
each one.
Step 4 requires the analyst
to
identify attributes for alternative selec-
tion. This sets the stage for the technique
to
apply. Step 5 utilizes engineering
economy models to complete the evaluation and perform any sensitivity analysis
upon which a decision is based (step 6).
Reconsider the questions presented for the engineers in the previous example about
co-owning
an
airplane. State some ways in which engineering economy contributes
to
decision making between the two alternatives.
Solution
Assume that the objective is the same for each
engineer-available,
reliable transporta-
tion that minimizes total cost.
Use the steps above.
Steps 2 and 3: The framework for
an
engineering economy study assists
in
identify-
ing what should be estimated or collected. For alternative 1 (buy the plane), estimate
the purchase cost, financing method and interest rate, annual operating costs, possible
SECTION 1.3 Performing
an
Engineering Economy Study
increase
in
annual sales revenue, and income tax deductions. For alternative 2 (fly com-
mercial) estimate commercial transportation costs, number
of
trips, annual sales rev-
enue, and other relevant data.
Step 4: The selection criterion
is
a numerically valued attribute called a measure
of
worth. Some measures
of
worth are
Present worth (PW)
Annual worth (AW)
Benefit/cost ratio
(B/C)
Future worth (FW)
Rate
of
return (ROR)
Capitalized cost (CC)
Payback period
Economic value added
When determining a measure
of
worth, the fact that money today is worth a different
amount
in
the future is considered; that
is,
the time value
of
money
is
accounted
for.
There are many noneconomic attributes-social, environmental, legal, political,
personal,
to
name a
few.
This multiple-attribute environment may result in less reliance
placed
on
the economic results
in
step
6.
But this is exactly why the decision maker
must have adequate information for
all
factors-economic
and
noneconomic-to
make
an
informed selection.
In
our case, the economic analysis may favor the co-owned plane
(alternative 1), but because
of
noneconomic factors, one or both engineers may select
alternative 2.
Steps 5 and 6: The actual computations, sensitivity analysis, and alternative selec-
tion are accomplished here.
The concept
of
the time value
of
money was mentioned above. It is often said
that money makes money. The statement is indeed true, for if we elect to invest
money today, we inherently expect to have more money in the future.
If
a per-
son or company borrows money today, by tomorrow more than the original
loan principal will be owed. This fact is also explained by the time value
of
money.
The
change in
the
amount
of money
over
a given time period is called
the
time value
of
money;
it
is
the
most
important
concept in engineering
economy.
1.3 PERFORMING
AN
ENGINEERING ECONOMY STUDY
Consider the terms engineering economy, engineering economic analysis, eco-
nomic decision making, capital allocation study, economic analysis,
and similar
terms to be synonymous throughout this book. There is a general approach,
called the
Engineering Economy Study Approach, that provides an overview
of
the engineering economic study. It
is
outlined in Figure 1-1 for two alternatives.
The decision-making process steps are keyed to the blocks in Figure 1-1.
Alternative Description The result
of
decision-making process step 1 is a basic
understanding
of
what the problem requires for solution. There may initially be
many alternatives, but only a few will be feasible and actually evaluated.
If
9
10
/
Decision making
process s lep
Step I
Step 2
Step 3
Step 4
Step 5
Step 6
Figure
1-1
Enginee
rin
g economy
study approach.
CHAPTER
I
Foundation
s
of
En
g
ineering
Economy
alternatives A, B, and C have been identified for analysis, when method D,
though not recognized as an alternative, is the most attractive, the wrong decision
is certain to be made.
Alternatives are stand-alone options that involve a word description and best
estimates
of
parameters, such as first cost (including purchase price, develop-
ment, installation),
useful life, estimated annual incomes and expenses, salvage
value
(resale
or
trade-in value), an interest rate (rate
of
return), and possibly in-
flation
and income tax effects. Estimates
of
annual expenses are usually lumped
together and called annual operating costs
(AOC) or maintenance and operation
(M&O) costs.
Problem identified; objective defined
Alternative
1
New
equipment
Description and
information
Cash flows
over some
time period
Analysis using an
engineering
economy model
Evaluated
alternative
I
• Income and cost estimates
• Financing strategies
• Tax laws
• Time value
of
money
• T nterest rate
• Measure
of
worth
• Calculated value
of
measure
of
worth
Alternative 2
Upgrade old
equipment
Description and
information
Cash flows
over some
time
period
Analysis using an
engineering
economy model
Evaluated
alternative
2
Noneconomic altributes to be considered
Qelect
alternative I )
" ,
c::)
o
o
o
o
o
o
Implement
alternati ve
1
o
o
o
o
o
o
SECTION 1.3 Performing an Engineering Economy Study
Cash Flows The estimated inflows (revenues) and outflows (costs)
of
money
are called cash flows. These estimates are made for each alternative (step 3).
Without cash flow estimates over a stated time period, no engineering economy
study can be conducted. Expected variation in cash flows indicates a real need
for sensitivity analysis in step
S.
Analysis Using Engineering Economy Computations that consider the time
value
of
money are performed on the cash flows
of
each alternative
to
obtain the
measure
of
worth.
Alternative Selection The measure-of-worth values are compared, and an
al
-
ternative
is
selected. This is the result
of
the engineering economy analysis. For
example, the result
of
a rate-of-return analysis may be: Select alternative
1,
where the rate
of
return
is
estimated at 18.4% per year, over alternative 2 with an
expected
10% per year return. Some combination
of
economic criteria using the
measure
of
worth, and the noneconomic and intangible factors, may be applied
to
help select one alternative.
If
only one feasible alternative
is
defined, a second is often present in the form
of the
do-nothing alternative. This
is
the as-is or status quo alternative. Do noth-
ing can be selected if
no
alternative has a favorable measure
of
worth.
Whether we are aware
of
it or not, we use criteria every day
to
choose between
alternatives. For example, when you drive to campus, you decide
to
take the
"best" route. But how did you define best? Was the best route the safest, shortest,
fastest, cheapest, most scenic, or what? Obviously, depending upon which crite-
rion or combination
of
criteria is used
to
identify the best, a different route might
be selected each time. In economic
analysis,jinancial units (dollars or other cur-
rency) are generally used
as
the tangible basis for evaluation. Thus, when there
are several ways
of
accomplishing a stated objective, the alternative with the
lowest overall cost or highest overall net income is selected.
An
after-tax analysis
is
performed during project evaluation, usually with
only significant effects for asset depreciation and income taxes accounted for.
Taxes imposed by local, state, federal, and international governments usually
take the form
of
an
income tax on revenues, value-added tax
(VAT),
import taxes,
sales taxes, real estate taxes, and others. Taxes affect alternative estimates for
cash flows; they tend
to
improve cash flow estimates for expenses, cost savings,
and asset depreciation, while they
reduce cash flow estimates for revenue and
after-tax net income. This text delays the details
of
after-tax analysis until the
fundamental tools and techniques
of
engineering economy are covered. Until
then,
it
is
assumed that all alternatives are taxed equally by prevailing tax laws.
(If
the effects
of
taxes must be considered earlier, it is recommended that Chap-
ters
16
and
17
be covered after Chapter
6,
8 or 11.)
Now, we turn
to
some fundamentals
of
engineering economy that are applic-
able in the everyday life
of
engineering practice,
as
well
as
personal decision
making.
11
12
Loan
interest
rate
Borrower
Bank
CHAPTER I Foundations
of
Engineering Economy
1.4
INTEREST
RATE
AND
RATE
OF
RETURN
Interest is the manifestation
of
the time value
of
money. Computationally, inter-
est
is
the difference between an ending amount
of
money and the beginning
amount.
If
the difference is zero
or
negative, there is no interest. There are always
two perspectives to an amount
of
interest-interest
paid and interest earned. In-
terest is
paid when a person
or
organization borrowed money (obtained a loan)
and repays a larger amount. Interest is
earned when a person or organization
saved, invested,
or
lent money and obtains a return
of
a larger amount. It
is
shown below that the computations and numerical values are essentially the
same for both perspectives, but there are different interpretations.
Interest paid on borrowed funds (a loan) is determined by using the relation
Interest
= amount owed now - original amount [1.1 ]
When interest paid over a specific time unit is expressed as a percentage
of
the
original amount (principal), the result is called the
interest rate.
(
rr!
interest accrued per time unit
OOrr!
Interest rate
70)
= . . I x 1 7 0
OrIgma
amount
[1.2]
The time unit
of
the rate
is
called the interest period. By far the most common in-
terest period used to state an interest rate is 1 year. Shorter time periods can be
used, such as, 1
% per month. Thus, the interest period
of
the interest rate should
always be included.
If
only the rate
is
stated, for example, 8.5%, a I-year inter-
est period
is
assumed.
EXAMPLE
1.3
r:'
An employee at LaserKinetics.com borrows $10,000
on
May 1 and must repay a total
of
$1
0,700 exactly 1 year later. Determine the interest amount and the interest rate paid.
Solution
The perspective here
is
that
of
the borrower since $10,700 repays a loan. Apply Equa-
tion
[1.1] to determine the interest paid.
Interest earned
= $10,700 - 10,000 = $700
Equation [1.2] determines the interest rate paid for 1 year.
.
$700
Percent mterest rate = $10,000 X 100% = 7% per year
EXAMPLE
1.4
2'
Stereophonics, Inc., plans to borrow $20,000 from a bank for 1 year at 9% interest for
new recording equipment.
(a) Compute the interest and the total amount due after
I year. (b) Construct a column graph that shows the original loan amount and total
amount due after 1 year used
to compute the loan interest rate
of
9% per year.
SECTION 1.4 Interest Rate and Rate
of
Return
Solution
(a) Compute the total
in
terest accrued
by
solving Equation [1.2] for interest accrued.
Interest
= $20,000(0.09) = $1800
The total amount due
is
the sum
of
principal and interest.
Total due
= $20,000 + 1800 = $21,800
(b) Figure 1
-2
shows the values used
in
Equation [1.2]: $1800 interest, $20,000
original loan principal, I-year interest period.
Comment
$
$21
,800
$20,
00/,
Original
lo
an
amount
Figure
1-2
________
Cl
___ ] Interest = $1800
__
C7
______
_
Now
I year
later
I
Interest
period is
I year
I
Interest rate
$1800
$20,000 X 100%
= 9% per year
Values used to compute
an
interest rate
of
9% per year, Example 1.
4.
Note that
in
part (a), the total amount due may also be computed
as
Total due = principal(1 + interest rate) = $20,000(1.09) = $21,800
Later we will
Llse
this method to determine future amounts for times longer than one
interest period.
From
the perspective
of
a saver, a lender, or an investor, interest earned is the
final amount minus the initial amount, or principal.
Interest earned
= total amount now - original amount [1.3]
Interest earned over a specific period
of
time is expressed
as
a percentage
of
the
original amount and
is
called rate
of
return (ROR).
interest accrued per time unit
Ra
teo
f
return
(%)
=
x100
% [1.4]
original amount
13
I Investment rate of return I
Saver
Bank
14
CHAPTER 1 Foundations
of
Engineering Economy
The time unit for rate
of
return is called the interest period, just
as
for the bor-
rower's perspective. Again, the most common period is 1 year.
The term
return on investment (ROJ) is used equivalently with ROR in different
industries and settings, especially where large capital funds are committed
to
engineering-oriented programs.
The numerical values in Equation [1.2] and Equation [1.4] are the same, but
the term
interest rate paid is more appropriate for the borrower's perspective,
while the
rate
of
return earned is better for the investor's perspective.
EXAMPLE 1.5
~:i
(a) Calculate the amount deposited 1 year ago to have $1000 now at an interest rate
of
5% per year.
(b) Calculate the amount
of
interest earned during this time period.
Solution
(a) The total amount accrued ($1000)
is
the sum
of
the original deposit and the
earned interest.
If
X is the original deposit,
Total accrued
= original + original(interest rate)
$1000 = X + X(0.05) = X(l + 0.05) = 1.05X
The original deposit
is
LOOO
X = - = $952.38
1.05
(b) Apply Equation [1.3] to determine interest earned.
Interest
= $1000 - 952.38 = $47.62
In Examples 1
.3
to
1.5 the interest period was 1 year, and the interest amount
was calculated at the end
of
one period. When more than one interest period is
involved (e.g.,
if
we wanted the amount
of
interest owed after 3 years in Exam-
ple 1.4), it is necessary
to
state whether the interest is accrued on a simple or
compound basis from one period to the next.
An
additional economic consideration for any engineering economy study is
inflation. Several comments about the fundamentals
of
inflation are warranted at
this early stage. First, inflation represents a decrease in the value
of
a given cur-
rency. That is,
$1
now will not purchase the same number
of
apples (or most
other things)
as
$1
did 20 years ago. The changing value
of
the currency affects
market interest rates. In simple terms, bank interest rates reflect two thing
s:
a
so-called real rate
of
return plus the expected inflation rate. The real rate
of
return
allows the investor
to
purchase more than he or she could have purchased before
the investment. The safest investments (such
as
U.S. government bonds) typi-
cally have a 3% to 4% real rate
of
return built into their overall interest rates.
Thus, an interest rate
of
, say, 9% per year on a U.S. government bond means that
investors expect the inflation rate
to
be in the range
of
5%
to
6% per year.
Clearly, then, inflation causes interest rates to rise.