Engineering Economics - Terminology and Symbols

 The equations and procedures of engineering economy utilize the following terms and symbols.
Sample units are indicated.

     P   =   value or amount of money at a time designated as the present or time 0. Also P   is referred to as present worth (PW), present value (PV), net present value (NPV), discounted cash fl  ow (DCF), and capitalized cost (CC); monetary units, such as dollars
     F   =   value or amount of money at some future time. Also   F  is called future worth (FW)  and future value (FV); dollars
     A   =   series of consecutive, equal, end-of-period amounts of money. Also A is called the annual worth (AW) and equivalent uniform annual worth (EUAW); dollars per year, euros per month

     n   =   number of interest periods; years, months, days
     i    =   interest rate per time period; percent per year, percent per month
     t   =    time, stated in periods; years, months, days

The symbols P and F represent one-time occurrences:  A occurs with the same value in each inter- est period for a specifi ed number of periods. It should be clear that a present value   P  represents a  single sum of money at some time prior to a future value   F  or prior to the fi rst occurrence of an  equivalent series amount A .

It is important to note that the symbol   A  always represents a uniform amount (i.e., the same
amount each period) that extends through   consecutive  interest periods. Both conditions must  exist before the series can be represented by   A .

The interest rate   i  is expressed in percent per interest period, for example, 12% per year. Un- less stated otherwise, assume that the rate applies throughout the entire   n  years or interest periods. The decimal equivalent for  i  is always used in formulas and equations in engineering econ- omy computations.

All engineering economy problems involve the element of time expressed as   n  and interest  rate   i . In general, every problem will involve at least four of the symbols   P , F , A , n , and  i , with at  least three of them estimated or known.

Additional symbols used in engineering economy are defi ned in Appendix E

EXAMPLE 1.6

Today, Julie borrowed $5000 to purchase furniture for her new house. She can repay the loan  in either of the two ways described below. Determine the engineering economy symbols and  their value for each option.

  (a)    Five equal annual installments with interest based on 5% per year.
  (b)    One payment 3 years from now with interest based on 7% per year.
 
Solution

  (a)    The repayment schedule requires an equivalent annual amount   A , which is unknown.
  P = $5000       i =5% per year         n = 5 years      A = ?
  (b)    Repayment requires a single future amount F, which is unknown.
  P = $5000       i = 7% per year        n = 3 years      F =  ? 

EXAMPLE 1.7

You plan to make a lump-sum deposit of $5000 now into an investment account that pays 6% per year, and you plan to withdraw an equal end-of-year amount of $1000 for 5 years, starting  next year. At the end of the sixth year, you plan to close your account by withdrawing the re- maining money. Defi ne the engineering economy symbols involved.
 
Solution

All  five symbols are present, but the future value in year 6 is the unknown.

P = $5000
A = $1000 per year for 5 years
F = ? at end of year 6
i = 6% per year
n = 5 years for the   A  series and 6 for the   F  value

EXAMPLE 1.8

Last year Jane’s grandmother offered to put enough money into a savings account to generate $5000 in interest this year to help pay Jane’s expenses at college. (a) Identify the symbols, and (b) calculate the amount that had to be deposited exactly 1 year ago to earn $5000 in interest now, if the rate of return is 6% per year.

Performing an Engineering Economy Study

An engineering economy study involves many elements: problem identifi  cation, defi  nition of the objective, cash flow estimation, fi nancial analysis, and decision making. Implementing a structured procedure is the best approach to select the best solution to the problem.

The steps in an engineering economy study are as follows:

1.    Identify and understand the problem; identify the objective of the project. 
2.    Collect relevant, available data and defi ne viable solution alternatives. 
3.    Make realistic cash fl  ow estimates. 
4.    Identify an economic measure of worth criterion for decision making.
5.    Evaluate each alternative; consider noneconomic factors; use sensitivity analysis as needed. 
6.    Select the best alternative. 
7.    Implement the solution and monitor the results.   

  Figure 1–1  Steps in an engineering economy study.

Technically, the last step is not part of the economy study, but it is, of course, a step needed to meet the project objective. There may be occasions when the best economic alternative  requires more capital funds than are available, or signifi cant noneconomic factors preclude the  most economic alternative from being chosen. Accordingly, steps 5 and 6 may result in selection of an alternative different from the economically best one. Also, sometimes more than one project may be selected and implemented. This occurs when projects are independent of one another. In this case, steps 5 through 7 vary from those above.  Figure 1–1  illustrates the steps above for one alternative. Descriptions of several of the elements in the steps are important to understand.
      
Problem Description and Objective Statement A succinct statement of the problem and  primary objective(s) is very important to the formation of an alternative solution. As an illustration, assume the problem is that a coal-fueled power plant must be shut down by 2015 due to the  production of excessive sulfur dioxide. The objectives may be to generate the forecasted  electricity needed for 2015 and beyond, plus to not exceed all the projected emission allowances in these future years. 

Alternatives These are stand-alone descriptions of viable solutions to problems that can meet the objectives. Words, pictures, graphs, equipment and service descriptions, simulations, etc.  define each alternative. The best estimates for parameters are also part of the alternative. Some parameters include equipment first cost, expected life, salvage value (estimated trade-in, resale, or market value), and annual operating cost (AOC), which can also be termed   maintenance and operating  (M&O)   cost,  and subcontract cost for specifi c services. If changes in income (revenue) may occur, this parameter must be estimated.

Detailing all viable alternatives at this stage is crucial. For example, if two alternatives are described and analyzed, one will likely be selected and implementation initiated. If a third, more attractive method that was available is later recognized, a wrong decision was made. 

Cash Flows All  cash  flows are estimated for each alternative. Since these are future expenditures and revenues, the results of step 3 usually prove to be inaccurate when an alternative is actually in place and operating. When cash fl ow estimates for specifi c parameters are expected to vary significantly from a   point estimate  made now, risk and sensitivity analyses (step 5) are needed to improve the chances of selecting the best alternative. Sizable variation is usually expected in estimates of revenues, AOC, salvage values, and subcontractor costs.

Engineering Economy Analysis The techniques and computations that you will learn and use throughout this text utilize the cash fl ow estimates, time value of money, and a selected measure of worth. The result of the analysis will be one or more numerical values; this can be  in one of several terms, such as money, an interest rate, number of years, or a probability. In the end, a selected measure of worth mentioned in the previous section will be used to select the best alternative.

Before an economic analysis technique is applied to the cash fl ows, some decisions about what to include in the analysis must be made. Two important possibilities are taxes and inflation. Federal, state or provincial, county, and city taxes will impact the costs of every alternative. An after-tax analysis includes some additional estimates and methods compared to a  before-tax a nalysis. If taxes and infl ation are expected to impact all alternatives equally, they  may be disregarded in the analysis. However, if the size of these projected costs is important,  taxes and infl ation should be considered. Also, if the impact of infl ation over time is important  to the decision, an additional set of computations must be added to the analysis.

Selection of the Best Alternative The measure of worth is a primary basis for selecting the best economic alternative. For example, if alternative A has a rate of return (ROR) of  15.2% per year and alternative B will result in an ROR of 16.9% per year, B is better economically. However, there can always be   noneconomic or intangible factors  that must be  considered and that may alter the decision. There are many possible noneconomic factors;  some typical ones are

   •     Market pressures, such as need for an increased international presence 
   •     Availability of certain resources, e.g., skilled labor force, water, power, tax incentives 
   •     Government laws that dictate safety, environmental, legal, or other aspects 
   •     Corporate management’s or the board of director’s interest in a particular alternative 
   •     Goodwill offered by an alternative toward a group: employees, union, county, etc.   

As indicated in  Figure 1–1 , once all the economic, noneconomic, and risk factors have been  evaluated, a final decision of the “best” alternative is made.

At times, only one viable alternative is identifi ed. In this case, the   do-nothing (DN) alternative  may be chosen provided the measure of worth and other factors result in the alternative being  a poor choice. The do-nothing alternative maintains the status quo.

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? Obvi- ously, depending upon which criterion or combination of criteria is used to identify the best, a different route might be selected each time. In economic analysis,   fi  nancial units (dollars or  other currency)  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.

Engineering Economics: Description and Role in Decision Making

Decisions are made routinely to choose one alternative over another by individuals in everyday life; by engineers on the job; by managers who supervise the activities of others; by corporate  presidents who operate a business; and by government offi cials who work for the public good.  Most decisions involve money, called   capital  or   capital funds , which is usually limited in  amount. The decision of where and how to invest this limited capital is motivated by a primary goal of   adding value  as future, anticipated results of the selected alternative are realized.

Engineers play a vital role in capital investment decisions based upon their ability and experience  to design, analyze, and synthesize. The factors upon which a decision is based are commonly a  combination of economic and noneconomic elements. Engineering economy deals with the economic factors. By defi  nition,
 
Engineering economy involves formulating, estimating, and evaluating the expected economic  outcomes of alternatives designed to accomplish a defi ned purpose. Mathematical techniques  simplify the economic evaluation of alternatives. 

Because the formulas and techniques used in engineering economics are applicable to all  types of money matters, they are equally useful in business and government, as well as for  individuals.   Therefore, besides applications to projects in your future jobs, what you learn  from this book and in this course may well offer you an economic analysis tool for making  personal decisions such as car purchases, house purchases, major purchases on credit, e.g.,  furniture, appliances, and electronics.

Other terms that mean the same as engineering economy  are   engineering economic analysis,  capital allocation study, economic analysis, and similar descriptors.

People make decisions; computers, mathematics, concepts, and guidelines assist people in  their decision-making process. Since most decisions affect what will be done, the time frame of  engineering economy is primarily the   future . Therefore, the numbers used in engineering econ- omy are   best estimates of what is expected to occur . The estimates and the decision usually  involve four essential elements:

  Cash flows 
  Times of occurrence of cash fl  ows
  Interest rates for time value of money
  Measure of economic worth for selecting an alternative

Since the estimates of cash fl ow amounts and timing are about the future, they will be some-what different than what is actually observed, due to changing circumstances and unplanned  events. In short, the variation between an amount or time estimated now and that observed  in the future is caused by the stochastic (random) nature of all economic events.   Sensitivity  analysis  is utilized to determine how a decision might change according to varying esti- mates, especially those expected to vary widely. Example 1.1 illustrates the fundamental  nature of variation in estimates and how this variation may be included in the analysis at a  very basic level.

EXAMPLE 1.1

An engineer is performing an analysis of warranty costs for drive train repairs within the first  year of ownership of luxury cars purchased in the United States. He found the average cost (to  the nearest dollar) to be $570 per repair from data taken over a 5-year period.

What range of repair costs should the engineer use to ensure that the analysis is sensitive to changing warranty costs?

Solution

At  first glance the range should be approximately –25% to +15% of the $570 average cost to  include the low of $430 and high of $650. However, the last 3 years of costs are higher and  more consistent with an average of $631. The observed values are approximately ±3% of this  more recent average.

If the analysis is to use the most recent data and trends, a range of, say, ±5% of $630 is recom- mended. If, however, the analysis is to be more inclusive of historical data and trends, a range  of, say, ±20% or ±25% of $570 is recommended.

The criterion used to select an alternative in engineering economy for a specifi c set of estimates  is called a   measure of worth . The measures developed and used in this text are

All these measures of worth account for the fact that money makes money over time. This is the  concept of the   time value of money.  

It is a well-known fact that money   makes  money. The time value of money explains the change  in the amount of money   over time  for funds that are owned (invested) or owed (borrowed). This is the most important concept in engineering economy.
       
The time value of money is very obvious in the world of economics. If we decide to invest  capital (money) in a project today, we inherently expect to have more money in the future than  we invested. If we borrow money today, in one form or another, we expect to return the original  amount plus some additional amount of money.
 
Engineering economics is equally well suited for the future and for the   analysis of past cash
flows  in order to determine if a specifi c criterion (measure of worth) was attained. For example,  assume you invested $4975 exactly 3 years ago in 53 shares of IBM stock as traded on the New  York Stock Exchange (NYSE) at $93.86 per share. You expect to make 8% per year appreciation,  not considering any dividends that IBM may declare. A quick check of the share value shows it  is currently worth $127.25 per share for a total of $6744.25. This increase in value represents a  rate of return of 10.67% per year. (These type of calculations are explained later.) This past  investment has well exceeded the 8% per year criterion over the last 3 years.