Engineering Finance
By Paul A. Jensen

Mechanical Engineering Department
Operations Research/Industrial Engineering Group
pjensen@mail.utexas.edu

This is a three day review of the topics given in the course Engineering Finance. To see the complete course, click on the title in the banner at the top of the page. To see a list of the lessons, click on the word Lessons in the banner. The presentation uses various media for the materials. Click the icon below to show the media and find out where you can get the latest players.

 Media

Generally, when you see a form like the one above as for the Media link, click on the graphic at the left of the title to open the material in a separate window. You can move the window around for better viewing. Click the close button when you are finished.

This review is presented by days, assuming a one hour lecture in each day.

Day 1: The Time Value of Money

The following presentations are used in the first day of the review to introduce the subject and to present the basic tools of engineering financial analysis. The materials draw from the lessons used in the course. Click the Quicktime symbol to view the presentation.

 Introduction
 Equivalency Factors

Use the Factor Calculator to solve the example problems.

 Factor Calculator

The materials below show information drawn from the lessons of the course. Some of the movies have audio.

Click the link on the title above to open the lesson. Use the back button to return to this review.

A characteristic common to most projects is that they involve money and, as the course title suggests, money is emphasized in this course. The life-cycle-cost (LCC) diagram shown below indicates that decisions made early in the project commit expenditures much earlier than they actually occur. Thus, estimation of the costs made for the purposes of decision making are very important. Revenues are not shown in the diagram, but they are equally important in the decision to accept or reject a project solution and also merit careful estimation.

Many projects are complete at the end of the production or construction phase and do not include the remaining parts of operation and retirement. Examples are the construction of a building, the design and construction of the prototype for an airplane, or the design and installation of a production line. The organization entrusted with the project may only be concerned about those aspects leading through the completion of the design, construction or installation. In this case we call the estimation process capital budgeting and the costs involved are called the capital costs.

In other cases the organization sponsoring a project may be the ultimate users of the building, design or production line. Although the cost of acquisition may be a large and important element, the majority of costs occur after acquisition and during operation. The purpose of some projects is to yield a profit or obtain savings in operating costs. For these projects the entire life cycle must be considered and we must estimate the life-cycle costs. We use the term costs primarily, because many projects must meet some functional goal. The revenues are not relevant as long as the project meets the goal. For other cases revenue is important and must be included in a life-cycle analysis.

A system is born, it lives and then it dies. Each phase of the project's life contributes to the project cost and has different requirements for cost estimation. Click on the icon to see a presentation.

 Phases of the Life Cycle

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.

 Growth with 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. Our 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. We use them to evaluate and compare alternative solutions. Factors are also useful for computing quantities related to loans and investments. Use the Factor Calculator to solve the example problems.

 Factor Calculator

We use the Simple Time Value questions in the presentation. Click the Q icon to open the questions.

 Simple Time Value

Click the Quicktime symbol to see the presentation.

 Equivalence Factors

Factors move money around. The factors used in this course and their purposes are listed below.

 Factor Purpose (F/P, i, N) Moves a single payment to N periods later in time (P/F, i, N) Moves a single payment to N periods earlier in time (A/F,i, N) Takes a single payment and spreads into a uniform series over N earlier periods. The last payment in the series occurs at the same time as F. (F/A, i, N) Takes a uniform series and moves it to a single value at the time of the last payment in the series. (A/P, i, N) Takes a single payment and spreads it into a uniform series over N later periods. The first payment in the series occurs one period later than P. (P/A, i, N) Takes a uniform series and moves it to a single payment one period earlier than the first payment of the series. (P/G, i, N) Takes an arithmetic gradient series and moves it to a single payment two periods earlier than the first nonzero payment of the series. (A/G, i, N) Takes an arithmetic gradient series and converts it to a uniform series. The two series cover the same interval, but the first payment of the gradient series is 0.

Traditional textbooks evaluate equivalence factors with Factor Tables. These give the values of the factors for selected interest rates and selected periods. In the class we require the tables for hand calculations during closed book examinations, so learn to use them. Instructions for using the tables are in the Computations section of this site. Click the icon for a list of interest rates. Clicking a rate will open a PDF document with values for the factors.

 Factor Tables

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.

 Limit Values for Factors

Application of a single factor can answer a variety of interesting questions. Review the Simple Time Value problems given in Lesson 10.

 Simple Time Value

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.

These problems show some simple practical situations that are solved by finding the present or annual worth.

 Time Value of Money

Day 2: Evaluation

Click the Quicktime symbol to view the presentation.

 Evaluation

The Economics add-in provides convenient tools for defining and evaluating projects. Click the icon to see a Quicktime movie of the process of defining a project. The movie has no audio.

If you have trouble with the add-in, see the additional instructions on this site.

The materials below show information drawn from the lessons of the course. Some of the movies have audio.

Consider this hypothetical situation. Brother is chronically short of cash and approaches sister with the following deal. Brother says "Hi sis. I need \$300 for a while. If you loan me \$300, I'll pay you back \$30 a month for the next year." How should sister respond?

She might wonder about brother's reliability for repayment, but again we neglect uncertainty in our analysis. We return to consider decision making with risk later.

She might be concerned about mother's reaction. Mother doesn't like sister to make money from brother, and she is more generally concerned about the morality of charging interest for loans. Again we put politics, morality and other issues aside. This is not to say money is the most important issue, but sister wants to be well aware of the economics of the situation. She might adjust her decision later to keep family peace.

Although our example is personal, it is representative of decisions that are made every day in corporate and government settings. In this section we will see how the time value of money models considered earlier can be used to provide a single objective measure with which projects can be evaluated. Once we have the measure, we will be able to answer whether to invest in a project or not. We will actually develop three equivalent measures: present worth, uniform worth and rate of return. Any one can be applied to a project and all give the same answer. We also investigate the payback measure that is widely used in practice. Later, we adjust the models to accommodate taxes and inflation. Both issues are important for the analysis of multiyear projects.

The methods of this section are used throughout the remainder of the course. In the section on Comparison of Alternatives the methods are adapted to the comparison of alternative solutions to a given problem. In the section on Risk we show how the measures are used when uncertainty is explicitly recognized. The methods will also be used for in the Project Management section.

This section is important to engineers. Projects proposed by engineers require the investment of capital funds, and the investment must be repaid with future revenues from sales or savings in operating costs. It is common corporate practice to require the engineer to justify the investment objectively and quantitatively. The methods of this section are often employed.

Click the Quicktime symbol to view an introductory presentation.

 Decision Making

Before going on, answer for yourself the question faced by sister. Should she accept brother's offer? Also answer the question: is this a good deal for the brother? The answers are on the bottom of this page.

The most common measure used to determine the acceptability of an investment is the net present worth (NPW). Click the Quicktime symbol to see the presentation. We use sister's decision problem to illustrate the NPW method for making investment decisions. Should sister make the investment in brother?

 Sister’s Dilemma

To keep our bullets simple, we state the main points of the lecture in terms of investments. This is our emphasis for most of the course.

 The present worth method computes the NPW of the cash flow using the investor's MARR. If the NPW ≥ 0, accept the investment. Otherwise, reject the investment.

Brother has a decision similar to sister, but his is a borrowing situation. Should brother accept the loan from sister? Click the icon to see.

 Brother’s Plight

The method also helps in decisions related to loans.

 For a borrowing situation, the present worth method computes the NPW of the cash flow using the borrower's MARB. If the NPW ≥ 0, accept the loan. Otherwise, reject the loan.

The NPW method can be used in a variety of contexts. The next very short presentation summarizes the present worth method for making decisions.

 The NPW Method

There are extensive instructions for the Economics add-in at the OM/IE sit . Click the icon below to go to the instructions.

Some simple problems are illustrated below.

 Economic Decisions
Day 3: Comparisons

Click the Quicktime symbol to view the presentation.

 Project Comparison

Click the icon to see a Quicktime movie describing how to compare projects with the Economics add-in. The movie has no audio.

Click the icon to see a Quicktime movie describing how to evaluate projects with the inflation. The movie has no audio.

The materials below show information drawn from the lessons of the course. Some of the movies have audio.

This lesson extends the present worth and annual worth evaluation methods to the comparison of alternative solutions. The 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 Net Present Worth 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.

Click the Quicktime symbol to see how to use the present worth method when the alternatives have the same lives.

 NPW Comparison

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 least-common-multiple of the lives. Replacements during the study period are like-for-like.

 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.

Click the Quicktime symbol to see how to use the present worth method when the alternatives have the different lives.

 Different 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 like-for-like 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 Net Annual Worth Method compute the equivalent uniform annual worth of the cash flows for the alternatives and choose the best.

Click the Quicktime symbol to see how to use the net annual worth for comparisons.

 NAW Comparison

Try the problems to test your skills. Don't look at the answers unless you solve the problem by yourself.

 Comparison Problems
 Homework

 Homework

Engineering Finance
by Paul A. Jensen