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https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | Series ISSN: 1939-5221 Series ISSN: 1939-5221 Series ISSN: 1939-5221 SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING SYNTHESIS LECTURES ON ENGINEERING Series Editor: Steven F. Barrett, University of Wyoming Series Editor: Steven F. Barrett, University of Wyoming Series Editor: Steven F. Barrett, Uni... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | These interest relationships are used to define certain project criteria that are used by engineers and project managers to select the best economic choice among several alternatives. Projects examined will project managers to select the best economic choice among several alternatives. Projects examined will project man... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | analyses are presented.The first is referred to as the range approach while the second uses probabilistic concepts to determine a measure of the risk the range approach while the second uses probabilistic concepts to determine a measure of the risk the range approach while the second uses probabilistic concepts to deter... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | topics, published quickly, in digital and print formats. For more information topics, published quickly, in digital and print formats. For more information topics, published quickly, in digital and print formats. For more information visit www.morganclaypool.com visit www.morganclaypool.com visit www.morganclaypool.com... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | E N N N G G G I I I N N N E E E E E E R R R I I I N N N G G G E E E C C C O O O N N N O O O M M M I I I C C C S S S A A A N N N D D D D D D E E E C C C I I I S S S I I I O O O N N N A A A N N N A A A L L L Y Y Y S S S I I I S S S M M M o o o r r r g g g a a a n n n & & & C C C l l l a a a y y y p p p o o o o o o l l l ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | F. Barrett, Series Editor Steven F. Barrett, Series Editor Steven F. Barrett, Series Editor Fundamentals of Engineering Economics and Decision Analysis Synthesis Lectures on Engineering Editor Steven S. Barrett, University of Wyoming Fundamentals of Engineering Economics and Decision Analysis David L. Whitman and Ronal... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | Machine: The DG/K-Based Approach Stephen P. Radzevich 2008 Tensor Properties of Solids, Part Two: Transport Properties of Solids Richard F. Tinder 2007 Tensor Properties of Solids, Part One: Equilibrium Tensor Properties of Solids Richard F. Tinder 2007 Essentials of Applied Mathematics for Scientists and Engineers Rob... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | discussions on the time value of money and interest relationships. These interest relationships are used to define certain project criteria that are used by engineers and project managers to select the best economic choice among several alternatives. Projects examined will include both income- and service-producing inve... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . xiii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Engineering Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Basic Engi... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . 1 1.2 Decision Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Fundamentals of Engineering Exam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Interest and the Time Value of Money . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Interest Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3.1 Simple Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . 5 Cash Flow Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Interest Formulas for Discrete Compounding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5.1 Single Payments . . . . . . . . . . . . . . . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . 11 2.5.4 The use of Financial Functions in Excel® . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5.5 Example Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Interest Formulas for Continuous Compounding . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . 20 3 Project Evaluation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1 3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Alterna... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 3.6 3.7 3.8 3.9 Equivalence Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Net Present Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.5.1 Analysis of a Single Investment Opportunity . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.6.1 Internal Rate of Return (IRR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.6.2 Spreadsheet Formula for IRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | Calculations . . . . . . . . . . . . . . . . . . 37 3.7.1 Perception #1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.7.2 Perception #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.7.3 Final Commen... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Service Producing Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2.1 Equivalence Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2.2 Rate of Return Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 4.3.2 Common Study Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Income Producing Investments . . . . . . . . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.3 Mutually Exclusive Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.3.1 Equivalence Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . 70 5.4 5.5 5.6 5.7 Unequal Life Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Independent and Contingent Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5.1 Independent Investments . . . . . . . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 77 Ranking Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 xi 6 Determination of Project Cash Flow . . . . . . . . .... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.3 Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 6.3.1 Straight-Line Depreciation (SL) . . . . . . . . . . . . . . . . . . . . . . . .... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . 102 6.4 Cash Flow Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.4.1 Capital Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.4.2 Gross Revenue . . . . . . . . . . . . . . . . . . . .... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . 107 6.4.5 Before-Tax Cash Flow Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.4.6 Depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.4.7 Taxable Income . . . . . . . . . . . . . .... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.4.10 Cash Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Financial Leverage and Associated Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Adjustment to Cash Flow Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.3.1 Lever... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 xii 8 Basic Statistics and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.1 8.2 8.3 8.4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2.2 Measures of Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 8.2.3 Frequency Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 8.2.4 Relative Frequency Distribu... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.3.2 Relative Frequency Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 8.3.3 Subjective Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 8.3.4 Probabil... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . 168 9 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 9.1 9.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 9.1.1 Range Approach . . . . . . . . . . .... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 A Compound Interest Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Authors’ Biographies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | evaluate projects to determine profitability.The subject has been called: Engineering Economics or Project Evaluation or Economic Evaluation or Decision Analysis. Whatever one chooses to call it, the reader who studies this material and becomes proficient in its content, will be able to analyze project cash flows and make... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | of escalation, inflation, and taxes on the economic analysis of alternatives are discussed. There is always risk involved in undertaking a project. Risk analysis incorporates the concepts of probability and statistics in the evaluation of alternatives. This allows management to determine the probability of success or fa... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | included in this textbook: basic engineering economics and risk analysis. A very brief overview of each of these topics is presented in the following paragraphs. 1.1.1 BASIC ENGINEERING ECONOMICS Within this topic are discussions on the time value of money and interest relationships. These interest relationships are us... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | concepts to determine a measure of the risk involved. 1.2 DECISION ANALYSIS As described above, the overall objective of any economic analysis is to provide a basis for making a sound decision regarding any particular project. For example, suppose that an engineer is given the assignment to implement a project for whic... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | the proper use of the time value of money formulas that will be presented. Financial aspects have to do with the obtaining of funds required to initiate the project. There are several sources which may be considered, i.e., internal company funds, lending institutions, the issuing of bonds, or the issuing of new stock. ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | considered. The effect of time on the value of money can be illustrated by the following examples. Consider a sum of $1000 that an individual has accumulated. If the $1000 were buried in a can under a tree for some future need, the individual, one year later, would still have $1000. However, if the $1000 were placed in... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | OF CAPITAL There are, in general, two sources of capital needed to make an investment. Capital can be obtained either from the investor’s own funds or from a lender. Wherever capital is obtained, there is a cost associated with the use of the funds. If they are obtained from a lender, the cost of capital is the interes... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | treated as an interest rate, i. 2.3 2.3.1 INTEREST CONCEPTS SIMPLE INTEREST The amount of interest earned by an investment (for example, a single principal deposit in a savings account) is called simple interest when the interest is found by Equation 2.1: I = P in (2.1) where, I = total interest, dollars P = amount of ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | B will pay A over 3 years would be calculated as the following: Iyr 1 = (1000)(0.1) = $100, which would result in a balance at the end of year 1 of $1100 Iyr 2 = (1100)(0.1) = $110, which would result in a balance at the end of year 2 of $1210 Iyr 3 = (1210)(0.1) = $121, which would result in a balance at the end of ye... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | The 10% annual interest compounded semi-annually means that every one-half year, 5% interest is earned or charged to the principal. This leads to the concept of effective yearly interest rate. The effective yearly interest rate can be found by computing the value that the principal has grown to at the end of year one, ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | yearly percentage rate that expresses the total finance charge on a loan over its entire term. The APR includes the nominal interest rate, fees, points, and mortgage insurance, and is therefore a more complete measure of a loan’s cost than the interest rate alone. The loan’s nominal interest rate, not its APR, is used t... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | the following method is utilized by the authors. A horizontal line is drawn which represents the length of time (life) of the investment opportunity (project). The interest periods are then marked off and labeled above the line. At the extreme left of the time line is time zero (or, as will be defined in the next sectio... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 1 2 3 CF0 CF1 CF2 CF3 … … 2.4. CASH FLOW DIAGRAMS 7 n-2 n-1 n CFn-2 CFn-1 CFn Example 2.1 Consider the example of a 3-year auto loan from the view of the lender. The lender provides $20,000 to the client (a negative cash flow for the lender) at month 0 at an interest rate of 0.5% per month. In exchange, the lender recei... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | in the cash flow diagram. The cash flow diagrams that follow should help to define these sums of money. 8 2. INTEREST AND THE TIME VALUE OF MONEY Present, P : 0 1 2 3 … n-2 n-1 n P Future, F : 0 1 2 3 … n-2 n-1 n Annuity, A: 0 1 2 3 … n-2 n-1 n F A Gradient, G: 0 1 A 2 A 3 … … A A n-2 n-1 A n G 2G … (n-3)G (n-2)G (n-1)G 2... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | in a bank account that earns i% interest per period. It will grow to a future amount, F , at the end of n interest periods according to: F = P (1 + i)n (2.4) The derivation of Equation 2.4 is given by: The factor (1 + i)n is frequently called the Single Payment Compound Amount Factor and is symbolized in this text by (... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | or a future sum, F . In the following formulas that relate P , F , and A, it is imperative that the reader understands that: 1) P occurs one interest period before the first value of A; 2) A occurs at the end of each interest period; and 3) F occurs at the same time as the last A (at time n). These relationships were il... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | F = A{[(1 + i)n − 1]/i} (2.10) The term in the {} brackets is called the Uniform Series Compound Amount Factor and is symbolized by (F /A)i,n. If one is given the amount of A, one uses the (F /A)i,n factor to find the equivalent value of F . That is, Rearranging Equation 2.10 and solving for A yields F = A(F /A)i,n A = ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | (A/P )i,n. If one is given the amount of P , one uses the (A/P )i,n factor to find the equivalent value of A. That is, A = P (A/P )i,n 2.5.3 UNIFORM GRADIENT In some applications, a series of cash flows will be generated from a project analysis which uniformly increase or decrease from an initial value. The cash flow diag... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | by (F /G)i,n. If one is given the amount of G, one uses the (F /G)i,n factor to find the equivalent value of F . That is, F = G(F /G)i,n (2.23) 12 2. INTEREST AND THE TIME VALUE OF MONEY The equations for the nine factors are given in Table 2.2 and numerical values are tabulated in Appendix A for various values of inter... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | Uniform Series Present Worth to A given F (A / F) i,n to P given A (P / A) i,n Capital Recovery to A given P (A/ P) i,n Uniform Gradient Present Worth Uniform Gradient Future Value Uniform Gradient Uniform Series to P given G (P/ G) i,n to F given G (F / G) i,n to A given G (A / G)i,n Formula (1 + i) n (1 + i) -n -1n (... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | these functions, the variables are as follows: (cid:129) rate is the interest rate (as a fraction) per period (cid:129) nper is the number of interest bearing periods (cid:129) pmt is an annuity (A) sum of money (cid:129) pv is a present (P ) value sum of money (occurs at time = 0) (cid:129) fv is a future (F ) value s... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | fact that there is no present value payment, and “B6” defines that the various payments are at the end of the period. Since the formula finds the future value of a $1 annuity, we have effectively computed (F/A). Some additional Excel® financial functions that might be of some interest at this point are: 14 2. INTEREST AND... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | consistency between the calculations in Excel® and those performed with the specific formula for ieff . The NPER function is useful for determining how many compounding periods are necessary to achieve a desired result. For example, one might want to determine how many years it will take for an original investment to do... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | close approximation of how long it will take for an investment to double. 2.5.5 EXAMPLE PROBLEMS At this point, it would be beneficial to examine some of the practical applications of these formulas. Example 2.2 If $10,000 is invested in a fund earning 15% compounded annually, what will it grow to in 10 years? Solution:... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | is 7% com- pounded annually, what uniform amount must be deposited at the end of each year? Solution: A = F (A/F )i,n = 6, 000(A/F )7,8 = 6, 000(0.09747) = $585 Example 2.6 An individual wishes to place an amount of money in a savings account and, at the end of one month and for every month thereafter for 30 months, dr... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | does not match the time frame of the interest rate (monthly), one must convert to an effective annual interest rate before computing the correct formulas. (cid:2) 1 + i m (cid:3) m (cid:2) (cid:3) 12 ie = F = A(F /A)i,n = 1, 000(F /A)8.30,10 = 1, 000{[(1 + 0.0830)10 − 1]/0.0830} − 1 = 0.0830 − 1 = 1 + 0.08 12 = 1, 000(... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 2. INTEREST AND THE TIME VALUE OF MONEY Solution 2: Convert the gradient to an equivalent annuity, add this value to the $1,000 annuity and then convert to the future. AGradient ATotal = G(A/G)i,n = 200(A/G)10,6 = 200(2.2236) = $444.72 = 1, 000 + 444.72 = $1, 444.72 F = A(F /A)i,n = 1, 444.72(F /A)10,6 = 1, 444.72(7.71... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | flow diagram if the annual interest rate is 20% compounded annually. 0 1 2 3 … 8 9 10 2000 1900 1800 … 1300 1200 1100 Solution: Again, there are a variety of methods to solve this problem. One technique is to recognize that the cash flow is made up of an annuity of $2,000 and a gradient of −$100. ATotal = 2, 000 − 100(A/... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 1)] (F /A)i,n = (ein − 1)/[(ei − 1)] (2.24) (2.25) (2.26) 2.6.2 CONTINUOUS COMPOUNDING FOR CONTINUOUS PAYMENTS The other application of continuous compounding is the case where the deposits or withdrawals to an account are being made on a nearly continuous basis. One example of this situation would be a credit card com... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | decided to invest in a project to make a product. The initial investment cost will be $1,000,000 to be spread over the first two years with $700,000 in the first year and $300,000 in the second. The plan calls for producing products at the following rates: 5,000 units in year 2; 10,000 in year 3; 30,000 in year 4; 30,000... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | of $10,000 if the series extends for 10 years and earns 12% interest compounded semi-annually? 2.9. An annual deposit of $1,000 is placed in an account at the beginning of each year for 5 years. What is the present value of that series if interest is 12% compounded annually? What is the future value at the end of the 5... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 5.75% interest compounded monthly. If the engineer can make a $20,000 down payment, what is the price of the most expensive house that the engineer can afford to purchase? 22 2. INTEREST AND THE TIME VALUE OF MONEY 2.15. A young woman placed $200.00 in a savings account paying monthly interest. After one year, her bala... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | at the end of year 4. Interest is 10% per year compounded annually. 0 1 2 3 4 5 6 7 8 9 10 1000 500 500 750 1000 800 600 400 2000 2.20. Calculate the future worth 5 years from now of a present sum of $2,000 if: 2.7. PROBLEMS 23 (a) Annual interest is 10% compounded annually (b) Annual interest is 10% compounded quarter... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 1%, 5%, 10%, 15%, 20%, and 25%. Can you determine an approximate “Rule” for how to quickly calculate how long it takes for an investment to triple in value? C H A P T E R 3 25 Project Evaluation Methods INTRODUCTION 3.1 In order to make informed decisions on one or more potential investments, methods must be devel- ope... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | or receiving $100,000 at the end of each year for 20 years. If interest is expected to be constant at 12% for the next 20 years as in the previous paragraph, which set of payments would you prefer? Since this question is represented by the cash flow diagrams shown above and the interest rate of 12%, the choice can be ma... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | the evaluator choose between multiple projects. These will be discussed in more detail later in this chapter. 3.2 ALTERNATE USES OF CAPITAL Investment analysis or project evaluation involves making a decision between alternative uses of capital. A cash flow diagram is constructed for each alternative according to the sp... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | The lower bound for the MARR is generally set at the cost of capital, which reflects the expense of obtaining funds for a given project. How much higher the MARR is above the cost of capital depends on a particular company’s or individual’s position and the particular project. For example, an individual who borrows mone... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | to choose the “best” project, the MARR is used as the interest rate in present, future, or annuity calculations. A net present value, NPV (sometimes called the net present worth), net future value, NFV, or net annual value, NAV, is calculated by one of the following equations: (cid:4) N P V = N F V = N AV = Present Val... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | and an NP V value of zero indicates that it earns the MARR. Since the MARR represents the decision point for determining the viability of a project for a particular investor, a positive NP V would indicate that the project is an acceptable one. Example 3.1 Consider the project represented by the following cash flow diag... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | is necessary. The function is: = NP V (rate, value1, value2, …). where, rate = interest rate per period (as a fraction). value1, value2, ... = cash flows that occur at the end of period 1, end of period 2, etc. One can see that the NPV function does not include the investment period 0. Therefore, in order to calculate t... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 3 4 5 6 7 8 9 10 11 Figure 3.1: Demonstration of the use of the NP V function in Excel®. N P V = −1000 + 150(P /A)10,5 + 50(P /G)10,5 = −1000 + 150(3.7908) + 50(6.8618) = −$88 Since the N P V is negative, the project will not earn the MARR and, therefore, is not accept- able to this investor. Now a question arises: Wha... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | the funds are already invested in a project that is earning the MARR. As mentioned before, for individuals, this could mean leaving their funds in their savings accounts. By definition, the NP V of the “do 30 3. PROJECT EVALUATION METHODS nothing” project is zero.Thus, when a single investment opportunity is being evalu... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | P V for Project A = −800 + 215(P /A)10,5 = $15.0 N P V for Project B = −800 + 100(P /A)10,5 + 800(P /F )10,5 = $75.8 Both projects show positive values of NP V . Therefore, both would be acceptable as long as the investor had at least $800 to invest. In addition, the “do nothing” alternative does not need to be conside... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | become apparent in the following discussion and example problems. INTERNAL RATE OF RETURN (IRR) 3.6.1 The I RR is defined as the interest rate which discounts a series of cash flows to an NP V value of zero: (cid:4) N P V = 0 = Present Value of Cash Flows with the interest rate equal to I RR (3.4) The equation can also b... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | as a function of interest rate. (Note, for this example, when NP V = 0, the interest rate, or I RR, is 0.125.) Example 3.4 Consider the two investment opportunities examined in Example 3.3. The investor’s MARR is 10% and the investor only has enough funds to invest in one of the projects. What are the I RRs for each pr... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | flows from Project B. Thus, the “true” answer for I RR is 12.5% compared to the interpolated value of 12.6%. 75.8−0 75.8−(−67.0) In this example, the I RRs of both projects are greater than the investor’s MARR, so both projects are acceptable. It would appear that since the I RR of Project B is greater than the I RR of ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 100 900 NPV = IRR = 75.8 12.5% 3 4 5 6 7 8 9 10 11 12 Year 0 1 2 3 4 5 CF -800 100 100 100 100 900 NPV = IRR = =B4+NPV(B1,B5:B9) =IRR(B4:B9,0.1) 1 3 4 5 6 7 8 9 10 11 12 Figure 3.3: Demonstration of the use of the NP V and I RR functions in Excel®. As in Figure 3.2, Excel provides the “true” value for I RR without the ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | to generate a present value, which is called PC, at year zero. The interest rate which will then discount FI to a value equal to the value of PC is determined to be the ERR. Another way of looking at the external rate of return is to set up a second project which is called the reinvestment project. The negative cash flo... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | over the I RR method in that the ERR can be solved for directly without a trial and error procedure. The steps in the calculation procedure are: Cj (P /F )MARR,j (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) (cid:7) n(cid:4) (cid:7) (cid:7) (cid:7) (cid:7) j =0 n(cid:4) Ij (F /P )MARR,n−j PC = FI = j =0 ERR =... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | This is, indeed, the proper interpretation – but only because the initial investment values for both projects were the same. Again, one must be very careful in ranking projects by ERR values as will be shown in Chapter 5. One additional observation can be made about the relationship between MARR, I RR, and ERR. The ERR... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | = 0.163 = 16.3% All three economic indicators show that this project is an acceptable one. SPREADSHEET FORMULA FOR ERR 3.6.4 Excel® has a built-in function that can be used to calculate the External Rate of Return. The function is: = MI RR(values, finance_rate, reinvestment_rate) where, values = cash flows that occur for... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 5 6 7 8 9 10 11 12 13 Year 0 1 2 3 4 5 CF -1000 500 500 -200 500 500 NPV = IRR = ERR = =B4+NPV(B1,B5:B9) =IRR(B4:B9,0.1) =MIRR(B4:B9,B1,B1) 1 3 4 5 6 7 8 9 10 11 12 13 Figure 3.4: Demonstration of the use of the NP V , I RR, and MI RR(ERR) functions in Excel®. evaluation methods used. Surveys have indicated that a vast... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | of $5000 will yield $1931.45 at the end of each year for 4 years. What is the value of the project’s I RR? If the MARR is 15%, what is the project’s ERR? 0 1 2 3 4 -5000 1931.45 1931.45 1931.45 1931.45 I RR : NP V = −5000 + 1931.45(P /A)i,4 (P /A)I RR,4 = 2.5887 For NP V = 0, Examining the interest tables in Appendix A... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | “earning” a particular interest rate. 3.7.1 PERCEPTION #1 The first perception of an investment “earning” a particular interest rate parallels the concept of investing money in a savings account for a specified period of time. In this perception, “earning” means that an initial investment will yield a future value given ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | order to “earn” the I RR (20%) interest rate on the entire initial investment ($5,000), any cash flows received before the end of the project must be reinvested in another project that has the same I RR. 3.7.2 PERCEPTION #2 The second perception more closely parallels the concept of making a loan to a project and having... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | However, banking institutions agree that this repayment scheme has indeed “earned” 20% on the original loan of $5,000. In the opinion of the authors, the final conclusion is that the question of whether reinvestment of the cash flows at the I RR must occur or not is really more of an issue of perceiving what is meant by ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | then ERR analysis should be used. Both the I RR and ERR are valid investment analysis techniques and, if applied correctly, will yield the same conclusion regarding the viability of an investment to the company or individual. It will be shown in the next section that the ERR method has some advantages in particular ana... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | of I RR rates calculated when there are multiple sign changes are difficult to interpret as to which might be the correct return on investment. Since the ERR equation does not form a polynomial, it always has a unique answer and, therefore, should be the rate of return technique of choice in acceleration projects. A mod... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 500 (1 + I RR)5 = 0 I RR5 + 4.5 I RR3 + 7.5 I RR3 + 5.7 I RR2 + 1.4 I RR − 0.8 = 0 Since the 5th order polynomial only has one sign change, there is only one positive value of I RR for the cash flows in Example 3.6. Example 3.8 will demonstrate a situation where more than one positive value exists. Example 3.8 Given the... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | + 0.3 = 0 One can see that there are two sign changes in the list of terms and, therefore, two positive values for I RR. As mentioned before, the multiple values of IRR cause difficulties in interpretation. With a total investment (without time value of money) of $320 and the total of the positive incomes (without time ... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | solution technique or Excel®, the modified I RR is 2.9%. Thus, the ERR, the modified I RR, and the NPV indicate that this project is not an acceptable project for the investor. In summary, acceleration projects have the potential to add another level of complexity to the calculation of I RR in that multiple positive rate... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | is 15%. 0 1 2 3 4 3.9. PAYOUT 45 -100 60 60 60 60 Undiscounted Payout: Year Cash Flow 0 1 2 (cid:1086) 100 60 60 Cumula(cid:415)ve Cash Flow (cid:1086) 100 (cid:1086) 40 20 Interpolate between years 1 and 2 to find when the cumulative cash flow equals zero: Payout = 1 + (cid:3) (cid:2) −40 − 0 −40 − (20) (2 − 1) = 1.67 y... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | is considering the purchase of a property that he believes he can resell for $25,000 at the end of 10 years. The property will generate positive cash flows of $1,500 per year for the 10 years. What is the maximum that the individual should pay for the property if his MARR is 12%? 3.4. An investment of $10,000 will yield... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | -75 50 50 -30 200 3.9. You are a project engineer and you have to make a choice between two contractors to perform some rebuilding work on a manufacturing facility. One contractor proposes that he will do the work for $1,300,000 payable immediately. The other contractor proposes that he will perform the same job for $1... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | 4 5 6 Calculate the undiscounted and discounted payout periods. The MARR is 15%. 3.12. Engineer A retires at the age of 65 with a retirement account worth $500,000. At what interest rate would this amount need to be invested in order to withdraw $50,000 at the end of each of the next 15 years? 3.13. Develop an Excel® s... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | produces income and one which produces a service. A service producing investment is one that results in a cash flow diagram that normally contains no positive cash flows with the exception of a possible salvage value of the service. Salvage value is the estimated value of an asset at the end of its useful life. It is ass... |
https://ieeexplore.ieee.org/xpl/ebooks/bookPdfWithBanner.jsp?fileName=6813339.pdf&bkn=6813338&pdfType=book | to conduct its business. Two or more alternatives have been identified that provide the same service over the same time period. These alternatives are known as equal life alternatives and they lend themselves to straight forward application of the evaluation methods that were presented in Chapter 3. 4.2.1 EQUIVALENCE TE... |
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