Engineering Economy
Chapter 1: Introduction to
Engineering Economy
The purpose of this course is to
develop and illustrate the principles
and methodology required to
answer the basic economic
question of any design:
Do its benefits exceed its cost?
Engineering Economy is Problem Solving
• Engineering is a profession devoted to
problem solving and design of alternative
courses of action.
• Engineering economy is a subset of
engineering devoted to deciding which course
of action best meets technical performance
criteria while using capital in a prudent
manner.
WHAT IS ECONOMICS ?
• The study of how limited resources is used to
satisfy unlimited human wants
• The study of how individuals and societies
choose to use scarce resources that nature
and previous generations have provided
Origins of Engineering Economy
• Pioneer: Arthur M. Wellington, civil engineer
latter part of nineteenth century;
addressed role of economic analysis in
engineering projects;
area of interest: railroad building
• Followed by other contributions which
emphasized techniques depending on
financial and actuarial mathematics.
Engineering economy…
involves the systematic
evaluation of the economic
merits of proposed solutions
to engineering problems.
Why Engineering Economy is Important to
Engineers
 Engineers design and create
 Designing involves economic decisions
 Engineers must be able to incorporate economic
analysis into their creative efforts
 Often engineers must select and implement from
multiple alternatives
 Understanding and applying time value of money,
economic equivalence, and cost estimation are vital
for engineers
 A proper economic analysis for selection and
execution is a fundamental task of engineering
Engineering Economy
• Engineering Economy involves
– Formulating
– Estimating, and
– Evaluating
expected economic outcomes of alternatives designed
to accomplish a defined purpose
• Easy-to-use math techniques simplify the
evaluation
• Estimates of economic outcomes can be
deterministic or stochastic in nature
Solutions to engineering
problems must
• promote the well-being and survival of an
organization,
• embody creative and innovative technology and
ideas,
• permit identification and scrutiny of their
estimated outcomes, and
• translate profitability to the “bottom line” through
a valid and acceptable measure of merit.
Engineering economic analysis can play a
role in many types of situations.
• Choosing the best design for a high-efficiency gas
furnace.
• Selecting the most suitable robot for a welding
operation on an automotive assembly line.
• Making a recommendation about whether jet
airplanes for an overnight delivery service should
be purchased or leased.
• Determining the optimal staffing plan for a
computer help desk.
There are seven fundamental
principles of engineering economy.
•
•
•
•
•
•
•
Develop the alternatives
Focus on the differences
Use a consistent viewpoint
Use a common unit of measure
Consider all relevant criteria
Make uncertainty explicit
Revisit your decisions
DEVELOP THE ALTERNATIVES
The final choice (decision) is among
alternatives. The alternatives need to be
identified and then defined for subsequent
analysis.
FOCUS ON THE DIFFERENCES
Only the differences in expected future
outcomes among the alternatives are relevant
to their comparison and should be considered
in the decision.
USE A CONSISTENT VIEWPOINT
The prospective outcomes of the alternatives,
economic and other, should be consistently
developed from a defined viewpoint
(perspective).
USE A COMMON UNIT OF MEASURE
Using a common unit of measurement to
enumerate as many of the prospective
outcomes as possible will make easier the
analysis and comparison of alternatives.
CONSIDER ALL RELEVANT CRITERIA
Selection of a preferred alternative (decision
making) requires the use of a criterion (or
several criteria). The decision process should
consider the outcomes enumerated in the
monetary unit and those expressed in some
other unit of measurement or made explicit
in a descriptive manner.
MAKE UNCERTAINTY EXPLICIT
Uncertainty is inherent in projecting (or
estimating) the future outcomes of the
alternatives and should be recognized in their
analysis and comparison.
REVISIT YOUR DECISIONS
Improved decision making results from an
adaptive process; to the extent practicable,
the initial projected outcomes of the
selected alternative should be subsequently
compared with actual results achieved.
Engineering economic analysis
procedure
•
•
•
•
•
•
•
Problem definition
Development of alternatives
Development of prospective outcomes
Selection of a decision criterion
Analysis and comparison of alternatives.
Selection of the preferred alternative.
Performance monitoring and postevaluation
of results.
Time Value of Money (TVM)
Description: TVM explains the change in the
amount of money over time for funds owed by
or owned by a corporation (or individual)
– Corporate investments are expected to earn a return
– Investment involves money
– Money has a ‘time value’
The time value of money is the most important concept in
engineering economy
Interest and Interest Rate
• Interest – the manifestation of the time value of
money
• Fee that one pays to use someone else’s money
• Difference between an ending amount of money
and a beginning amount of money
 Interest = amount owed now – principal
• Interest rate – Interest paid over a time period
expressed as a percentage of principal

1-28
Rate of Return
• Interest earned over a period of time is expressed as a
percentage of the original amount (principal)
interest accrued per time unit
Rate of return (%) =
x 100%
original amount
 Borrower’s perspective – interest rate paid
 Lender’s or investor’s perspective – rate of return earned
Interest paid
Interest rate
Interest
earned
Rate of return
Cash Flow
• Engineering projects generally have economic
consequences that occur over an extended period of
time
– For example, if an expensive piece of machinery is
installed in a plant were brought on credit, the simple
process of paying for it may take several years
– The resulting favorable consequences may last as long as
the equipment performs its useful function
• Each project is described as cash receipts or
disbursements (expenses) at different points in time
31
Categories of Cash Flows
• The expenses and receipts due to engineering
projects usually fall into one of the following
categories:
– First cost: expense to build or to buy and install
– Operations and maintenance (O&M): annual expense,
such as electricity, labor, and minor repairs
– Salvage value: receipt at project termination for sale or
transfer of the equipment (can be a salvage cost)
– Revenues: annual receipts due to sale of products or
services
– Overhaul: major capital expenditure that occurs during
the asset’s life
Cash Flow diagrams
• The costs and benefits of engineering projects
over time are summarized on a cash flow diagram
(CFD). Specifically, CFD illustrates the size, sign,
and timing of individual cash flows, and forms the
basis for engineering economic analysis
• A CFD is created by first drawing a segmented
time-based horizontal line, divided into
appropriate time unit. Each time when there is a
cash flow, a vertical arrow is added  pointing
down for costs and up for revenues or benefits.
The cost flows are drawn to relative scale
Drawing a Cash Flow Diagram
• In a cash flow diagram (CFD) the end of period t is the
same as the beginning of period (t+1)
• Beginning of period cash flows are: rent, lease, and
insurance payments
• End-of-period cash flows are: O&M, salvages, revenues,
overhauls
• The choice of time 0 is arbitrary. It can be when a project
is analyzed, when funding is approved, or when
construction begins
• One person’s cash outflow (represented as a negative
value) is another person’s inflow (represented as a
positive value)
• It is better to show two or more cash flows occurring in
the same year individually so that there is a clear
connection from the problem statement to each cash flow
in the diagram
An Example of Cash Flow Diagram
• A man borrowed $1,000 from a bank at 8%
interest. Two end-of-year payments: at the end of
the first year, he will repay half of the $1000
principal plus the interest that is due. At the end
of the second year, he will repay the remaining
half plus the interest for the second year.
• Cash flow for this problem is:
End of year
0
1
2
Cash flow
+$1000
-$580 (-$500 - $80)
-$540 (-$500 - $40)
Cash Flow Diagram
$1,000
1
2
0
$580
$540
Commonly used Symbols
t = time, usually in periods such as years or months
P = value or amount of money at a time t
designated as present or time 0
F = value or amount of money at some future
time, such as at t = n periods in the future
A = series of consecutive, equal, end-of-period
amounts of money
n = number of interest periods; years, months
i = interest rate or rate of return per time period;
percent per year or month
Time Value of Money
Nature of Interest
Interest

Payment for the use of money.

Excess cash received or repaid over the amount borrowed
(principal).
Variables involved in financing transaction:
1.
Principal (p) - Amount borrowed or invested.
2.
Interest Rate (i) – An annual percentage.
3.
Time (n) - The number of years or portion of a year that the
principal is borrowed or invested.
SO 1 Distinguish between simple and compound interest.
Nature of Interest
Simple Interest

Interest computed on the principal only.
Illustration: Assume you borrow $5,000 for 2 years at a simple
interest of 12% annually. Calculate the annual interest cost.
Interest = p x i x n
FULL YEAR
= $5,000 x .12 x 2
= $1,200
SO 1 Distinguish between simple and compound interest.
Nature of Interest
Compound Interest

Computes interest on
►
the principal and
►
any interest earned that has not been paid or
withdrawn.

Most business situations use compound interest.
SO 1 Distinguish between simple and compound interest.
Compound Interest
Illustration: Assume that you deposit $1,000 in Bank Two, where it will earn
simple interest of 9% per year, and you deposit another $1,000 in Citizens
Bank, where it will earn compound interest of 9% per year compounded
annually. Also assume that in both cases you will not withdraw any interest
until three years from the date of deposit.
Year 1 $1,000.00 x 9%
$ 90.00
$ 1,090.00
Year 2 $1,090.00 x 9%
$ 98.10
$ 1,188.10
Year 3 $1,188.10 x 9%
$106.93
$ 1,295.03
Present Value Variables
Present value is the value now of a given amount to be paid or
received in the future, assuming compound interest.
Present value variables:
1. Dollar amount to be received in the future,
2. Length of time until amount is received, and
3. Interest rate (the discount rate).
SO 2 Identify the variables fundamental to solving present value problems.
Present Value of a Single Amount
Present Value = Future Value / (1 + i )n
p
= principal (or present value)
i = interest rate for one period
n
= number of periods
SO 3 Solve for present value of a single amount.
Present Value of a Single Amount
Illustration: If you want a 10% rate of return, you would compute
the present value of $1,000 for one year as follows:
SO 3 Solve for present value of a single amount.
Present Value of a Single Amount
Illustration: If you want a 10% rate of return, you can also
compute the present value of $1,000 for one year by using a
present value table.
What table do we use?
SO 3 Solve for present value of a single amount.
Present Value of a Single Amount
What factor do we use?
$1,000 x .90909 = $909.09
Future Value
Factor
Present Value
SO 3 Solve for present value of a single amount.
Present Value of a Single Amount
Illustration: If you receive the single amount of $1,000 in two years,
discounted at 10% [PV = $1,000 / 1.102], the present value of your
$1,000 is $826.45.
What table do we use?
SO 3 Solve for present value of a single amount.
Present Value of a Single Amount
What factor do we use?
$1,000
Future Value
x
.82645
=
Factor
$826.45
Present Value
SO 3 Solve for present value of a single amount.
Present Value of a Single Amount
Illustration: Suppose you have a winning lottery ticket and the state gives you
the option of taking $10,000 three years from now or taking the present value
of $10,000 now. The state uses an 8% rate in discounting. How much will you
receive if you accept your winnings now?
$10,000
Future Value
x
.79383
Factor
=
$7,938.30
Present Value
SO 3 Solve for present value of a single amount.
Present Value of a Single Amount
Illustration: Determine the amount you must deposit now in a bond
investment, paying 9% interest, in order to accumulate $5,000 for a down
payment 4 years from now on a new Toyota Prius.
$5,000
Future Value
x
.70843
Factor
=
$3,542.15
Present Value
SO 3 Solve for present value of a single amount.
Present Value of an Annuity
The value now of a series of future receipts or payments, discounted assuming
compound interest.
Present Value
$100,000
100,000
100,000
100,000
100,000
100,000
19
20
.....
0
1
2
3
4
SO 4 Solve for present value of an annuity.
Present Value of an Annuity
Illustration: Assume that you will receive $1,000 cash annually for
three years at a time when the discount rate is 10%.
What table do we use?
SO 4 Solve for present value of an annuity.
Present Value of an Annuity
What factor do we use?
$1,000
Future Value
x
2.48685
Factor
=
$2,486.85
Present Value
SO 4 Solve for present value of an annuity.
Present Value of an Annuity
Illustration: Kildare Company has just signed a capitalizable lease contract for
equipment that requires rental payments of $6,000 each, to be paid at the end
of each of the next 5 years. The appropriate discount rate is 12%. What is the
amount used to capitalize the leased equipment?
$6,000 x 3.60478 = $21,628.68
SO 4 Solve for present value of an annuity.
Time Periods and Discounting
Illustration: When the time frame is less than one year, you need to
convert the annual interest rate to the applicable time frame. Assume that
the investor received $500 semiannually for three years instead of $1,000
annually when the discount rate was 10%.
$500 x 5.07569 = $2,537.85
SO 4
Present Value of a Long-term Note or Bond
Two Cash Flows:

Periodic interest payments (annuity).

Principal paid at maturity (single-sum).
100,000
$5,000
5,000
5,000
5,000
5,000
5,000
9
10
.....
0
1
2
3
4
SO 5 Compute the present value of notes and bonds.
Present Value of a Long-term Note or Bond
Illustration: Assume a bond issue of 10%, five-year bonds with a face
value of $100,000 with interest payable semiannually on January 1 and
July 1. Calculate the present value of the principal and interest
payments.
100,000
$5,000
5,000
5,000
5,000
5,000
5,000
9
10
.....
0
1
2
3
4
SO 5 Compute the present value of notes and bonds.
Present Value of a Long-term Note or Bond
PV of Principal
$100,000
Principal
x
.61391
Factor
=
$61,391
Present Value
SO 5 Compute the present value of notes and bonds.
Present Value of a Long-term Note or Bond
PV of Interest
$5,000
Principal
x
7.72173
Factor
=
$38,609
Present Value
SO 5 Compute the present value of notes and bonds.
Present Value of a Long-term Note or Bond
Illustration: Assume a bond issue of 10%, five-year bonds with a face
value of $100,000 with interest payable semiannually on January 1 and
July 1.
Present value of Principal
$61,391
Present value of Interest
38,609
Bond current market value
Date Account Title
Cash
Bonds Payable
$100,000
Debit
Credit
100,000
100,000
SO 5 Compute the present value of notes and bonds.
Present Value of a Long-term Note or Bond
Illustration: Now assume that the investor’s required rate of return is 12%,
not 10%. The future amounts are again $100,000 and $5,000, respectively,
but now a discount rate of 6% (12% / 2) must be used. Calculate the
present value of the principal and interest payments.
SO 5 Compute the present value of notes and bonds.
Present Value of a Long-term Note or Bond
Illustration: Now assume that the investor’s required rate of return is
8%. The future amounts are again $100,000 and $5,000, respectively, but
now a discount rate of 4% (8% / 2) must be used. Calculate the present
value of the principal and interest payments.
SO 5 Compute the present value of notes and bonds.
Tables…
=i
F3 = 50 000(F/P,10%,3) = 50 000(1.3310) = $66 550
Formulas…
F3 = 50 000(F/P, 10%,3) = 50 000(1+.10)3 = 50 000(1.3310) = $66 550