Comparing alternatives in Engineering Economics and Management In the real world, the majority of engineering economic analysis problems are alternative comparisons. In these problems, two or more mutually exclusive investments compete for limited funds. A variety of methods exists for selecting the superior alternative from a group of proposals. Each method has its own merits and applications

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Comparing alternatives
Student Name:
Class: 4
Course Title: Engineering Economics and Management
Department: Geomatics (Surveying)
College of Engineering
Salahaddin University-Erbil
Academic Year 2019-2020
Copyright

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ABSTRACT
In the real world, the majority of engineering economic analysis problems are
alternative comparisons. In these problems, two or more mutually exclusive
investments compete for limited funds. A variety of methods exists for selecting
the superior alternative from a group of proposals. Each method has its own merits
and applications.
There are three classes of relations among projects: (1) independent, (2) mutually
exclusive, and (3) related but not mutually exclusive. We then showed how the
third class of projects, those that are related but not mutually exclusive, could be
combined into sets of mutually exclusive projects. This enabled us to limit the
discussion to the first two classes—independent and mutually exclusive.
Independent projects are considered one at a time and are either accepted or
rejected. Only the best of a set of mutually exclusive projects is chosen. The
present worth method compares projects on the basis of converting all cash flows
for the project to a present worth. An independent project is acceptable if its
present worth is greater than zero. The mutually exclusive project with the highest
present worth should be taken. Projects with unequal lives must be compared by
assuming that the projects are repeated or by specifying a study period. Annual
worth is similar to present worth, except that the cash flows are converted to a
uniform series. The annual worth method may be more meaningful and does not
require more complicated calculations when the projects have different service
lives.
In this report we will go into detail about the ways of comparing alternatives in
engineering economics. We will explain the types of ways, and to help further
understand we will show a solved example.

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TABLE OF CONTENTS
Abstract 2
Table of contents 3
Chapter one – Introduction 4
Chapter two – background & review 6
Chapter three – methods
3.1 Minimum acceptable rate of return (MARR) 8
3.2 Present worth (PW) & Annual worth (AW) comparisons 8
Chapter four – theory & design
4.1 present worth analysis 11
4.2 annual cost analysis 11
4.3 rate of return analysis 11
4.4 benefit-cost analysis 13
4.5 break-even analysis 13
4.6 example 14
Chapter five – conclusion 15
References 16

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CHAPTER ONE – INTRODUCTION
Economics is the study of how people and society choose to utilize scarce
resources that could have alternative uses in order to produce various commodities
and to distribute them for consumption, now or in the future. Economics is the
science which studies human behavior which aims at meeting maximum objectives
of an individual with the help of scarce means.
Why should an engineer care about economics?
- Economics is the fundamental theory of business.
- Business decisions based on economic principles determine the success
or failure of engineering projects.
Engineering economy
Engineers must decide if the benefits of a project exceed its costs, and must make
this comparison in a unified framework. The framework within which to make this
comparison is the field of engineering economics, which strives to answer exactly
these questions, and perhaps more. Engineering economics:
• deals with the concepts and techniques of analysis useful in evaluating the worth
of systems, products, and services in relation to their costs.
• is used to answer many different questions
• Which engineering projects are worthwhile?
• Which engineering projects should have a higher priority?
• How should the engineering project be designed?
The essential idea of investing is to give up something valuable now for the
expectation of receiving something of greater value later. An investment may be
thought of as an exchange of resources now for an expected flow of benefits in the
future. Business firms, other organizations, and individuals all have opportunities
to make such exchanges. A company may be able to use funds to install equipment
that will reduce labor costs in the future.

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These funds might otherwise have been used on another project or returned to the
shareholders or owners. An individual may be able to study to become an engineer.
Studying requires that time be given up that could have been used to earn money or
to travel. The benefit of study, though, is the expectation of a good income from an
interesting job in the future.
Not all investment opportunities should be taken. The company considering a
laborsaving investment may find that the value of the savings is less than the cost
of installing the equipment. Not all investment opportunities can be taken. The
person spending the next four years studying engineering cannot also spend that
time getting degrees in law and science. Engineers play a major role in making
decisions about investment opportunities. In many cases, they are the ones who
estimate the expected costs of and returns from an investment. They then must
decide whether the expected returns outweigh the costs to see if the opportunity is
potentially acceptable. They may also have to examine competing investment
opportunities to see which is best. Engineers frequently refer to investment
opportunities as projects. Throughout most of this text, the term project will be
used to mean investment opportunity.
A basic part of engineering is choosing between alternative designs. Economic
comparisons are tremendously important in our society, and are usually used to
select between alternatives. We will discuss the tools available for making
economic comparisons between alternatives.
Economic comparisons can be made if costs and revenues are reduced to a
common basis, such as present worth, annual worth, or future worth. All three
methods select the same alternative if the underlying assumptions are satisfied.
Comparisons are sensitive to the interest rate, which is based on the M.A.R.R.
Comparisons are also sensitive to the inflation rate.

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CHAPTER TWO – BACKGROUND & REVIEW
Companies and individuals are often faced with a large number of investment
opportunities at the same time. Relations among these opportunities can range
from the simple to the complex. We can distinguish three types of connections
among projects that cover all the possibilities.
Projects may be
1. Independent
2. Mutually exclusive
3. Related but not mutually exclusive
The simplest relation between projects occurs when they are independent. Two
projects are independent if the expected costs and the expected benefits of each
project do not depend on whether the other one is chosen. A student considering
the purchase of a vacuum cleaner and the purchase of a personal computer would
probably find that the expected costs and benefits of the computer did not depend
on whether he or she bought the vacuum cleaner. Similarly, the benefits and costs
of the vacuum cleaner would be the same whether or not the computer was
purchased. If there are more than two projects under consideration, they are said to
be independent if all possible pairs of projects in the set are independent. When
two or more projects are independent, evaluation is simple. Consider each
opportunity one at a time, and accept or reject it on its own merits.
Projects are mutually exclusive if, in the process of choosing one, all other
alternatives are excluded. In other words, two projects are mutually exclusive if it
is impossible to do both or it clearly would not make sense to do both.
The third class of projects consists of those that are related but not mutually
exclusive. For pairs of projects in this category, the expected costs and benefits of
one project depend on whether the other one is chosen.
For example, Klamath Petroleum may be considering a service station at Fourth
Avenue and Main Street as well as one at Twelfth and Main. The costs and
benefits from either station will clearly depend on whether the other is built, but it
may be possible, and may make sense, to have both stations. Evaluation of related
but not mutually exclusive projects can be simplified by combining them into

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exhaustive, mutually exclusive sets. For example, the two projects being
considered by Klamath can be put into four mutually exclusive sets:
1. Neither station—the “do nothing” option
2. Just the station at Fourth and Main
3. Just the station at Twelfth and Main
4. Both stations
In general, n related projects can be put into 2n sets, including the “do nothing”
option. Once the related projects are put into mutually exclusive sets, the analyst
treats these sets as the alternatives. We can make 2n mutually exclusive sets with n
related projects by noting that for any single set, there are exactly two possibilities
for each project. The project may be in or out of that set. To get the total number of
sets, we multiply the n twos to get 2n. In the Klamath example, there were two
possibilities for the station at Fourth and Main—accept or reject. These are
combined with the two possibilities for the station at Twelfth and Main to give the
four sets that we listed. A special case of related projects is where one project is
contingent on another. Consider the case where project A could be done alone or A
and B could be done together, but B could not be done by itself. Project B is then
contingent on project A because it cannot be taken unless A is taken first. For
example, the Athens and Manchester Development Company is considering
building a shopping mall on the outskirts of town. It is also considering building a
parking garage to avoid long outdoor walks by patrons. Clearly, it would not build
the parking garage unless it were also building the mall. Another special case of
related projects is due to resource constraints. Usually the constraints are financial.
Fig. 1

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CHAPTER THREE - METHODS
3.1 Minimum acceptable rate of return (MARR)
A company evaluating projects will set for itself a lower limit for investment
acceptability known as the minimum acceptable rate of return (MARR). The
MARR is an interest rate that must be earned for any project to be accepted.
Projects that earn at least the MARR are desirable, since this means that the money
is earning at least as much as can be
earned elsewhere. Projects that earn less than the MARR are not desirable, since
investing money in these projects denies the opportunity to use the money more
profitably elsewhere. The MARR can also be viewed as the rate of return required
to get investors to invest in a business. If a company accepts projects that earn less
than the MARR, investors will not be willing to put money into the company. This
minimum return required to induce investors to invest in the company is the
company’s cost of capital.
The MARR is thus an opportunity cost in two senses. First, investors have
investment opportunities outside any given company. Investing in a given
company implies forgoing the opportunity of investing elsewhere. Second, once a
company sets a MARR, investing in a given project implies giving up the
opportunity of using company funds to invest in other projects that pay at least the
MARR.
3.2 Present worth (PW) & Annual worth (AW) comparisons
The present worth (PW) comparison method and the annual worth (AW)
comparison method are based on finding a comparable basis to evaluate projects in
monetary units. With the present worth method, the analyst compares project A
and project B by computing the present worths of the two projects at the MARR.
The preferred project is the one with the greater present worth. The value of any
company can be considered to be the present worth of all of its projects. Therefore,
choosing projects with the greatest present worth maximizes the value of the
company. With the annual worth method, the analyst compares projects A and B
by transforming all disbursements and receipts of the two projects to a uniform

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series at the MARR. The preferred project is the one with the greater annual worth.
One can also speak of present cost and annual cost.
 Present worth comparisons for independent projects
The alternative to investing money in an independent project is to “do nothing.”
Doing nothing doesn’t mean that the money is not used productively. In fact, it
would be used for some other project, earning interest at a rate at least equal to the
MARR.
 Present worth comparisons for mutually exclusive projects
It is very easy to use the present worth method to choose the best project among a
set of mutually exclusive projects when the service lives are the same. One just
computes the present worth of each project using the MARR. The project with the
greatest present worth is the preferred project because it is the one with the greatest
profit.
 Annual worth comparisons
Annual worth comparisons are essentially the same as present worth comparisons,
except that all disbursements and receipts are transformed to a uniform series at the
MARR, rather than to the present worth. Any present worth P can be converted to
an annuity A by the capital recovery factor (A/P,i,N). Therefore, a comparison of
two projects that have the same life by the present worth and annual worth
methods will always indicate the same preferred alternative. Note that, although
the method is called annual worth, the uniform series is not necessarily on a yearly
basis. Present worth comparisons make sense because they compare the worth
today of each alternative, but annual worth comparisons can sometimes be more
easily grasped mentally. For example, to say that operating an automobile over five
years has a present cost of $20 000 is less meaningful than saying that it will cost
about $5300 per year for each of the following five years.

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 Comparisons of alternatives with unequal lives
When making present worth comparisons, we must always use the same time
period in order to take into account the full benefits and costs of each alternative. If
the lives of the alternatives are not the same, we can transform them to equal lives
with one of the following two methods:
1. Repeat the service life of each alternative to arrive at a common time period for
all alternatives. Here we assume that each alternative can be repeated with the
same costs and benefits in the future—an assumption known as repeated lives.
Usually we use the least common multiple of the lives of the various alternatives.
Sometimes it is convenient to assume that the lives of the various alternatives are
repeated indefinitely.
Note that the assumption of repeated lives may not be valid where it is reasonable
to expect technological improvements.
2. Adopt a specified study period—a time period that is given for the analysis. To
set an appropriate study period, a company will usually take into account the time
of required service or the length of time it can be relatively certain of its forecasts.
The study period method necessitates an additional assumption about salvage value
whenever the life of one of the alternatives exceeds that of the given study period.
Arriving at a reliable estimate of salvage value may be difficult sometimes.
Because they rest on different assumptions, the repeated lives and the study period
methods can lead to different conclusions when applied to a particular project
choice.

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CHAPTER FOUR – THEORY/DESIGN
4.1 Present worth analysis
When two or more alternatives are capable of performing the same functions, the
economically superior alternative will have the largest present worth. The present
worth method is restricted to evaluating alternatives that are mutually exclusive
and that have the same lives. This method is suitable for ranking the desirability of
alternatives.
4.2 Annual cost analysis
Alternatives that accomplish the same purpose but that have unequal lives must be
compared by the annual cost method. The annual cost method assumes that each
alternative will be replaced by an identical twin at the end of its useful life (i.e.,
infinite renewal). This method, which may also be used to rank alternatives
according to their desirability, is also called the annual return method or capital
recovery method.
The alternatives must be mutually exclusive and repeatedly renewed up to the
duration of the longest-lived alternative. The calculated annual cost is known as the
equivalent uniform annual cost (EUAC) or equivalent annual cost (EAC). Cost is a
positive number when expenses exceed income.
4.3 Rate of return analysis
An intuitive definition of the rate of return (ROR) is the effective annual interest
rate at which an investment accrues income. That is, the rate of return of an
investment is the interest rate that would yield identical profits if all money was
invested at that rate. Although this definition is correct, it does not provide a
method of determining the rate of return. The present worth of a $100 investment
invested at 5% is zero when i = 5% is used to determine equivalence. Therefore, a
working definition of rate of return would be the effective annual interest rate that
makes the present worth of the investment zero. Alternatively, rate of return could
be defined as the effective annual interest rate that makes the benefits and costs
equal. A company may not know what effective interest rate, i, to use in

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engineering economic analysis. In such a case, the company can establish a
minimum level of economic performance that it would like to realize on all
investments. This criterion is known as the minimum attractive rate of return, or
MARR. Once a rate of return for an investment is known, it can be compared with
the minimum attractive rate of return. If the rate of return is equal to or exceeds the
minimum attractive rate of return, the investment is qualified (i.e., the alternative is
viable). This is the basis for the rate of return method of alternative viability
analysis. If rate of return is used to select among two or more investments, an
incremental analysis must be performed. An incremental analysis begins by
ranking the alternatives in order of increasing initial investment. Then, the cash
flows for the investment with the lower initial cost are subtracted from the cash
flows for the higher-priced alternative on a year-by-year basis. This produces, in
effect, a third alternative representing the costs and benefits of the added
investment. The added expense of the higher-priced investment is not warranted
unless the rate of return of this third alternative exceeds the minimum attractive
rate of return as well. The alternative with the higher initial investment is superior
if the incremental rate of return exceeds the minimum attractive rate of return.
Finding the rate of return can be a long, iterative process, requiring either
interpolation or trial and error. Sometimes, the actual numerical value of rate of
return is not needed; it is sufficient to know whether or not the rate of return
exceeds the minimum attractive rate of return This analysis can be accomplished
without calculating the rate of returns by finding the present worth of the
investment using the minimum attractive rate of return as the effective interest rate
(i.e., i= MARR).
If the present worth is zero or positive, the investment is qualified.
If the present worth is negative, the rate of return is less than the minimum
attractive rate of return and the additional investment is not warranted.
The present worth, annual cost, and rate of return methods of comparing
alternatives yield equivalent results, but they are distinctly different approaches.
The present worth and annual cost methods may use either effective interest rates
or the minimum attractive rate of return to rank alternatives or compare them to the
MARR. If the incremental rate of return of pairs of alternatives are compared with
the MARR, the analysis is considered a rate of return analysis.

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4.4 benefit-cost analysis
The benefit-cost ratio method is often used in municipal project evaluations where
benefits and costs accrue to different segments of the community. With this
method, the present worth of all benefits (irrespective of the beneficiaries) is
divided by the present worth of all costs. (Equivalent uniform annual costs can be
used in place of present worth’s). The project is considered acceptable if the ratio
equals or exceeds 1.0 (i.e., B/ C 2: 1.0). This will be true whenever B- C 2: 0.
When the benefit-cost ratio method is used, disbursements by the initiators or
sponsors are costs. Disbursements by the users of the project are known as
disbenefits. It is often difficult to determine whether a cash flow is a cost or a
disbenefit (whether to place it in the denominator or numerator of the benefit-cost
ratio calculation).
Regardless of where the cash flow is placed, an acceptable project will always
have a benefit-cost ratio greater than or equal to 1.0, although the actual numerical
result will depend on the placement. For this reason, the benefit-cost ratio alone
should not be used to rank competing projects. If ranking is to be done by the
benefit-cost ratio method, an incremental analysis is required, as it is for the rateof-
return method. The incremental analysis is accomplished by calculating the ratio of
differences in benefits to differences in costs for each possible pair of alternatives.
If the ratio exceeds 1.0, alternative 2 is superior to alternative 1. Otherwise,
alternative 1 is superior.
𝐵2 − 𝐵1
𝐶2 − 𝐶1
≥ 1
4.5 Break-even analysis
Break-even analysis is a method of determining when the value of one alternative
becomes equal to the value of one alternative becomes equal to the value of
another. It is commonly used to determine when costs exactly equal revenue. If the
manufactured quantity is less than the break-even quantity, a loss is incurred. If the
manufactured quantity is greater than the breakeven quantity, a profit is made. An
alternative form of the break-even problem is to find the number of units per
period for which two alternatives have the same total costs. Fixed costs are spread

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over a period longer than one year using the EUAC concept. One of the
alternatives will have a lower cost if production is less than the break-even point.
The other will have a lower cost if production is greater than the break-even point.
The pay-back period, PBP, is defined as the length of time, n, usually in years, for
the cumulative net annual profit to equal the initial investment. It is tempting to
introduce equivalence into pay-back period calculations, but the convention is not
to.
C - (PBP)(net annual profit) = 0
4.6 Example
To help better understand we use an example:
Instead of paying $10,000 in annual rent for office space at the beginning of each
year for the next 10 years, an engineering firm has decided to take out a 10-year,
$100,000 loan for a new building at 6% interest. The firm will invest $10,000 of
the rent saved and earn 18% annual interest on that amount. What will be the
difference between the firm's annual revenue and expenses?
(A) The firm will need $3300 extra.
(B) The firm will need $1800 extra.
(C) The firm will break even.
(D) The firm will have $1600 left over.
The annual loan payment will be
P(A/ P, 6%, 10) = ($100,000)(0.1359) = $13,590
The annual return from the investment will be
P(AI P, 18%, 1) = ($10,000)(1.1800) = $11,800
The difference between the loan payment and the return
on the investment is
$13,590-$11,800 = $1790 ($1800)

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CHAPTER FIVE – CONCLUSION
Economic comparisons can be made if costs and revenues are reduced to a
common basis, such as present worth, annual worth, or future worth. o All three
methods select the same alternative if the underlying assumptions are satisfied.
Comparisons are sensitive to the interest rate, which is based on the M.A.R.R.
Comparisons are also sensitive to the inflation rate.
Most engineering projects can be accomplished by more than one feasible design
alternative. When the selection of one of these alternatives excludes the choice of
any of others, the alternatives are called mutually exclusive. Typically, the
alternatives being considered require the investment of different amounts of
capital, and their annual revenues and costs may vary. Sometimes the alternatives
may have different useful lives. Because different levels of investment normally
produce varying economic outcomes, we must perform an analysis to determine
which one of the mutually exclusive alternatives is preferred and, consequently,
how much capital should be invested.
In this report we explained the ways of comparing alternatives, and showed a
solved example to better explain.

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REFERENCES
“Engineering Economics: Financial Decision Making for Engineers” by Elizabeth
M. Jewkes and Niall M. Fraser, fifth edition, 2012
https://www.coursehero.com/file/28815257/Alternativespdf/
https://slideplayer.com/slide/5011480/
https://www.academia.edu/9319979/ENGINEERING_ECONOMICS
https://slideplayer.com/slide/12033639/
https://webpages.uidaho.edu/rnielsen/ce215/Fall2003/EngrEcon%20Examples/Co
mparing%20Alternatives.pdf
https://www.webpages.uidaho.edu/~mlowry/Teaching/EngineeringEconomy/Suppl
emental/FE_Ch._53.pdf