EGR 312 Notes PDF

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Proffessor W. H. Shaw...

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Excel

Using the symbols P , F , A , i , and n defined in the previous section, the functions most used in engineering economic analysis are formulated as follows.

If some of the parameters don’t apply to a particular problem, they can be omitted and zero is assumed. To understand how the spreadsheet functions work, look back at Example 1.6 a , where the equivalent annual amount A is unknown, as indicated by A ?. The following example demonstrates the use of a spreadsheet to develop relations (not built-in functions) to calculate interest and cash fl ows.

Practice

Chapter 1

Terms: - Most decisions involve money, which is usually limited in amount. - The decision of where and how to invest this limited capital is motivated by a primary as future, anticipated results of the selected alternative are realized. nvolves 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. Other terms that mean the same as engineering economy are engineering economic analysis,

descriptors. It is a well-known fact that ey makes money. The time e 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 frame of engineering economy is p Therefore, the numbers used in engineering economy are best estimates of r . The estimates and the decision usuall involve four essential elements: ws

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 - Present worth (PW) - Future worth (FW) - Annual worth (AW) - Rate of return (ROR) - Benefi t/cost (B/C) - Capitalized cost (CC) - Payback period Economic value added (EVA) - Cost Effectiveness

The time value of money is very obvious in the world of economics. 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. 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 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. Words, pictures, graphs, equipment and service descriptions, simulations, etc. define each alternative. . Some parameters include d 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

All cash fl ows are estimated for each alternative. g. When cash fl ow estimates for specifi c parameters are expected to vary signifi cantly from a point estimate made now, risk and sensitivity analyses (step 5) are needed to improve the chances of selecting the best alternative.

s: . 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. Two important possibilities are taxes and infl ation. 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,

However, there can always be at There are many possible noneconomic factors; some typical ones are • such as need for an increased international presence • tain resources, e.g., skilled labor force, water, power, tax incentives • y, environmental, legal, or other aspects • • employees, union, county, etc.

the

may be chosen provided the measure of worth and other factors result in The do-nothing alternative

The different interpretations. Morals usually relate to the n ight and wrong. an be evaluated by using a that forms the standards to g and organizations in a profession, These are

e

hese are the These usually parallel the common morals in that stealing, lying, murdering, etc. are immoral acts. n a specifi c discipline are guided in their decision making and performance of work activities by a formal standard or code. The code states the commonly accepted standards of honesty and integrity that each individual is expected to demonstrate in her or his practice. T s. Although each engineering profession has its own code of ethics Here are three examples from the Code: “ ” (section I.1) from material or equipment suppliers for specifying their product.” (section III.5.a) “

y

(section III.9.b) • Safety factors are compromised to ensure that a price bid comes in as low as possible. •F with individuals in a company offer unfair or insider information that allows costs to be cut in strategic areas of a project. for company-specifi c equipment, and the design engineer does not have suffi cient time to determine if this equipment will meet the needs of the project being designed and costed.

• tenance can be performed to save money when cost overruns exist in other segments of a project. parts can save money for a subcontractor working on a fi xed-price contract. e of cost, personal inconvenience to workers, tight time schedules, etc.

When an engineering economy study is performed, it is important for the engineer performing the study to consider all ethically related matters to ensure that the cost and revenue estimates refl ect what is likely to happen once the project or system is operating.

Interest is the manifestation of the time value of money . (obtained a loan) and when

, r

funds (a loan) is determined u

a the principal, the result is called the interest rate. The

called the interest

From the r, interest earned ( he final amount minus the initial amount, or principal.

expressed as a percentage of the original amount and is called The otal amount now - principal

ation are warranted at this early stage

just as for the borrower’s perspective. Again, the most common period is 1 year. The term OI) is used in different industries and settings, especially where large capital funds are committed to engineering-oriented programs. , some comments about the fundamentals of infl , infl ation represents a decrease

In simple terms, i e. The real rate of return allows the investor to purchase more than he or she could have purchased before the investment, while infl ation raises the real rate to the market rate that we use on a daily basis.

uces the real rate of return on the investment. n means that This increase is , thus making a unit of currency (such as the dollar) worth less relative to its value at a previous time. We see the effect of infl ation in that money purchases less now than it did at a previous time. urrency onsumer price index) t of equipment and its maintenance salaried professionals and hourly employees •A The equations and procedures of engineering economy utilize the following terms and symbols. Sample units are indicated. value o 0. Also P is referred to a , 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 f nd 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 interest rate per time period; percent per year, percent per month t time, stated in periods; years, months, days

.e., the same amount each period) that extends through consecutive interest periods. Engineering economy bases its computations on the timing, size, and direction of cash fl ows.

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activity. A cash outfl ow. When a project involves only costs, the minus sign may be omitted for some techniques, such as benefi t/cost analysis. point estimates, that is, single-value estimates for cash fl ow elements of an alternative, except for the last revenue and cost estimates listed above. They provide a range estimate, because the persons estimating the revenue and cost do not have enough knowledge or experience with the systems to be more accurate.

e NCF is net cash fl ow, R is receipts, and D is disbursements. The end-of-period convention means that all cash infl ows and all cash outfl ows are assumed to take place at the end of the interest period in which they actually occur. s The cash fl ow diagram is a very important tool in an economic analysis, especially when the cash fl ow series is complex. We will use a bold, colored arrow to indicate what is unknown and to be determined sa

ng are based.

Economic equivalence is a combination of interest rate and time value of money to determine the different amounts of money at different points in time that are equal in economic value. T in Section 1.4) are useful in calculating equivalent sums of money for one interest period in the past and one period in the future. is calculated using the principal only, ignoring any interest accrued in preceding rest periods.

e I is the amount of interest earned or paid and the interest rate i is expressed in decimal form. In most fi nancial and economic analyses, we use compound interest calculations. For compound interest, the interest accrued for each interest period is calculated on the principal plus the total amount of interest accumulated in all previous periods. Thus, compound interest means interest on top of interest.

In this case, the total amount due at the end of each year is Year 1: $100,000(1.10) 1 $110,000 Year 2: $100,000(1.10) 2 $121,000 Year 3: $100,000(1.10) 3 $133,100 This allows future totals owed to be calculated directly without intermediate steps. The general form of the equation is

For any i or individual) expects to receive more money than the amount of capital invested. In other words, a fair rate of return, or return on investment, must be realizable T

ar A project is not economically viable unless

it is expected to return at least the MARR. Although the MARR is used as a c needed capital funds. It always costs money in the form of interest to raise capital. The interest, expressed as a percentage rate per year, is called the cost of capital. ng The corporation borrows from outside sources and repays the principal and interest according to some schedule, much like the plans in Table 1–1. Sources of debt capital may be bonds, loans, mortgages, venture capital pools, and many others. Individuals, too, can utilize debt sources, such as the credit card (15% rate) and bank options (9% rate) described above.

n uses its own funds from cash on hand, stock sales, or retained earnings. Individuals can use their own cash, savings, or investments. In the example above, using money from the 5% savings account is equity financing.

a

results

ARR >WACC The pursue a project. Nu

nability to

The functions on a computer spreadsheet can greatly reduce the amount of hand work for equivalency computations involving compound interest and the terms Engineering economy is the application of economic factors and criteria to evaluate alternatives, considering the time value of money Also, we learned a lot about cash fl ows: onvention for cash fl ow location Net cash fl ow computation the cash fl ow sign Construction of a cash fl ow diagram future cash fl ows accurately

The most fundamental factor in engineering economy is the

P (1 + i ) From the for a stated amount F that occurs n periods in the future.

To fi nd F , given P ,

The notation includes two cash fl ow symbols, the interest rate, and the number of periods. It is always in the general for letter X represents what is sought, while the letter Y represents what is given. For example, FP means fi nd F when given P. The i is the interest rate in percent, and n represents the number of periods involved. The equivalent present worth P of a uniform nd-of-period cash fl ows (investments)

The term in brackets in Equation [2.8] is the

(USPWF). It is the PA factor used to calculate the equivalent P value in year 0 for a uniform end-of-period series of A values beginning at the end of period 1 and extending for n periods

The fi rst A value occurs at the end of period 1, that is, one period after P occurs. Solve Equation [2.8] for A to obtain

The term in brackets is called the capital recovery factor (CRF), or AP factor. It calculates the equivalent uniform annual worth A over n years for a given P in year 0, when the interest rate is i.

The term in brackets is called the uniform series compound amount factor (USCAF), or FA factor. When multiplied by the given uniform annual amount A , it yields the future worth of the uniform series. It is important to remember that the future amount F occurs in the same period as the last A .

The PA and AP factors are derived with the present worth P and the fi rst uniform annual amount A one year (period) apart. That is, the present worth P must always be located one period prior to the fi rst A . The expression in brackets in Equation [2.12] is the AF or sinking fund factor. It determines the uniform annual series A that is equivalent to a given future amount F . This is shown graphically in Figure 2–6 a , where A is a uniform annual investment.

The uniform series A begins at the end of year (period) 1 and continues through the year of the given F. The last A value and F occur at the same time.

Often it is necessary to know the correct numerical value of a factor with an i or n value that is not listed in the compound interest tables in the rear of the book. Given specifi c values of i and n , there are several ways to obtain any factor value. • Use the formula listed in this chapter or the front cover of the book, • Use an Excel function with the corresponding P , F , or A value set to 1. • Use linear interpolation in the interest tables. When the formula is applied, the factor value is accurate since the specifi c i and n values are input. However, it is possible to make mistakes since the formulas are similar to each other, especially when uniform series are involved. Additionally, the formulas become more complex when gradients are introduced, as you will see in the following sections Linear interpolation for an untabulated interest rate i or number of years n takes more time to complete than using the formula or spreadsheet function. Also interpolation introduces some level of inaccuracy, depending upon the distance between the two boundary values selected for i or n , as the formulas themselves are nonlinear functions

An arithmetic gradient series is a cash fl ow series that either increases or decreases by a constant amount each period. The amount of change is called the gradient. Formulas previously developed for an A series have year-end amounts of equal value. In the case of a gradient, each year-end cash fl ow is different, so new formulas must be derived. First, assume that the cash fl ow at the end of year 1 is the base amount of the cash fl ow series and, therefore, not part of the gradient series. This is convenient because in actual applications, the base amount is usually signifi cantly different in size compared to the gradient.

G constant arithmetic change in cash fl ows from one time period to the next; G may be positive or negative.

It is important to realize that the base amount defi nes a uniform cash fl ow series of the size A that occurs eash time period. We will use this fact when calculating equivalent amounts that involve arithmetic gradients. If the base amount is ignored, a generalized arithmetic (increasing) gradient cash fl ow diagram is as shown in Figure 2–12. Note that the gradient begins between years 1 and 2. This is called a conventional gradient . The corresponding equivalent annual worth A T is the sum of the base amount series annual worth A A and gradient series annual worth A G , that is,

The total present worth PT for a series that includes a base amount A and conventional arithmetic gradient must consider the present worth of both the uniform series defi ned by A and the arithmetic gradient series. The addition of the two results in P T .

where P A is the present worth of the uniform series only, P G is the present worth of the gradient series only, and the or sign is used for an increasing (G ) or decreasing (G ) gradient, respectively.

Three factors are derived for arithmetic gradients: the PG factor for present worth, the AG factor for annual series, and the FG factor for future worth. There are several ways to derive them. We use the single-payment present worth factor ( PF , i , n ), but the same result can be obtained by using the FP , FA , or PA factor. Equation [2.24] is the general relation to convert an arithmetic gradient G (not including the base amount) for n years into a present worth at year 0 . Figure 2–14 a is converted into the equivalent cash fl ow in Figure 2–14 b . T

Remember: The conventional arithmetic gradient starts in year 2, and P is located in year 0. The equivalent uniform annual series A /G for an arithmetic gradient G is found by multiplying the present worth in Equation [2.26] by the ( A/P , i , n ) formula. In standard notation form, the equivalent of algebraic cancellation of P can be used. AG = G(P/G,i,n)(A/P,i,n) = G(A/G,i,n)

A geometric gradient series is a cash fl ow series that either increases or decreases by a constant percentage each period. The uniform change is called the rate of change. g = constant rate of change , in decimal form, by which cash fl ow values increase or decrease from one period to the next. The gradient g can be or . A1 = initial cash fl ow in year 1 of the geometric series P g = present worth of the entire geometric gradient series, including the initial amount A1 Note that the initial cash fl ow A1 is not considered separately when working with geometric gradients. The relation to determine the total present worth Pg for the entire cash fl ow series may be derived by multiplying each cash fl ow in Figure 2–21 a by the PF factor 1(1 i ) n. The (PA,g,i,n) factor calculates Pg in period t 0 for a geometric gradient series starting in period 1 in the amount A1 and increasing by a constant rate of g each period.

Formulas and factors derived and applied in this chapter perform equivalence calculations for present, future, annual, and gradient cash fl ows. Capability in using these formulas and their standard notation manually and with spreadsheets is critical to complete an engineering economy study. Using these formulas and spreadsheet functions, you can convert single cash fl ows into uniform cash fl ows, gradients into present worths, and much more. Additionally, you can solve for rate of return i or...