Review
This is a review for the second exam. The purpose is to summarize the
contents of lessons 9  16, which contain the material that we have studied since the first exam. You should also review
the event and homework keys on the class Canvas site.
A final suggestion is to visit the
Presentations section that can be found under the Resources tab. There, the QuickTime movies are listed in order for easy viewing. For the example problem in this lesson, use the calculators
in the Toolbox to find the solutions.


Goals 

Each lesson in the section has a collection
of goals. Most of them describe an activity that you should understand
and be able to perform. The paragraphs below describe the purpose
of each lesson. Click the bush icon to see the goals of the individual
lessons.


9. Time
Value of Money
The lesson describes how compounding, time and interest
rate are used to express an amount of money at one
point in time as an equivalent amount at another. These
ideas are central to the procedures used to economically
evaluate and compare project solutions.

10. Equivalence
Factors
The subjects of Engineering Economics and Business
Finance traditionally use equivalence factors to
express a complicated cash flow as a single equivalent
number. This lesson introduces these factors and shows
how they can be used to answer a variety of interesting
business and personal finance questions.

11. Net
Worth
For investment analysis, common economic
measures are the net present worth and net
annual worth of a cash flow. This lesson shows
how these measures are computed using the equivalence
factors.

12. Selection
To accept or not accept is the question
posed for project selection. This lesson shows that
the answer depends on the investor's minimum acceptable
rate of return (MARR). The lesson provides a simple
rule to make the decision.

13. Comparisons
with Net Worth
This lesson uses the present and annual worth criteria for selection between
mutually exclusive alternatives. Both methods yield the same selection, but we
will see that there are important differences in application and interpretation.

14. Rate
of Return
The rate of return discussed
in this lesson gives the same answers as the net worth
methods, but it is more familiar to most decision makers.
The lesson shows how to calculate the internal
rate of return (IRR) for a cash flow and how it
is used to make selection decisions.

15. Comparisons with Rate
of Return
This lesson explores the rate of return method for
comparing alternatives. We learn the important principle
that the rate of return method must be applied to
increments of investment rather than directly to
the individual alternatives.

16. Inflation
Inflation of costs and revenues is inevitable
in modern economies, measurabley complicating economic decision
making. Although the present worth, annual worth, and
rate of return methods can be used when the effects
of inflation are included, this lesson shows how the
methods must be adjusted.




Exam Format 

This midterm exam will be administered during the regular
class meetings. The exam will have both closed and open book
parts. The closedbook part will be distributed first. When you
turn in the closedbook part, you will receive the openbook
part. No strict time limit is enforced for the completion of
the closed bookpart, but leave at least one hour for the openbook
part. The openbook part must be submitted by the end of the
class meeting. You will have 1.75 hours to complete both parts.
Closed Book 
The closedbook part will
have questions about conceptual topics. The homework
and example problems presented throughout the lessons
have many questions that start with "Write
the formula ..." You should be able to use the equivalence
factors in formulas for the NPW and NAW. You should be
able to write the formulas that can be solved for the
IRR. You should know the concepts introduced in all the
lessons including the concept of incremental analysis
for rate of return comparisons.
The closedbook exam will not require extensive
computations. You may use personal calculators when necessary,
but no other materials are allowed.
The closedbook part might ask you to replicate the
computations of the Economics addin. One
example is illustrated below. You should know all about
the cells on this form. For example, you might be
asked to write the formulas for the cells in the factor
column. You should also know the meaning and use of
the forms that include inflation, although you will
be not be asked to write the formulas of the factors
considering inflation.

Open Book 
For the openbook part, you may use calculators, computers, Excel, the
ME353 website, the Excel addins and the course textbook.
You may not use cell phones, iPads, the Canvas site or open files such as homework and event keys, and summary sheets prepared
before the exam. Any device not mentioned is not permitted. The exam will be presented on paper
and space will be provided for your answers.
To receive credit you must answer the questions on the
paper form.
You will be able to submit an Excel workbook through
Canvas when you are finished with the exam. Your answers must be supported by calculations in the uploaded file, especially if only partial credit is in order.
Problems will be similar to those given in the events
and homework. Be able to use the Economics addin for
problems with and without inflation. 


Text 

Chapter 3 in the textbook covers
most of the topics for this exam.


3.13.5: Engineering
Economic Analysis 




Click the link on the title above to open the
lesson. Use the back button to return to this review.
This is an introductory lesson to show how money
grows with interest. Review the flash movie to see how interest
affects growth and the difference between simple and compound
interest.
The lesson also introduces discounting as the inverse
of compounding. Be sure you know what both mean. Be able to say
why invested money grows even if there were no inflation. 

Equivalence factors move money around. The purpose
for doing that is to replace a complex cash flow with a single
equivalent. With a single measure, solutions can be judged for
economic acceptability. In the next section we use them to compare
alternative solutions. Factors are also useful for computing
quantities related to loans and investments.
Review the formulas that define the equivalence
factors. The factors are derived for endofperiod payments.
You don't have to know these formulas but be aware of the timing
of the cash flows assumed for each factor.
When the interest rate is zero, the single value
factors simply compute the sum of the amounts in the cash flow.
The distribution factors such as A/P or A/F divide a single value
by the number of payments. When the number of periods goes to
infinity, some of the factors have limiting values. Review the
limit values of the factors.
The normal compounding period is one year, but
when there are several compounding periods in a year, it is often
necessary to compute the effective rate.


Effective
Interest Formulas



The payments and payoff values for installment
loans can be computed with simple applications of equivalence
factors. For loans, the interest rate, number of periods, initial
principal and the amount of payment are well defined. Given any
three of these quantities, the other can be determined. Review
the use of the formulas for loans.
Application of a single factor can answer a variety
of interesting questions. Review the Simple Time Value problems
given in Lesson 10.


In Lesson 11 we use the equivalence
factors to find the net present worth and net annual worth of
given cash flows. For simple problems this course adopts the
goal of using the fewest time value of money factors as possible
to express the present or annual worth. This involves moving
money around. Review the Flash movie to see some examples.
The cash flow exercises show more examples including
some with periodic payments. Answer the questions and use the
scorecard and the answer key to see how you did.
These problems show some simple
practical situations that are solved by finding the present or
annual worth.


Lesson 12 applies the equivalence factors to decision making
with the goal of deciding whether to accept or reject the cash
flow for a particular solution. Of primary importance are are
the minimum
acceptable rate of return (MARR) for an investment situation
and the maximum acceptable rate of borrowing (MARB)
for a borrowing situation. We primarily focus on investments because
these are most often required for engineering projects.
Some simple problems are illustrated below.


This lesson extends the present worth and annual
worth evaluation methods to the comparison of alternative solutions.
When extension is simple when the lives are equal. The best alternative
is the one with the greatest NPW value. This assumes revenues
are positive and costs are negative.

For
the NPW method, compute the net present
worth of the cash flows for the alternatives and
choose the best. Be careful when the lives of the
alternatives are not equal. 

When the alternatives have different lives, a study
period must be selected. A present worth comparison is meaningless
unless the time represented by the present worth is the same
for all alternatives. There are several ways to choose a study
period, but we usually use the leastcommonmultiple of the lives.
Replacements during the study period are likeforlike.

When
the alternatives have different lives, they must
be compared over a common study period. It is common
to choose the least common multiple of the lives. 

With the annual worth method, NAW values can be
compared. Although it is not necessary to select a study period,
the implicit assumption is the likeforlike replacements over
the least common multiple of the lives. This makes the NAW method
easier for comparisons with different lives. NPW and NAW comparisons
always result in the same selection.

For
the NAW method, compute the equivalent
uniform annual worth of the cash flows for the alternatives
and choose the best. 

Try the problems to test your skills. Don't look
at the answers until you have tried to solve the problem by yourself.
The following link opens shortanswer questions regarding the
use of the present and annual worth measures.
The Economics addin is
easy to use and is one of the tools available for openbook
exams. For a review of the addin basics without audio, click
on the QuickTime icon.


For lesson 14 we provide a new measure
called the rate of return of the investment or the internal
rate of return (IRR). This value is computed by solving for the interest
rate that makes the NPW or NAW equal to zero.
Click the QuickTime symbol to see the
introductory presentation for rate of return comparisons.

The IRR is the interest rate
for which the NPW (or NAW) calculated with the IRR
is exactly 0.
If the IRR ≥ MARR, accept
the investment; otherwise, reject it.


It is good to be able to recognize the simple cases for the
IRR calculations. These will often save time over the alternative
of trial and error.
Students should
be able to demonstrate the trial and error approach
for finding the IRR. This approach is not too difficult for
a simple investment since the NPW is a decreasing function of i.
When searching for the solution if one computes a positive NPW
for some i, the IRR must be greater than i.
If one computes a negative NPW, the IRR must be smaller than i.
The IRR search process seeks two different interest rates,
one with a positive NPW and one with a negative NPW. The IRR
estimate is found with linear interpolation by computing the approximate
zerocrossing point. When
demonstrating trial and error the student cannot use an automatic
numerical solver such as the one built into Excel or implemented
into the Economics addin.
For simple investments (with positive profit) there is a single
solution for IRR. For mixed (or nonsimple) investments there
may be more than one solution. A second measure called return
on invested capital (RIC) provides a single solution for
all problems, so it can be used for decision making.
The problems illustrate some ROR problems.


This lesson considers the project selection problem
and the comparison of alternatives problem. They are quite different
in both statement and solution, but both use the IRR as a measure.
The project selection problem chooses a subset
of the projects from a proposed set. For this problem compute
the IRR for each alternative.

An
organization has a set proposed projects from which
some subset must be chosen. The IRR provides a measure
for project selection. 

When the MARR is given, all projects with IRR greater
than the MARR are acceptable. The solution assumes there is no
budget limit for capital expenditures.

With
a given MARR and no budget restriction, select the
projects that have IRR ≥ MARR 

When there is a budget limit, use the selection
rule below.

With
restricted budget, rank the projects by IRR and in
order of the ranking choose the largest subset that
does not exceed the budget. 

The rate of return method can also be used to select
one solution from a set of mutually exclusive alternatives. Be
sure to learn the incremental method. Generally, it is not necessary
to calculate the IRR values for the individual alternatives.
You must calculate the IRR for increments of investment. For
examinations, you must follow the procedure completely in order
to receive full credit.

To choose among mutually exclusive
alternatives, you must use incremental analysis.
The IRR of each increment of investment must satisfy
the MARR requirement.


Try solving the problems with calculators in the
toolbox before looking at the answers.
The following link opens shortanswer questions regarding the
use of the rate of return method for evaluation and comparison.


Inflation complicates the evaluation
of projects because dollars at different times have different
buying power. This lesson introduces the language associated
with inflation and provides tools for evaluating solutions.
With inflation there are two kinds of dollars, actual dollars
and real dollars. There are also two values for the
MARR. The market MARR evaluates cash flows expressed
in actual dollars. The real MARR evaluates cash flows
expressed in real dollars. Cost or revenue estimates are expressed in today's prices. Escalation rates convert the estimates
to actual dollars. The linked formulas calculate the economic
measures for both real and actual dollars.


Economic
Analysis Formulas



Because NPW is the equivalent at time zero, the value
is the same whether the evaluation comes from real or actual
dollars.

When
the cash flow is in actual dollars use the market
MARR to find the NPW. When the cash flow is in real
dollars use the real MARR to find the NPW. The NPW
values computed with the two methods are the same.


When component escalation rates are the same as
the rate of general inflation, it is not necessary to change
the estimates to actual dollars. Use the estimated cash flow
and the real MARR to compute the NPW. This makes it easier to
solve some problems.

When
the escalation rates of all cash flow components
are the same as general inflation, the estimated
cash flow is the same as the real cash flow. Do not
adjust it for inflation, but use the real MARR to
find the NPW.


When inflation is present, comparison of alternatives
may be more complex. When using the NPW method evaluate each
alternative as indicated above and choose the best. For the NAW
method, use real NAW values to compare the alternatives.
For the ROR method, use incremental analysis. When
the cash flow is expressed in real dollars, the IRR is a real
rate of return. When the cash flow is expressed in actual dollars,
the IRR is a market rate of return. When making decisions to
accept or reject incremental investments, be sure to compare
the IRR with the correct type of MARR. Real IRR values compare
to the real MARR. Market IRR values compare to the market MARR.
The link opens shortanswer questions regarding
the analysis of the effects of inflation.
For a review
of the Economics addin for problems with
inflation, click on the QuickTime icon. This movie has no audio.


Economics
addin with Inflation 




Summary 



Project
Evaluation Summary 



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