1. Seeveentth EdiittiionENGINEERINGECONOMY

2. Seventh EditionENGINEERINGECONOMYLeland Blank , P. E.Texas A & M UniversityAmerican University of Sharjah, United Arab EmiratesAnthony Tarquin , P. E.University of Texas at El PasoTM 3. ENGINEERING ECONOMY: SEVENTH EDITIONPublished by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, NewYork, NY 10020. Copyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Previous editions 2005, 2002, and 1998. No part of this publication may be reproduced or distributed in any form or by any means, orstored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc.,including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distancelearning.Some ancillaries, including electronic and print components, may not be available to customers outside the UnitedStates.This book is printed on recycled, acid-free paper containing 10% postconsumer waste.1 2 3 4 5 6 7 8 9 0 QDB/QDB 1 0 9 8 7 6 5 4 3 2 1ISBN 978-0-07-337630-1MHID 0-07-337630-2Vice President & Editor-in-Chief: Marty LangeVice President EDP/Central Publishing Services: Kimberly Meriwether DavidGlobal Publisher: Raghothaman SrinivasanSponsoring Editor: Peter E. MassarSenior Marketing Manager: Curt ReynoldsDevelopment Editor: Lorraine K. BuczekSenior Project Manager: Jane MohrDesign Coordinator: Brenda A. RolwesCover Designer: Studio Montage, St. Louis, MissouriCover Image: Brand X Pictures/PunchStock RFBuyer: Kara KudronowiczMedia Project Manager: Balaji SundararamanCompositor: MPS Limited, a Macmillan CompanyTypeface: 10/12 TimesPrinter: Quad/Graphics-DubuqueAll credits appearing on page or at the end of the book are considered to be an extension of the copyright page.Library of Congress Cataloging-in-Publication DataBlank, Leland T.Engineering economy / Leland Blank, Anthony Tarquin. 7th ed.p. cm.Includes bibliographical references and index.ISBN-13: 978-0-07-337630-1 (alk. paper)ISBN-10: 0-07-337630-21. Engineering economy. I. Tarquin, Anthony J. II. Title.TA177.4.B58 2012658.15dc222010052297www.mhhe.comTM 4. This book is dedicated to Dr. Frank W. Sheppard, Jr. His lifelongcommitment to education, fair fi nancial practices, internationaloutreach, and family values has been an inspiration to manyoneperson at a time. 5. 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CONTENTSPreface to Seventh Edition xiiiLEARNINGSTAGE 1THE FUNDAMENTALSChapter 1 Foundations of Engineering Economy 21.1 Engineering Economics: Description andRole in Decision Making 31.2 Performing an Engineering Economy Study 41.3 Professional Ethics and Economic Decisions 71.4 Interest Rate and Rate of Return 101.5 Terminology and Symbols 131.6 Cash Flows: Estimation and Diagramming 151.7 Economic Equivalence 191.8 Simple and Compound Interest 211.9 Minimum Attractive Rate of Return 251.10 Introduction to Spreadsheet Use 27Chapter Summary 31Problems 31Additional Problems and FE Exam Review Questions 35Case StudyRenewable Energy Sources for Electricity Generation 36Case StudyRefrigerator Shells 37Chapter 2 Factors: How Time and Interest Affect Money 38PE Progressive ExampleThe Cement Factory Case 392.1 Single-Amount Factors (FP and PF ) 392.2 Uniform Series Present Worth Factor and Capital Recovery Factor (PA and AP) 432.3 Sinking Fund Factor and Uniform Series Compound Amount Factor (AF and FA) 462.4 Factor Values for Untabulated i or n Values 482.5 Arithmetic Gradient Factors (PG and AG) 502.6 Geometric Gradient Series Factors 582.7 Determining i or n for Known Cash Flow Values 61Chapter Summary 64Problems 64Additional Problems and FE Exam Review Questions 69Case StudyTime Marches On; So Does the Interest Rate 70Chapter 3 Combining Factors and Spreadsheet Functions 723.1 Calculations for Uniform Series That Are Shifted 733.2 Calculations Involving Uniform Series and Randomly Placed Single Amounts 763.3 Calculations for Shifted Gradients 80Chapter Summary 86Problems 86Additional Problems and FE Exam Review Questions 92Case StudyPreserving Land for Public Use 93Chapter 4 Nominal and Effective Interest Rates 94PE Progressive ExampleThe Credit Card Offer Case 954.1 Nominal and Effective Interest Rate Statements 964.2 Effective Annual Interest Rates 994.3 Effective Interest Rates for Any Time Period 1054.4 Equivalence Relations: Payment Period and Compounding Period 1064.5 Equivalence Relations: Single Amounts with PPCP 107 7. viii Contents4.6 Equivalence Relations: Series with PPCP 1094.7 Equivalence Relations: Single Amounts and Series with PPCP 1124.8 Effective Interest Rate for Continuous Compounding 1144.9 Interest Rates That Vary over Time 116Chapter Summary 117Problems 118Additional Problems and FE Exam Review Questions 122Case StudyIs Owning a Home a Net Gain or Net Loss over Time? 124LEARNINGSTAGE 2BASIC ANALYSIS TOOLSChapter 5 Present Worth Analysis 128PE Progressive ExampleWater for Semiconductor Manufacturing Case 1295.1 Formulating Alternatives 1295.2 Present Worth Analysis of Equal-Life Alternatives 1315.3 Present Worth Analysis of Different-Life Alternatives 1335.4 Future Worth Analysis 1375.5 Capitalized Cost Analysis 138Chapter Summary 142Problems 142Additional Problems and FE Exam Review Questions 147Case StudyComparing Social Security Benefi ts 149Chapter 6 Annual Worth Analysis 1506.1 Advantages and Uses of Annual Worth Analysis 1516.2 Calculation of Capital Recovery and AW Values 1536.3 Evaluating Alternatives by Annual Worth Analysis 1556.4 AW of a Permanent Investment 1576.5 Life-Cycle Cost Analysis 160Chapter Summary 164Problems 164Additional Problems and FE Exam Review Questions 169Case StudyThe Changing Scene of an Annual Worth Analysis 171Chapter 7 Rate of Return Analysis: One Project 1727.1 Interpretation of a Rate of Return Value 1737.2 Rate of Return Calculation Using a PW or AW Relation 1757.3 Special Considerations When Using the ROR Method 1797.4 Multiple Rate of Return Values 1807.5 Techniques to Remove Multiple Rates of Return 1847.6 Rate of Return of a Bond Investment 190Chapter Summary 193Problems 193Additional Problems and FE Exam Review Questions 198Case StudyDeveloping and Selling an Innovative Idea 200Chapter 8 Rate of Return Analysis: Multiple Alternatives 2028.1 Why Incremental Analysis Is Necessary 2038.2 Calculation of Incremental Cash Flows for ROR Analysis 2038.3 Interpretation of Rate of Return on the Extra Investment 2068.4 Rate of Return Evaluation Using PW: Incremental and Breakeven 2078.5 Rate of Return Evaluation Using AW 2138.6 Incremental ROR Analysis of Multiple Alternatives 214 8. Contents ix8.7 All-in-One Spreadsheet Analysis (Optional) 218Chapter Summary 219Problems 220Additional Problems and FE Exam Review Questions 225Case StudyROR Analysis with Estimated Lives That Vary 226Case StudyHow a New Engineering Graduate Can Help His Father 227Chapter 9 Benefi t/Cost Analysis and Public Sector Economics 228PE Progressive ExampleWater Treatment Facility #3 Case 2299.1 Public Sector Projects 2309.2 Benefi t/Cost Analysis of a Single Project 2359.3 Alternative Selection Using Incremental B/C Analysis 2389.4 Incremental B/C Analysis of Multiple, Mutually Exclusive Alternatives 2429.5 Service Sector Projects and Cost-Effectiveness Analysis 2469.6 Ethical Considerations in the Public Sector 250Chapter Summary 251Problems 252Additional Problems and FE Exam Review Questions 258Case StudyComparing B/C Analysis and CEA of Traffi c Accident Reduction 259LEARNINGSTAGE 2EPILOGUE: SELECTING THE BASIC ANALYSIS TOOLLEARNINGSTAGE 3MAKING BETTER DECISIONSChapter 10 Project Financing and Noneconomic Attributes 26610.1 MARR Relative to the Cost of Capital 26710.2 Debt-Equity Mix and Weighted Average Cost of Capital 26910.3 Determination of the Cost of Debt Capital 27110.4 Determination of the Cost of Equity Capital and the MARR 27310.5 Effect of Debt-Equity Mix on Investment Risk 27510.6 Multiple Attribute Analysis: Identifi cation and Importance of Each Attribute 27810.7 Evaluation Measure for Multiple Attributes 282Chapter Summary 283Problems 284Additional Problems and FE Exam Review Questions 289Case StudyWhich Is BetterDebt or Equity Financing? 290Chapter 11 Replacement and Retention Decisions 292PE Progressive ExampleKeep or Replace the Kiln Case 29311.1 Basics of a Replacement Study 29411.2 Economic Service Life 29611.3 Performing a Replacement Study 30211.4 Additional Considerations in a Replacement Study 30611.5 Replacement Study over a Specifi ed Study Period 30711.6 Replacement Value 312Chapter Summary 312Problems 313Additional Problems and FE Exam Review Questions 319Case StudyWill the Correct ESL Please Stand? 321 9. x ContentsChapter 12 Independent Projects with Budget Limitation 32212.1 An Overview of Capital Rationing among Projects 32312.2 Capital Rationing Using PW Analysis of Equal-Life Projects 32512.3 Capital Rationing Using PW Analysis of Unequal-Life Projects 32712.4 Capital Budgeting Problem Formulation Using Linear Programming 32912.5 Additional Project Ranking Measures 332Chapter Summary 334Problems 334Additional Problems and FE Exam Review Questions 338Chapter 13 Breakeven and Payback Analysis 34013.1 Breakeven Analysis for a Single Project 34113.2 Breakeven Analysis Between Two Alternatives 34513.3 Payback Analysis 34813.4 More Breakeven and Payback Analysis on Spreadsheets 352Chapter Summary 355Problems 355Additional Problems and FE Exam Review Questions 361Case StudyWater Treatment Plant Process Costs 363LEARNINGSTAGE 4ROUNDING OUT THE STUDYChapter 14 Effects of Infl ation 36614.1 Understanding the Impact of Infl ation 36714.2 Present Worth Calculations Adjusted for Infl ation 36914.3 Future Worth Calculations Adjusted for Infl ation 37414.4 Capital Recovery Calculations Adjusted for Infl ation 377Chapter Summary 378Problems 379Additional Problems and FE Exam Review Questions 384Case StudyInfl ation versus Stock and Bond Investments 385Chapter 15 Cost Estimation and Indirect Cost Allocation 38615.1 Understanding How Cost Estimation Is Accomplished 38715.2 Unit Method 39015.3 Cost Indexes 39115.4 Cost-Estimating Relationships: Cost-Capacity Equations 39415.5 Cost-Estimating Relationships: Factor Method 39515.6 Traditional Indirect Cost Rates and Allocation 39715.7 Activity-Based Costing (ABC) for Indirect Costs 40115.8 Making Estimates and Maintaining Ethical Practices 403Chapter Summary 404Problems 404Additional Problems and FE Exam Review Questions 410Case StudyIndirect Cost Analysis of Medical Equipment Manufacturing Costs 411Case StudyDeceptive Acts Can Get You in Trouble 412Chapter 16 Depreciation Methods 41416.1 Depreciation Terminology 41516.2 Straight Line (SL) Depreciation 41816.3 Declining Balance (DB) and Double Declining Balance (DDB) Depreciation 41916.4 Modifi ed Accelerated Cost Recovery System (MACRS) 42216.5 Determining the MACRS Recovery Period 426 10. Contents xi16.6 Depletion Methods 427Chapter Summary 429Appendix 43016A.1 Sum-of-Years-Digits (SYD) and Unit-of-Production (UOP) Depreciation 43016A.2 Switching between Depreciation Methods 43216A.3 Determination of MACRS Rates 435Problems 438Additional Problems and FE Exam Review Questions 442Appendix Problems 443Chapter 17 After-Tax Economic Analysis 44417.1 Income Tax Terminology and Basic Relations 44517.2 Calculation of Cash Flow after Taxes 44817.3 Effect on Taxes of Different Depreciation Methods and Recovery Periods 45017.4 Depreciation Recapture and Capital Gains (Losses) 45317.5 After-Tax Evaluation 45617.6 After-Tax Replacement Study 46217.7 After-Tax Value-Added Analysis 46517.8 After-Tax Analysis for International Projects 46817.9 Value-Added Tax 470Chapter Summary 472Problems 473Additional Problems and FE Exam Review Questions 481Case StudyAfter-Tax Analysis for Business Expansion 482Chapter 18 Sensitivity Analysis and Staged Decisions 48418.1 Determining Sensitivity to Parameter Variation 48518.2 Sensitivity Analysis Using Three Estimates 49018.3 Estimate Variability and the Expected Value 49118.4 Expected Value Computations for Alternatives 49218.5 Staged Evaluation of Alternatives Using a Decision Tree 49418.6 Real Options in Engineering Economics 498Chapter Summary 503Problems 503Additional Problems and FE Exam Review Questions 509Case StudySensitivity to the Economic Environment 510Case StudySensitivity Analysis of Public Sector ProjectsWater Supply Plans 511Chapter 19 More on Variation and Decision Making under Risk 51419.1 Interpretation of Certainty, Risk, and Uncertainty 51519.2 Elements Important to Decision Making under Risk 51819.3 Random Samples 52319.4 Expected Value and Standard Deviation 52619.5 Monte Carlo Sampling and Simulation Analysis 533Chapter Summary 540Problems 540Additional Problems and FE Exam Review Questions 543Case StudyUsing Simulation and Three-Estimate Sensitivity Analysis 544Appendix A Using Spreadsheets and Microsoft Excel 547A.1 Introduction to Using Excel 547A.2 Organization (Layout) of the Spreadsheet 549A.3 Excel Functions Important to Engineering Economy 550A.4 Goal SeekA Tool for Breakeven and Sensitivity Analysis 558A.5 SolverAn Optimizing Tool for Capital Budgeting, Breakeven, and Sensitivity Analysis 559A.6 Error Messages 560 11. xii ContentsAppendix B Basics of Accounting Reports and Business Ratios 561B.1 The Balance Sheet 561B.2 Income Statement and Cost of Goods Sold Statement 562B.3 Business Ratios 563Appendix C Code of Ethics for Engineers 566Appendix D Alternate Methods for Equivalence Calculations 569D.1 Using Programmable Calculators 569D.2 Using the Summation of a Geometric Series 570Appendix E Glossary of Concepts and Terms 573E.1 Important Concepts and Guidelines 573E.2 Symbols and Terms 576Reference Materials 579Factor Tables 581Photo Credits 610Index 611 12. PREFACE TO SEVENTH EDITIONThis edition includes the time-tested approach and topics of previous editions and introduces signifi -cantly new print and electronic features useful to learning about and successfully applying the excit-ingfi eld of engineering economics. Money makes a huge difference in the life of a corporation, anindividual, and a government. Learning to understand, analyze, and manage the money side of anyproject is vital to its success. To be professionally successful, every engineer must be able to deal withthe time value of money, economic facts, infl ation, cost estimation, tax considerations, as well asspreadsheet and calculator use. This book is a great help to the learner and the instructor in accom-plishingthese goals by using easy-to-understand language, simple graphics, and online features.What's New and What's BestThis seventh edition is full of new information and features. Plus the supporting online materialsare new and updated to enhance the teaching and learning experience.New topics: Ethics and the economics of engineering Service sector projects and their evaluation Real options development and analysis Value-added taxes and how they work Multiple rates of return and ways to eliminate them using spreadsheets No tabulated factors needed for equivalence computations (Appendix D)New features in print and online: Totally new design to highlight important terms, concepts, and decision guidelines Progressive examples that continue throughout a chapter Downloadable online presentations featuring voice-over slides and animation Vital concepts and guidelines identifi ed in margins; brief descriptions available (Appendix E) Fresh spreadsheet displays with on-image comments and function details Case studies (21 of them) ranging in topics from ethics to energy to simulationRetained features: Many end-of-chapter problems (over 90% are new or revised) Easy-to-read language to enhance understanding in a variety of course environments Fundamentals of Engineering (FE) Exam review questions that double as additional orreview problems for quizzes and tests Hand and spreadsheet solutions presented for many examples Flexible chapter ordering after fundamental topics are understood Complete solutions manual available online (with access approval for instructors)How to Use This TextThis textbook is best suited for a one-semester or one-quarter undergraduate course. Studentsshould be at the sophomore level or above with a basic understanding of engineering conceptsand terminology. A course in calculus is not necessary; however, knowledge of the concepts inadvanced mathematics and elementary probability will make the topics more meaningful.Practitioners and professional engineers who need a refresher in economic analysis and costestimation will fi nd this book very useful as a reference document as well as a learning medium.Chapter Organization and Coverage OptionsThe textbook contains 19 chapters arranged into four learning stages, as indicated in the fl owcharton the next page, and fi ve appendices. Each chapter starts with a statement of purpose and a spe-cific learning outcome (ABET style) for each section. Chapters include a summary, numerous 13. xiv Preface to Seventh EditionChapter 1Foundations ofEngineering EconomyChapter 2Factors: How Time andInterest Affect MoneyChapter 3Combining Factors andSpreadsheet Functionsend-of-chapter problems (essay and numerical), multiple-choice problems useful for course re-viewand FE Exam preparation, and a case study.The appendices are important elements of learning for this text:Appendix A Spreadsheet layout and functions (Excel is featured)Appendix B Accounting reports and business ratiosAppendix C Code of Ethics for Engineers (from NSPE)Appendix D Equivalence computations using calculators and geometric series; no tablesAppendix E Concepts, guidelines, terms, and symbols for engineering economicsThere is considerable fl exibility in the sequencing of topics and chapters once the fi rst sixchapters are covered, as shown in the progression graphic on the next page. If the course is de-signedto emphasize sensitivity and risk analysis, Chapters 18 and 19 can be covered immediatelyLearningStage 1:TheFundamentalsLearningStage 2:BasicAnalysisToolsLearningStage 3:MakingBetterDecisionsLearningStage 4:RoundingOut theStudyChapter 5Present WorthAnalysisChapter 6Annual WorthAnalysisChapter 7Rate of ReturnAnalysis:One ProjectChapter 8Rate of ReturnAnalysis: MultipleAlternativesLearning Stage 2 EpilogueSelecting the BasicAnalysis ToolChapter 12Independent Projectswith Budget LimitationChapter 11Replacement andRetention DecisionsChapter 10Project Financing andNoneconomic AttributesChapter 18Sensitivity Analysisand Staged DecisionsChapter 19More on Variationand Decision Makingunder RiskChapter 15Cost Estimation andIndirect Cost AllocationChapter 17After-Tax EconomicAnalysisChapter 14Effects ofInflationComposition by levelChapter 13Breakeven andPayback AnalysisChapter 4Nominal and EffectiveInterest RatesChapter 16DepreciationMethodsChapter 9Benefit/Cost Analysisand Public SectorEconomicsCHAPTERS IN EACH LEARNING STAGE 14. Chapter Organization and Coverage Options xvCHAPTER AND TOPIC PROGRESSION OPTIONSTopics may be introduced at the point indicated or any point thereafter(Alternative entry points are indicated by )Numerical progressionthrough chaptersFoundationsFactorsMore FactorsEffective iPresent WorthAnnual WorthRate of ReturnMore RORBenefit/CostFinancing andNoneconomic AttributesReplacementCapital BudgetingBreakeven andPaybackInflation1.2.3.4.5.6.7.8.9.10.11.12.13.14. InflationCostEstimation15. EstimationSensitivity, StagedDecisions, and Risk16. Depreciation17. After-Tax18. Sensitivity, DecisionTrees, and Real Options19. Risk and SimulationTaxes andDepreciationafter Learning Stage 2 (Chapter 9) is completed. If depreciation and tax emphasis are vitallyimportant to the goals of the course, Chapters 16 and 17 can be covered once Chapter 6 (annualworth) is completed. The progression graphic can help in the design of the course content andtopic ordering. 15. SAMPLE OF RESOURCES FORLEARNING OUTCOMESEach chapter begins with a purpose, listof topics, and learning outcomes(ABET style) for each correspondingsection. This behavioral-basedapproach sensitizes the reader to whatis ahead, leading to improvedunderstanding and learning.L E A R N I N G O U T C O M E SPurpose: Use multiple factors and spreadsheet functions to fi nd equivalent amounts for cash fl ows that have nonstan-dardS E C T I O N T O P I C L E A R N I N G O U T C O M E3.1 Shifted series Determine the P , F or A values of a seriesstarting at a time other than period 1.3.2 Shifted series and single cashfl ows Determine the P , F , or A values of a shifted seriesand randomly placed single cash fl ows.3.3 Shifted gradients Make equivalence calculations for shiftedarithmetic or geometric gradient series thatincrease or decrease in size of cash fl ows.placement.CONCEPTS AND GUIDELINESTo highlight the fundamental buildingblocks of the course, a checkmark and titlein the margin call attention to particularlyimportant concepts and decision-makingguidelines. Appendix E includes a briefdescription of each fundamental concept.It is a well-known fact that money makes money. The time value of money explains the changein the amount of money over time for funds that are owned (invested) or owed (borrowed).Time value of money This is the most important concept in engineering economy.IN-CHAPTER EXAMPLESNumerous in-chapter examplesthroughout the book reinforce thebasic concepts and makeunderstanding easier. Whereappropriate, the example is solvedusing separately marked hand andspreadsheet solutions.A dot-com company plans to place money in a new venture capital fund that currently returns18% per year, compounded daily. What effective rate is this ( a ) yearly and ( b ) semiannually?Solution(a) Use Equation [4.7], with r0.18 and m365.Effective i % per year( 1 0.18 365)365 119.716%(b) Here r0.09 per 6 months and m182 days.Effective i % per 6 months( 1 0.09 182)182 19.415%EXAMPLE 4.6bla76302_ch04_094-126.indd 106 12/22/10 8:24 PMWater for Semiconductor Manufactur-ingCase: The worldwide contribution ofsemiconductor sales is about $250 billionper year, or about 10% of the worldsGDP (gross domestic product). This indus-tryproduces the microchips used in manyof the communication, entertainment,transportation, and computing deviceswe use every day. Depending upon thetype and size of fabrication plant (fab),the need for ultrapure water (UPW) tomanufacture these tiny integrated circuitsis high, ranging from 500 to 2000 gpm(gallons per minute). Ultrapure water isobtained by special processes that com-monlyinclude reverse osmosis deionizingresin bed technologies. Potable waterobtained from purifying seawater orbrackish groundwater may cost from$2 to $3 per 1000 gallons, but to obtainUPW on-site for semiconductor manufac-turingmay cost an additional $1 to $3 per1000 gallons.A fab costs upward of $2.5 billion toconstruct, with approximately 1% of thistotal, or $25 million, required to providethe ultrapure water needed, includingthe necessary wastewater and recyclingequipment.A newcomer to the industry, AngularEnterprises, has estimated the cost pro-files for two options to supply its antici-patedfab with water. It is fortunate tohave the option of desalinated seawateror purifi ed groundwater sources in thelocation chosen for its new fab. The ini-tialcost estimates for the UPW system aregiven below.SourceSeawater(S)Groundwater(G)Equipment fi rstcost, $M20 22AOC, $M per year 0.5 0.3Salvage value, % of5 10fi rst costCost of UPW, $ per1000 gallons4 5Angular has made some initial estimatesfor the UPW system.Life of UPW equipment 10 yearsUPW needs 1500 gpmOperating time 16 hours perday for 250 daysper yearThis case is used in the following topics(Sections) and problems of this chapter:PW analysis of equal-life alternatives(Section 5.2)PW analysis of different-life alterna-tives(Section 5.3)Capitalized cost analysis (Section 5.5)Problems 5.20 and 5.34PEPROGRESSIVE EXAMPLESSeveral chapters include a progressiveexamplea more detailed problem statementintroduced at the beginning of the chapter andexpanded upon throughout the chapter inspecially marked examples. This approachillustrates different techniques and someincreasingly complex aspects of a real-worldproblem. 16. INSTRUCTORS AND STUDENTSContents xvii3.1 Calculations for Uniform Series That Are ShiftedWhen a uniform series begins at a time other than at the end of period 1, it is called a shiftedseries. In this case several methods can be used to fi nd the equivalent present worth P . Forexample, P of the uniform series shown in Figure 31 could be determined by any of thefollowing methods: Use the PF factor to fi nd the present worth of each disbursement at year 0 and add them. Use the FP factor to fi nd the future worth of each disbursement in year 13, add them, andthen fi nd the present worth of the total, using PF ( PF , i ,13). Use the FA factor to fi nd the future amount FA ( FA , i ,10), and then compute the presentworth, using PF ( PF , i ,13). Use the PA factor to compute the present worth P 3A ( PA , i ,10) (which will be locatedin year 3, not year 0), and then fi nd the present worth in year 0 by using the ( PF , i ,3) factor.ONLINE PRESENTATIONSAn icon in the margin indicates theavailability of an animated voice-over slidepresentation that summarizes the material inthe section and provides a brief example forlearners who need a review or prefer video-basedmaterials. Presentations are keyed tobla76302_ch07_172-201.indd 189 12/11/10 4:32 PMbla76302_ch03_072-093.indd 73 12/7/10 7:26 AMthe sections of the text.SPREADSHEETSThe text integrates spreadsheets to showhow easy they are to use in solving virtuallyany type of engineering economic analysisproblem. Cell tags or full cells detailbuilt-in functions and relations developedto solve a specifi c problem.BreakevenIncremental ROR17%Breakeven ROR17%MARRFilter 2 ROR23%MARRFilter 1 ROR25%Figure 86PW versus i graph and PW versus incremental i graph, Example 8.4 .bla76302_ch08_202-227.indd 212 12/11/10 6:52 PMChris and her father just purchased a small offi ce building for $160,000 that is in need of a lotof repairs, but is located in a prime commercial area of the city. The estimated costs each yearfor repairs, insurance, etc. are $18,000 the fi rst year, increasing by $1000 per year thereafter.At an expected 8% per year return, use spreadsheet analysis to determine the payback periodif the building is (a) kept for 2 years and sold for $290,000 sometime beyond year 2 or (b) keptfor 3 years and sold for $370,000 sometime beyond 3 years.SolutionFigure 1311 shows the annual costs (column B) and the sales prices if the building is kept 2or 3 years (columns C and E, respectively). The NPV function is applied (columns D and F) todetermine when the PW changes sign from plus to minus. These results bracket the paybackperiod for each retention period and sales price. When PW0, the 8% return is exceeded.(a) The 8% return payback period is between 3 and 4 years (column D). If the building is soldFigure 712Spreadsheet application of ROIC method using Goal Seek, Example 7.6 .after exactly 3 years for $290,000, the payback period was not exceeded; but after 4 yearsit is exceeded.(b) At a sales price of $370,000, the 8% return payback period is between 5 and 6 years (col-umnF). If the building is sold after 4 or 5 years, the payback is not exceeded; however, asale after 6 years is beyond the 8%-return payback period.EXAMPLE 13.8 NPV(8%,$B$4:B7)+$B$3PV(8%,A7,,290000)Figure 1311Payback period analysis, Example 13.8If kept 2 years andsold, payback isbetween 3 and 4If kept 3 years andsold, payback isbetween 5 and 6bla76302_ch13_340-364.indd 354 12/17/10 1:02 PMFE EXAM AND COURSEREVIEWSEach chapter concludes with severalmultiple-choice, FE Examstyleproblems that provide a simplifi edreview of chapter material. Additionally,these problems cover topics for testreviews and homework assignments.ADDITIONAL PROBLEMS AND FE EXAM REVIEW QUESTIONS8.38 When conducting a rate of return (ROR) analysisinvolving multiple mutually exclusive alterna-tives,the fi rst step is to:(a) Rank the alternatives according to decreas-inginitial investment cost(b) Rank the alternatives according to increasinginitial investment cost(c) Calculate the present worth of each alterna-tiveusing the MARR(d) Find the LCM between all of the alternatives8.39 In comparing mutually exclusive alternatives bythe ROR method, you should:(a) Find the ROR of each alternative and pickthe one with the highest ROR(b) S l h l i h i l8.43 For these alternatives, the sum of the incrementalcash fl ows is:Year A B0 10,000 14,0001 2,500 4,0002 2,500 4,0003 2,500 4,0004 2,500 4,0005 2,500 4,000(a) $2500(b) $3500(c) $6000(d) $8000 17. CASE STUDIESNew and updated case studies at theend of most chapters present real-world,in-depth treatments andexercises in the engineeringprofession. Each case includes abackground, relevant information,and an exercise section.CASE STUDYRENEWABLE ENERGY SOURCES FOR ELECTRICITY GENERATIONBackgroundPedernales Electric Cooperative (PEC) is the largestmember-owned electric co-op in the United States with over232,000 meters in 12 Central Texas counties. PEC has a ca-pacityof approximately 1300 MW (megawatts) of power, ofwhich 277 MW, or about 21%, is from renewable sources.The latest addition is 60 MW of power from a wind farm insouth Texas close to the city of Corpus Christi. A constantquestion is how much of PECs generation capacity should befrom renewable sources, especially given the environmentalissues with coal-generated electricity and the rising costs ofhydrocarbon fuels.Wind and nuclear sources are the current consideration forthe PEC leadership as Texas is increasing its generation bynuclear power and the state is the national leader in windfarmproduced electricity.Consider yourself a member of the board of directors ofPEC. You are an engineer who has been newly elected by thePEC membership to serve a 3-year term as a director-at-large.As such, you do not represent a specifi c district within theentire service area; all other directors do represent a specifi cdistrict. You have many questions about the operations ofPEC, plus you are interested in the economic and societalbenefi ts of pursuing more renewable source generationcapacity.InformationHere are some data that you have obtained. The informationis sketchy, as this point, and the numbers are very approxi-mate.Electricity generation cost estimates are nationalin scope, not PEC-specifi c, and are provided in cents perkilowatt-hour (/kWh).Generation Cost, /kWhFuel Source Likely Range Reasonable AverageCoal 4 to 9 7.4Natural gas 4 to 10.5 8.6Wind 4.8 to 9.1 8.2Solar 4.5 to 15.5 8.8National average cost of electricity to residential custom-ers:11/kWhPEC average cost to residential customers: 10.27 /kWh(from primary sources) and 10.92 /kWh (renewable sources)Expected life of a generation facility: 20 to 40 years (it islikely closer to 20 than 40)Time to construct a facility: 2 to 5 yearsCapital cost to build a generation facility: $900 to $1500per kWYou have also learned that the PEC staff uses the well-recognizedlevelized energy cost (LEC) method to determinethe price of electricity that must be charged to customers tobreak even. The formula takes into account the capital cost ofthe generation facilities, the cost of capital of borrowedmoney, annual maintenance and operation (MO) costs, andthe expected life of the facility. The LEC formula, expressedin dollars per kWh for ( t1, 2, . . . , n ), isLEC tnt1P tA tC t(1i) t tnt1E t (1i) twhere P tcapital investments made in year tA tannual maintenance and operating (MO) costsfor year tC tfuel costs for year tE tamount of electricity generated in year tnexpected life of facilityidiscount rate (cost of capital)Case Study Exercises1. If you wanted to know more about the new arrange-mentwith the wind farm in south Texas for the addi-tional60 MW per year, what types of questions wouldyou ask of a staff member in your fi rst meeting withhim or her?2. Much of the current generation capacity of PEC facilitiesutilizes coal and natural gas as the primary fuel source.What about the ethical aspects of the governments allow-ancefor these plants to continue polluting the atmospherewith the emissions that may cause health problems forcitizens and further the effects of global warming? Whattypes of regulations, if any, should be developed for PEC(and other generators) to follow in the future? 18. ACKNOWLEDGMENT OF CONTRIBUTORSIt takes the input and efforts of many individuals to make signifi cant improvements in a textbook.We wish to give special thanks to the following persons for their contributions to this edition.Paul Askenasy, Texas Commission on Environmental QualityJack Beltran, Bristol-Myers SquibbRobert Lundquist, Ohio State UniversityWilliam Peet, Infrastructure Coordination, Government of NiueSallie Sheppard, Texas AM UniversityWe thank the following individuals for their comments, feedback, and review of material to assistin making this edition a real success.Ahmed Alim, University of HoustonAlan Atalah, Bowling Green State UniversityFola Michael Ayokanmbi, Alabama AM UniversityWilliam Brown, West Virginia University at ParkersburgHector Carrasco, Colorado State UniversityPuebloRobert Chiang, California State University, PomonaRonald Cutwright, Florida State UniversityJohn F. Dacquisto, Gonzaga UniversityHoushang Darabi, University of Illinois at ChicagoFreddie Davis, West Texas AM UniversityEdward Lester Dollar, Southern Polytechnic State UniversityTed Eschenbach, University of AlaskaClara Fang, University of HartfordAbel Fernandez, University of the Pacifi cDaniel A. Franchi, California Polytechnic State University, San Luis ObispoMark Frascatore, Clarkson UniversityBenjamin M. Fries, University of Central FloridaNathan Gartner, University of MassachusettsLowellJohnny R. Graham, University of North CarolinaCharlotteLiling Huang, Northern Virginia Community CollegeDavid Jacobs, University of HartfordAdam Jannik, Northwestern State UniversityPeter E. Johnson, Valparaiso UniversityJustin W. Kile, University of WisconsinPlattevilleJohn Kushner, Lawrence Technological UniversityClifford D. Madrid, New Mexico State UniversitySaeed Manafzadeh, University of Illinois at ChicagoQuamrul Mazumder, University of MichiganFlintDeb McAvoy, Ohio UniversityGene McGinnis, Christian Brothers UniversityBruce V. Mutter, Bluefi eld State CollegeHong Sioe Oey, University of Texas at El PasoRichard Palmer, University of MassachusettsMichael J. Rider, Ohio Northern UniversityJohn Ristroph, University of Louisiana at LafayetteSaeid L. Sadri, Georgia Institute of TechnologyScott Schultz, Mercer UniversityKyo D. Song, Norfolk State UniversityJames Stevens, University of Colorado at Colorado SpringsJohn A. Stratton, Rochester Institute of TechnologyMathias J. Sutton, Purdue UniversityPete Weiss, Valparaiso University 19. xx Acknowledgment of ContributorsGreg Wiles, Southern Polytechnic State UniversityRichard Youchak, University of Pittsburgh at JohnstownWilliam A. Young, II, Ohio UniversityIf you discover errors that require correction in the next printing of the textbook or in updates ofthe online resources, please contact us. We hope you fi nd the contents of this edition helpful inyour academic and professional activities.Leland Blank lelandblank@yahoo.comAnthony Tarquin atarquin@utep.edu 20. L E A R N I N G S TA G E 1The FundamentalsLEARNING STAGE 1The FundamentalsCHAPTER 1Foundations ofEngineering EconomyCHAPTER 2Factors: How Timeand Interest AffectMoneyCHAPTER 3Combining Factorsand SpreadsheetFunctionsCHAPTER 4Nominal and EffectiveInterest RatesThe fundamentals of engineering economy are introduced inthese chapters. When you have completed stage 1, you will beable to understand and work problems that account for thetime value of money, cash fl ows occurring at different times withdifferent amounts, and equivalence at different interest rates. Thetechniques you master here form the basis of how an engineer inany discipline can take economic value into account in virtually anyproject environment.The factors commonly used in all engineering economy computa-tionsare introduced and applied here. Combinations of these fac-torsassist in moving monetary values forward and backward throughtime and at different interest rates. Also, after these chapters, youshould be comfortable using many of the spreadsheet functions.Many of the terms common to economic decision making areintroduced in learning stage 1 and used in later chapters. A check-markicon in the margin indicates that a new concept or guidelineis introduced at this point. 21. Purpose: Understand and apply fundamental concepts and use the terminology of engineering economics.CHAPTER 1Foundationsof EngineeringEconomyL E A R N I N G O U T C O M E SS E C T I O N T O P I C L E A R N I N G O U T C O M E1.1 Description and role Defi ne engineering economics and describe itsrole in decision making.1.2 Engineering economy studyapproach Understand and identify the steps in anengineering economy study.1.3 Ethics and economics Identify areas in which economic decisions canpresent questionable ethics.1.4 Interest rate Perform calculations for interest rates and ratesof return.1.5 Terms and symbols Identify and use engineering economicterminology and symbols.1.6 Cash fl ows Understand cash fl ows and how to graphicallyrepresent them.1.7 Economic equivalence Describe and calculate economic equivalence.1.8 Simple and compound interest Calculate simple and compound interestamounts for one or more time periods.1.9 MARR and opportunity cost State the meaning and role of MinimumAttractive Rate of Return (MARR) andopportunity costs.1.10 Spreadsheet functions Identify and use some Excel functionscommonly applied in engineering economics. 22. he need for engineering economy is primarily motivated by the work that engineersdo in performing analyses, synthesizing, and coming to a conclusion as they work onprojects of all sizes. In other words, engineering economy is at the heart of makingTdecisions . These decisions involve the fundamental elements of cash fl ows of money, time,and interest rates. This chapter introduces the basic concepts and terminology necessary foran engineer to combine these three essential elements in organized, mathematically correctways to solve problems that will lead to better decisions.1.1 Engineering Economics: Description andRole in Decision MakingDecisions are made routinely to choose one alternative over another by individuals in everydaylife; by engineers on the job; by managers who supervise the activities of others; by corporatepresidents 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 inamount. The decision of where and how to invest this limited capital is motivated by a primarygoal 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 experienceto design, analyze, and synthesize. The factors upon which a decision is based are commonly acombination of economic and noneconomic elements. Engineering economy deals with theeconomic factors. By defi nition,Engineering economy involves formulating, estimating, and evaluating the expected economicoutcomes of alternatives designed to accomplish a defi ned purpose. Mathematical techniquessimplify the economic evaluation of alternatives.Because the formulas and techniques used in engineering economics are applicable to alltypes of money matters, they are equally useful in business and government, as well as forindividuals. Therefore, besides applications to projects in your future jobs, what you learnfrom this book and in this course may well offer you an economic analysis tool for makingpersonal 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 intheir decision-making process. Since most decisions affect what will be done, the time frame ofengineering economy is primarily the future . Therefore, the numbers used in engineering econ-omyare best estimates of what is expected to occur . The estimates and the decision usuallyinvolve four essential elements:Cash fl owsTimes of occurrence of cash fl owsInterest rates for time value of moneyMeasure of economic worth for selecting an alternativeSince the estimates of cash fl ow amounts and timing are about the future, they will be some-whatdifferent than what is actually observed, due to changing circumstances and unplannedevents. In short, the variation between an amount or time estimated now and that observedin the future is caused by the stochastic (random) nature of all economic events. Sensitivityanalysis 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 fundamentalnature of variation in estimates and how this variation may be included in the analysis at avery basic level.EXAMPLE 1.1An engineer is performing an analysis of warranty costs for drive train repairs within the fi rstyear of ownership of luxury cars purchased in the United States. He found the average cost (tothe nearest dollar) to be $570 per repair from data taken over a 5-year period. 23. 4 Chapter 1 Foundations of Engineering EconomyYear 2006 2007 2008 2009 2010Average Cost, $/repair 525 430 619 650 625What range of repair costs should the engineer use to ensure that the analysis is sensitive tochanging warranty costs?SolutionAt fi rst glance the range should be approximately 25% to 15% of the $570 average cost toinclude the low of $430 and high of $650. However, the last 3 years of costs are higher andmore consistent with an average of $631. The observed values are approximately 3% of thismore 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 rangeof, say, 20% or 25% of $570 is recommended.The criterion used to select an alternative in engineering economy for a specifi c set of estimatesis called a measure of worth . The measures developed and used in this text arePresent 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 EffectivenessAll these measures of worth account for the fact that money makes money over time. This is theconcept of the time value of money.It is a well-known fact that money makes money. The time value of money explains the changein 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 investcapital (money) in a project today, we inherently expect to have more money in the future thanwe invested. If we borrow money today, in one form or another, we expect to return the originalamount plus some additional amount of money.Engineering economics is equally well suited for the future and for the analysis of past cashfl ows 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 NewYork 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 itis currently worth $127.25 per share for a total of $6744.25. This increase in value represents arate of return of 10.67% per year. (These type of calculations are explained later.) This pasti nvestment has well exceeded the 8% per year criterion over the last 3 years.1.2 Performing an Engineering Economy StudyAn engineering economy study involves many elements: problem identifi cation, defi nition of theobjective, cash fl ow estimation, fi nancial analysis, and decision making. Implementing a struc-turedprocedure 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.Time value of money 24. 1.2 Performing an Engineering Economy Study 55. Evaluate each alternative; consider noneconomic factors; use sensitivity analysis as needed.6. Select the best alternative.7. Implement the solution and monitor the results.Technically, the last step is not part of the economy study, but it is, of course, a step needed tomeet the project objective. There may be occasions when the best economic alternativerequires more capital funds than are available, or signifi cant noneconomic factors preclude themost economic alternative from being chosen. Accordingly, steps 5 and 6 may result in selectionof an alternative different from the economically best one. Also, sometimes more than one proj-ectmay 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 11 illustrates the steps above forone 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 andprimary objective(s) is very important to the formation of an alternative solution. As an illustra-tion,assume the problem is that a coal-fueled power plant must be shut down by 2015 due to theproduction of excessive sulfur dioxide. The objectives may be to generate the forecasted electricityStep instudy1Expected lifeRevenuesCostsTaxesProject financingPW, ROR, B/C, etc.New engineeringeconomy studybegins35671Timepasses24ProblemdescriptionObjectivestatementAvailable dataAlternatives forsolutionCash flows andother estimatesMeasure of worthcriterionEngineeringeconomic analysisBest alternativeselectionImplementationand monitoringNew problemdescriptionOne or more approachesto meet objectiveConsider: Noneconomic factors Sensitivity analysis Risk analysisFigure 11Steps in an engineering economy study. 25. 6 Chapter 1 Foundations of Engineering Economyneeded for 2015 and beyond, plus to not exceed all the projected emission allowances in thesefuture years.Alternatives These are stand-alone descriptions of viable solutions to problems that can meetthe objectives. Words, pictures, graphs, equipment and service descriptions, simulations, etc.defi ne each alternative. The best estimates for parameters are also part of the alternative. Someparameters include equipment fi rst cost, expected life, salvage value (estimated trade-in, resale,or market value), and annual operating cost (AOC), which can also be termed maintenance andoperating (MO) 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 aredescribed and analyzed, one will likely be selected and implementation initiated. If a third, moreattractive method that was available is later recognized, a wrong decision was made.Cash Flows All cash fl ows are estimated for each alternative. Since these are future expendi-turesand revenues, the results of step 3 usually prove to be inaccurate when an alternative isactually in place and operating. When cash fl ow estimates for specifi c parameters are expected tovary signifi cantly from a point estimate made now, risk and sensitivity analyses (step 5) areneeded to improve the chances of selecting the best alternative. Sizable variation is usually ex-pectedin estimates of revenues, AOC, salvage values, and subcontractor costs. Estimation ofcosts is discussed in Chapter 15, and the elements of variation (risk) and sensitivity analysis areincluded throughout the text.Engineering Economy Analysis The techniques and computations that you will learn anduse throughout this text utilize the cash fl ow estimates, time value of money, and a selectedmeasure of worth. The result of the analysis will be one or more numerical values; this can bein one of several terms, such as money, an interest rate, number of years, or a probability. Inthe end, a selected measure of worth mentioned in the previous section will be used to selectthe best alternative.Before an economic analysis technique is applied to the cash fl ows, some decisions aboutwhat to include in the analysis must be made. Two important possibilities are taxes andinfl ation. Federal, state or provincial, county, and city taxes will impact the costs of everyalternative. An after-tax analysis includes some additional estimates and methods compared toa before-tax a nalysis. If taxes and infl ation are expected to impact all alternatives equally, theymay 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 importantto the decision, an additional set of computations must be added to the analysis; Chapter 14covers the details.Selection of the Best Alternative The measure of worth is a primary basis for selectingthe best economic alternative. For example, if alternative A has a rate of return (ROR) of15.2% per year and alternative B will result in an ROR of 16.9% per year, B is better eco-nomically.However, there can always be noneconomic or intangible factors that must beconsidered 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 managements or the board of directors interest in a particular alternative Goodwill offered by an alternative toward a group: employees, union, county, etc.As indicated in Figure 11 , once all the economic, noneconomic, and risk factors have beenevaluated, a fi nal decision of the best alternative is made.At times, only one viable alternative is identifi ed. In this case, the do-nothing (DN) alterna-tivemay be chosen provided the measure of worth and other factors result in the alternative beinga poor choice. The do-nothing alternative maintains the status quo. 26. 1.3 Professional Ethics and Economic Decisions 7Whether 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 youdefi ne 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, adifferent route might be selected each time. In economic analysis, fi nancial units (dollars orother currency) are generally used as the tangible basis for evaluation. Thus, when there areseveral ways of accomplishing a stated objective, the alternative with the lowest overall cost orhighest overall net income is selected.1.3 Professional Ethics and Economic DecisionsMany of the fundamentals of engineering ethics are intertwined with the roles of money andeconomics-based decisions in the making of professionally ethical judgments. Some of theseintegral connections are discussed here, plus sections in later chapters discuss additional aspectsof ethics and economics. For example, Chapter 9, Benefi t/Cost Analysis and Public Sector Eco-nomics,includes material on the ethics of public project contracts and public policy. Although itis very limited in scope and space, it is anticipated that this coverage of the important role ofeconomics in engineering ethics will prompt further interest on the part of students and instruc-torsof engineering economy.The terms morals and ethics are commonly used interchangeably, yet they have slightlydifferent interpretations. Morals usually relate to the underlying tenets that form the characterand conduct of a person in judging right and wrong. Ethical practices can be evaluated byusing a code of morals or code of ethics that forms the standards to guide decisions andactions of individuals and organizations in a profession, for example, electrical, chemical,mechanical, industrial, or civil engineering. There are several different levels and types ofmorals and ethics.Universal or common morals These are fundamental moral beliefs held by virtually all peo-ple.Most people agree that to steal, murder, lie, or physically harm someone is wrong.It is possible for actions and intentions to come into confl ict concerning a common moral.Consider the World Trade Center buildings in New York City. After their collapse on September 11,2001, it was apparent that the design was not suffi cient to withstand the heat generated by thefi restorm caused by the impact of an aircraft. The structural engineers who worked on the designsurely did not have the intent to harm or kill occupants in the buildings. However, their designactions did not foresee this outcome as a measurable possibility. Did they violate the commonmoral belief of not doing harm to others or murdering?Individual or personal morals These are the moral beliefs that a person has and maintainsover time. These usually parallel the common morals in that stealing, lying, murdering, etc. areimmoral acts.It is quite possible that an individual strongly supports the common morals and has excellentpersonal morals, but these may confl ict from time to time when decisions must be made. Con-siderthe engineering student who genuinely believes that cheating is wrong. If he or she does notknow how to work some test problems, but must make a certain minimum grade on the fi nalexam to graduate, the decision to cheat or not on the fi nal exam is an exercise in following orviolating a personal moral.Professional or engineering ethics Professionals in a specifi c discipline are guided in theirdecision making and performance of work activities by a formal standard or code. The codestates the commonly accepted standards of honesty and integrity that each individual is expectedto demonstrate in her or his practice. There are codes of ethics for medical doctors, attorneys,and, of course, engineers.Although each engineering profession has its own code of ethics, the Code of Ethics forEngineers published by the National Society of Professional Engineers (NSPE) is very com-monlyused and quoted. This code, reprinted in its entirety in Appendix C, includes numeroussections that have direct or indirect economic and fi nancial impact upon the designs, actions, 27. 8 Chapter 1 Foundations of Engineering Economyand decisions that engineers make in their professional dealings. Here are three examples fromthe Code:Engineers, in the fulfi llment of their duties, shall hold paramount the safety, health, and wel-fareof the public . (section I.1)Engineers shall not accept fi nancial or other considerations , including free engineering de-signs,from material or equipment suppliers for specifying their product. (section III.5.a)Engineers using designs supplied by a client recognize that the designs remain the propertyof the client and may not be duplicated by the engineer for others without express permission.(section III.9.b)As with common and personal morals, confl icts can easily rise in the mind of an engineerbetween his or her own ethics and that of the employing corporation. Consider a manufacturingengineer who has recently come to fi rmly disagree morally with war and its negative effects onhuman beings. Suppose the engineer has worked for years in a military defense contractorsfacility and does the detailed cost estimations and economic evaluations of producing fi ghterjets for the Air Force. The Code of Ethics for Engineers is silent on the ethics of producing andusing war materiel. Although the employer and the engineer are not violating any ethics code,the engineer, as an individual, is stressed in this position. Like many people during a decliningnational economy, retention of this job is of paramount importance to the family and the engi-neer.Confl icts such as this can place individuals in real dilemmas with no or mostly unsatisfactoryalternatives.At fi rst thought, it may not be apparent how activities related to engineering economics maypresent an ethical challenge to an individual, a company, or a public servant in government ser-vice.Many money-related situations, such as those that follow, can have ethical dimensions.In the design stage: Safety factors are compromised to ensure that a price bid comes in as low as possible. Family or personal connections with individuals in a company offer unfair or insider informa-tionthat allows costs to be cut in strategic areas of a project. A potential vendor offers specifi cations for company-specifi c equipment, and the design engi-neerdoes not have suffi cient time to determine if this equipment will meet the needs of theproject being designed and costed.While the system is operating: Delayed or below-standard maintenance can be performed to save money when cost overrunsexist in other segments of a project. Opportunities to purchase cheaper repair parts can save money for a subcontractor working ona fi xed-price contract. Safety margins are compromised because of cost, personal inconvenience to workers, tighttime schedules, etc.A good example of the last itemsafety is compromised while operating the systemis thesituation that arose in 1984 in Bhopal, India (Martin and Schinzinger 2005, pp. 2458). A UnionCarbide plant manufacturing the highly toxic pesticide chemical methyl isocyanate (MIC) expe-rienceda large gas leak from high-pressure tanks. Some 500,000 persons were exposed to inhala-tionof this deadly gas that burns moist parts of the body. There were 2500 to 3000 deaths withindays, and over the following 10-year period, some 12,000 death claims and 870,000 personalinjury claims were recorded. Although Union Carbide owned the facility, the Indian governmenthad only Indian workers in the plant. Safety practices clearly eroded due to cost-cutting mea-sures,insuffi cient repair parts, and reduction in personnel to save salary money. However, one ofthe surprising practices that caused unnecessary harm to workers was the fact that masks, gloves,and other protective gear were not worn by workers in close proximity to the tanks containingMIC. Why? Unlike in plants in the United States and other countries, there was no air condition-ingin the Indian plant, resulting in high ambient temperatures in the facility.Many ethical questions arise when corporations operate in international settings where thecorporate rules, worker incentives, cultural practices, and costs in the home country differ fromthose in the host country. Often these ethical dilemmas are fundamentally based in the economicsthat provide cheaper labor, reduced raw material costs, less government oversight, and a host of 28. 1.3 Professional Ethics and Economic Decisions 9other cost-reducing factors. When an engineering economy study is performed, it is important forthe engineer performing the study to consider all ethically related matters to ensure that the costand revenue estimates refl ect what is likely to happen once the project or system is operating.It is important to understand that the translation from universal morals to personal morals andprofessional ethics does vary from one culture and country to another. As an example, consider thecommon belief (universal moral) that the awarding of contracts and fi nancial arrangements for ser-vicesto be performed (for government or business) should be accomplished in a fair and transparentfashion. In some societies and cultures, corruption in the process of contract making is common andoften overlooked by the local authorities, who may also be involved in the affairs. Are these im-moralor unethical practices? Most would say, Yes, this should not be allowed. Find and punish theindividuals involved. Yet, such practices do continue, thus indicating the differences in interpreta-tionof common morals as they are translated into the ethics of individuals and professionals.EXAMPLE 1.2Jamie is an engineer employed by Burris, a United Statesbased company that develops sub-wayand surface transportation systems for medium-sized municipalities in the United Statesand Canada. He has been a registered professional engineer (PE) for the last 15 years. Lastyear, Carol, an engineer friend from university days who works as an individual consultant,asked Jamie to help her with some cost estimates on a metro train job. Carol offered to pay forhis time and talent, but Jamie saw no reason to take money for helping with data commonlyused by him in performing his job at Burris. The estimates took one weekend to complete, andonce Jamie delivered them to Carol, he did not hear from her again; nor did he learn the iden-tityof the company for which Carol was preparing the estimates.Yesterday, Jamie was called into his supervisors offi ce and told that Burris had not receivedthe contract award in Sharpstown, where a metro system is to be installed. The project esti-mateswere prepared by Jamie and others at Burris over the past several months. This job wasgreatly needed by Burris, as the country and most municipalities were in a real economicslump, so much so that Burris was considering furloughing several engineers if the Sharpstownbid was not accepted. Jamie was told he was to be laid off immediately, not because the bid wasrejected, but because he had been secretly working without management approval for a primeconsultant of Burris main competitor. Jamie was astounded and angry. He knew he had donenothing to warrant fi ring, but the evidence was clearly there. The numbers used by the com-petitorto win the Sharpstown award were the same numbers that Jamie had prepared for Burrison this bid, and they closely matched the values that he gave Carol when he helped her.Jamie was told he was fortunate, because Burris president had decided to not legally chargeJamie with unethical behavior and to not request that his PE license be rescinded. As a result,Jamie was escorted out of his offi ce and the building within one hour and told to not ask anyoneat Burris for a reference letter if he attempted to get another engineering job.Discuss the ethical dimensions of this situation for Jamie, Carol, and Burris management.Refer to the NSPE Code of Ethics for Engineers (Appendix C) for specifi c points of concern.SolutionThere are several obvious errors and omissions present in the actions of Jamie, Carol, andB urris management in this situation. Some of these mistakes, oversights, and possible codeviolations are summarized here.Jamie Did not learn identity of company Carol was working for and whether the company was tobe a bidder on the Sharpstown project Helped a friend with confi dential data, probably innocently, without the knowledge or ap-provalof his employer Assisted a competitor, probably unknowingly, without the knowledge or approval of hisemployer Likely violated, at least, Code of Ethics for Engineers section II.1.c, which reads, Engi-neersshall not reveal facts, data, or information without the prior consent of the client oremployer except as authorized or required by law or this Code. 29. 10 Chapter 1 Foundations of Engineering EconomyCarol Did not share the intended use of Jamies work Did not seek information from Jamie concerning his employers intention to bid on thesame project as her client Misled Jamie in that she did not seek approval from Jamie to use and quote his informationand assistance Did not inform her client that portions of her work originated from a source employed by apossible bid competitor Likely violated, at least, Code of Ethics for Engineers section III.9.a, which reads, Engi-neersshall, whenever possible, name the person or persons who may be individually re-sponsiblefor designs, inventions, writings, or other accomplishments.Burris management Acted too fast in dismissing Jamie; they should have listened to Jamie and conducted aninvestigation Did not put him on administrative leave during a review Possibly did not take Jamies previous good work record into accountThese are not all ethical considerations; some are just plain good business practices for Jamie,Carol, and Burris.1.4 Interest Rate and Rate of ReturnInterest is the manifestation of the time value of money. Computationally, interest is the differencebetween an ending amount of money and the beginning amount. If the difference is zero or nega-tive,there is no interest. There are always two perspectives to an amount of interestinterest paidand interest earned. These are illustrated in Figure 12 . Interest is paid when a person or organiza-tionborrowed money (obtained a loan) and repays a larger amount over time. Interest is earnedwhen a person or organization saved, invested, or lent money and obtains a return of a largeramount over time. The numerical values and formulas used are the same for both perspectives, butthe interpretations are different.Interest paid on borrowed funds (a loan) is determined using the original amount, also calledthe principal,Interestamount owed nowprincipal [1.1]When interest paid over a specifi c time unit is expressed as a percentage of the principal, the re-sultis called the interest rate.Interest rate (%) interest accrued per time unit principal 100% [1.2]The time unit of the rate is called the interest period. By far the most common interest periodused to state an interest rate is 1 year. Shorter time periods can be used, such as 1% per month.Thus, the interest period of the interest rate should always be included. If only the rate is stated,for example, 8.5%, a 1-year interest period is assumed.LoanRepayment(a) (b)Bank interest BorrowerCorporationInvestorLoanRepayment interestFigure 12(a) Interest paid over time to lender. (b) Interest earned over time by investor. 30. 1.4 Interest Rate and Rate of Return 11EXAMPLE 1.3An employee at LaserKinetics.com borrows $10,000 on May 1 and must repay a total of$10,700 exactly 1 year later. Determine the interest amount and the interest rate paid.SolutionThe perspective here is that of the borrower since $10,700 repays a loan. Apply Equation [1.1]to determine the interest paid.Interest paid$10,70010,000$700Equation [1.2] determines the interest rate paid for 1 year.Percent interest rate$700 $10,000 100%7% per yearEXAMPLE 1.4Stereophonics, Inc., plans to borrow $20,000 from a bank for 1 year at 9% interest for newrecording equipment. ( a ) Compute the interest and the total amount due after 1 year. ( b ) Con-structa column graph that shows the original loan amount and total amount due after 1 yearused to compute the loan interest rate of 9% per year.Solution(a) Compute the total interest accrued by solving Equation [1.2] for interest accrued.Interest$20,000(0.09)$1800The total amount due is the sum of principal and interest.Total due$20,0001800$21,800(b) Figure 13 shows the values used in Equation [1.2]: $1800 interest, $20,000 original loanprincipal, 1-year interest period.$Now$21,800$20,000Interest = $1800Originalloanamount1 yearlaterInterestperiod is1 yearInterest rate$1800$20,00 0100%= 9% per yearFigure 13Values used to compute an interest rate of 9% per year. Example 1.4.CommentNote that in part ( a ), the total amount due may also be computed asTotal dueprincipal(1interest rate)$20,000(1.09)$21,800Later we will use this method to determine future amounts for times longer than one interestperiod. 31. 12 Chapter 1 Foundations of Engineering EconomyFrom the perspective of a saver, a lender, or an investor, interest earned ( Figure 12 b ) is thefi nal amount minus the initial amount, or principal.Interest earnedtotal amount nowprincipal [1.3]Interest earned over a specifi c period of time is expressed as a percentage of the original amountand is called rate of return (ROR).Rate of return (%) interest accrued per time unit principal 100% [1.4]The time unit for rate of return is called the interest period, just as for the borrowers perspec-tive.Again, the most common period is 1 year.The term return on investment (ROI) is used equivalently with ROR in different industries andsettings, especially where large capital funds are committed to engineering-oriented programs.The numerical values in Equations [1.2] and [1.4] are the same, but the term interest rate paidis more appropriate for the borrowers perspective, while the rate of return earned is better forthe investors perspective.(a) Calculate the amount deposited 1 year ago to have $1000 now at an interest rate of 5%per year.(b) Calculate the amount of interest earned during this time period.Solution(a) The total amount accrued ($1000) is the sum of the original deposit and the earned interest.If X is the original deposit,Total accrueddepositdeposit(interest rate)$1000XX (0.05)X (10.05)1.05 XThe original deposit isX 10001.05 $952.38(b) Apply Equation [1.3] to determine the interest earned.Interest$1000952.38$47.62EXAMPLE 1.5In Examples 1.3 to 1.5 the interest period was 1 year, and the interest amount was calculatedat the end of one period. When more than one interest period is involved, e.g., the amount of in-terestafter 3 years, it is necessary to state whether the interest is accrued on a simple or compoundbasis from one period to the next. This topic is covered later in this chapter.Since infl ation can signifi cantly increase an interest rate, some comments about the funda-mentalsof infl ation are warranted at this early stage. By defi nition, infl ation represents a decreasein the value of a given currency. That is, $10 now will not purchase the same amount of gasolinefor your car (or most other things) as $10 did 10 years ago. The changing value of the currencyaffects market interest rates.In simple terms, interest rates refl ect two things: a so-called real rate of return plus the expectedinfl ation rate. The real rate of return allows the investor to purchase more than he or she couldhave purchased before the investment, while infl ation raises the real rate to the market rate thatwe use on a daily basis.The safest investments (such as government bonds) typically have a 3% to 4% real rate ofreturn built into their overall interest rates. Thus, a market interest rate of, say, 8% per year on abond means that investors expect the infl ation rate to be in the range of 4% to 5% per year.Clearly, infl ation causes interest rates to rise.From the borrowers perspective, the rate of infl ation is another interest rate tacked on to thereal interest rate . And from the vantage point of the saver or investor in a fi xed-interest account,Infl ation 32. 1.5 Terminology and Symbols 13infl ation reduces the real rate of return on the investment. Infl ation means that cost and revenuecash fl ow estimates increase over time. This increase is due to the changing value of money thatis forced upon a countrys currency by infl ation, thus making a unit of currency (such as the dol-lar)worth less relative to its value at a previous time. We see the effect of infl ation in that moneypurchases less now than it did at a previous time. Infl ation contributes to A reduction in purchasing power of the currency An increase in the CPI (consumer price index) An increase in the cost of equipment and its maintenance An increase in the cost of salaried professionals and hourly employees A reduction in the real rate of return on personal savings and certain corporate investmentsIn other words, infl ation can materially contribute to changes in corporate and personal economicanalysis.Commonly, engineering economy studies assume that infl ation affects all estimated valuesequally. Accordingly, an interest rate or rate of return, such as 8% per year, is applied throughoutthe analysis without accounting for an additional infl ation rate. However, if infl ation were explic-itlytaken into account, and it was reducing the value of money at, say, an average of 4% per year,then it would be necessary to perform the economic analysis using an infl ated interest rate. (Therate is 12.32% per year using the relations derived in Chapter 14.)1.5 Terminology and SymbolsThe equations and procedures of engineering economy utilize the following terms and symbols.Sample units are indicated.Pvalue or amount of money at a time designated as the present or time 0. Also P isreferred to as present worth (PW), present value (PV), net present value (NPV), dis-countedcash fl ow (DCF), and capitalized cost (CC); monetary units, such as dollarsFvalue or amount of money at some future time. Also F is called future worth (FW)and future value (FV); dollarsAseries of consecutive, equal, end-of-period amounts of money. Also A is called theannual worth (AW) and equivalent uniform annual worth (EUAW); dollars peryear, euros per monthnnumber of interest periods; years, months, daysiinterest rate per time period; percent per year, percent per monthttime, stated in periods; years, months, daysThe symbols P and F represent one-time occurrences: A occurs with the same value in each inter-estperiod for a specifi ed number of periods. It should be clear that a present value P represents asingle sum of money at some time prior to a future value F or prior to the fi rst occurrence of anequivalent series amount A .It is important to note that the symbol A always represents a uniform amount (i.e., the sameamount each period) that extends through consecutive interest periods. Both conditions mustexist 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-lessstated otherwise, assume that the rate applies throughout the entire n years or interest peri-ods.The decimal equivalent for i is always used in formulas and equations in engineering econ-omycomputations.All engineering economy problems involve the element of time expressed as n and interestrate i . In general, every problem will involve at least four of the symbols P , F , A , n , and i , with atleast three of them estimated or known.Additional symbols used in engineering economy are defi ned in Appendix E.EXAMPLE 1.6Today, Julie borrowed $5000 to purchase furniture for her new house. She can repay the loanin either of the two ways described below. Determine the engineering economy symbols andtheir value for each option. 33. 14 Chapter 1 Foundations of Engineering Economy(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 i5% per year n5 years A?(b) Repayment requires a single future amount F, which is unknown.P$5000 i7% per year n3 years F?EXAMPLE 1.7You 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, startingnext year. At the end of the sixth year, you plan to close your account by withdrawing the re-mainingmoney. Defi ne the engineering economy symbols involved.SolutionAll fi ve symbols are present, but the future value in year 6 is the unknown.P$5000A$1000 per year for 5 yearsF? at end of year 6i6% per yearn5 years for the A series and 6 for the F valueEXAMPLE 1.8Last year Janes grandmother offered to put enough money into a savings account to generate$5000 in interest this year to help pay Janes 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 interestnow, if the rate of return is 6% per year.Solution(a) Symbols P (last year is 1) and F (this year) are needed.P?i6% per yearn1 yearFPinterest?$5000(b) Let Ftotal amount now and Poriginal amount. We know that F P$5000 isaccrued interest. Now we can determine P . Refer to Equations [1.1] through [1.4].FPPiThe $5000 interest can be expressed asInterestF P( PPi ) P Pi$5000P (0.06)P$5000 0.06 $83,333.33 34. 1.6 Cash Flows: Estimation and Diagramming 151.6 Cash Flows: Estimation and DiagrammingAs mentioned in earlier sections, cash fl ows are the amounts of money estimated for future projectsor observed for project events that have taken place. All cash fl ows occur during specifi c time peri-ods,such as 1 month, every 6 months, or 1 year. Annual is the most common time period. Forexample, a payment of $10,000 once every year in December for 5 years is a series of 5 outgoingcash fl ows. And an estimated receipt of $500 every month for 2 years is a series of 24 incoming cashfl ows. Engineering economy bases its computations on the timing, size, and direction of cash fl ows.Cash infl ows are the receipts, revenues, incomes, and savings generated by project and businessactivity. A plus sign indicates a cash infl ow.Cash outfl ows are costs, disbursements, expenses, and taxes caused by projects and business Cash fl owactivity. A negative or minus sign indicates 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.Of all the steps in Figure 11 that outline the engineering economy study, estimating cash fl ows(step 3) is the most diffi cult, primarily because it is an attempt to predict the future. Some ex-amplesof cash fl ow estimates are shown here. As you scan these, consider how the cash infl owor outfl ow may be estimated most accurately.Cash Infl ow EstimatesIncome: $150,000 per year from sales of solar-powered watchesSavings: $24,500 tax savings from capital loss on equipment salvageReceipt: $750,000 received on large business loan plus accrued interestSavings: $150,000 per year saved by installing more effi cient air conditioningRevenue: $50,000 to $75,000 per month in sales for extended battery life iPhonesCash Outfl ow EstimatesOperating costs: $230,000 per year annual operating costs for software servicesFirst cost: $800,000 next year to purchase replacement earthmoving equipmentExpense: $20,000 per year for loan interest payment to bankInitial cost: $1 to $1.2 million in capital expenditures for a water recycling unitAll of these are point estimates, that is, single-value estimates for cash fl ow elements of analternative, 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 experiencewith the systems to be more accurate. For the initial chapters, we will utilize point estimates. The useof risk and sensitivity analysis for range estimates is covered in the later chapters of this book.Once all cash infl ows and outfl ows are estimated (or determined for a completed project), thenet cash fl ow for each time period is calculated.Net cash fl owcash infl owscash outfl ows [1.5]NCFRD [1.6]where NCF is net cash fl ow, R is receipts, and D is disbursements.At the beginning of this section, the timing, size, and direction of cash fl ows were mentionedas important. Because cash fl ows may take place at any time during an interest period, as a matterof convention, all cash fl ows are assumed to occur at the end of an interest period.The end-of-period convention means that all cash infl ows and all cash outfl ows are assumed totake place at the end of the interest period in which they actually occur. When several infl owsand outfl ows occur within the same period, the net cash fl ow is assumed to occur at the end ofthe period.End-of-period convention 35. 16 Chapter 1 Foundations of Engineering EconomyYear 13 4i = 4% per year2 YearIn assuming end-of-period cash fl ows, it is important to understand that future (F) and uniformannual (A) amounts are located at the end of the interest period, which is not necessarilyDecember 31. If in Example 1.7 the lump-sum deposit took place on July 1, 2011, the withdraw-alswill take place on July 1 of each succeeding year for 6 years. Remember, end of the periodmeans end of interest period, not end of calendar year.The cash fl ow diagram is a very important tool in an economic analysis, especially when thecash fl ow series is complex. It is a graphical representation of cash fl ows drawn on the y axis witha time scale on the x axis. The diagram includes what is known, what is estimated, and what isneeded. That is, once the cash fl ow diagram is complete, another person should be able to workthe problem by looking at the diagram.Cash fl ow diagram time t0 is the present, and t1 is the end of time period 1. We assumethat the periods are in years for now. The time scale of Figure 14 is set up for 5 years. Since theend-of-year convention places cash fl ows at the ends of years, the 1 marks the end of year 1.While it is not necessary to use an exact scale on the cash fl ow diagram, you will probablyavoid errors if you make a neat diagram to approximate scale for both time and relative cash fl owmagnitudes.The direction of the arrows on the diagram is important to differentiate income from outgo. Avertical arrow pointing up indicates a positive cash fl ow. Conversely, a down-pointing arrow in-dicatesa negative cash fl ow. We will use a bold, colored arrow to indicate what is unknownand to be determined. For example, if a future value F is to be determined in year 5, a wide,colored arrow with F? is shown in year 5. The interest rate is also indicated on the diagram.Figure 15 illustrates a cash infl ow at the end of year 1, equal cash outfl ows at the end of years 2and 3, an interest rate of 4% per year, and the unknown future value F after 5 years. The arrowfor the unknown value is generally drawn in the opposite direction from the other cash fl ows;however, the engineering economy computations will determine the actual sign on the F value.Before the diagramming of cash fl ows, a perspective or vantage point must be determined sothator signs can be assigned and the economic analysis performed correctly. Assume youborrow $8500 from a bank today to purchase an $8000 used car for cash next week, and you planto spend the remaining $500 on a new paint job for the car two weeks from now. There are sev-eralperspectives possible when developing the cash fl ow diagramthose of the borrower (thatsyou), the banker, the car dealer, or the paint shop owner. The cash fl ow signs and amounts forthese perspectives are as follows.Perspective Activity Cash fl ow with Sign, $ Time, weekYou Borrow 8500 0Buy car 8000 1Paint job 500 2Banker Lender 8500 0Car dealer Car sale 8000 1Painter Paint job 500 2Figure 14A typical cash fl ow timescale for 5 years.0 12Time scaleYear 551F = ?+3 4 5Cash flowFigure 15Example of positive andnegative cash fl ows. 36. 1.6 Cash Flows: Estimation and Diagramming 17$850001$80002$500WeekFigure 16Cash fl ows from perspective of borrower for loan and purchases.One, and only one, of the perspectives is selected to develop the diagram. For your perspective,all three cash fl ows are involved and the diagram appears as shown in Figure 16 with a time scaleof weeks. Applying the end-of-period convention, you have a receipt of $8500 now (time 0) andcash outfl ows of $8000 at the end of week 1, followed by $500 at the end of week 2.EXAMPLE 1.9Each year Exxon-Mobil expends large amounts of funds for mechanical safety featuresthroughout its worldwide operations. Carla Ramos, a lead engineer for Mexico and CentralAmerican operations, plans expenditures of $1 million now and each of the next 4 years justfor the improvement of fi eld-based pressure-release valves. Construct the cash fl ow diagram tofi nd the equivalent value of these expenditures at the end of year 4, using a cost of capital esti-matefor safety-related funds of 12% per year.SolutionFigure 17 indicates the uniform and negative cash fl ow series (expenditures) for fi ve periods,and the unknown F value (positive cash fl ow equivalent) at exactly the same time as the fi fthexpenditure. Since the expenditures start immediately, the fi rst $1 million is shown at time 0,not time 1. Therefore, the last negative cash fl ow occurs at the end of the fourth year, when Falso occurs. To make this diagram have a full 5 years on the time scale, the addition of theyear 1 completes the diagram. This addition demonstrates that year 0 is the end-of-periodpoint for the year 1.i = 12% F = ?0 1 2A = $1,000,000Figure 17Cash fl ow diagram, Example 1.9.31 4 YearEXAMPLE 1.10An electrical engineer wants to deposit an amount P now such that she can withdraw an equalannual amount of A1$2000 per year for the fi rst 5 years, starting 1 year after the deposit, anda different annual withdrawal of A2 $3000 per year for the following 3 years. How would thecash fl ow diagram appear if i8.5% per year? 37. 18 Chapter 1 Foundations of Engineering EconomySolutionThe cash fl ows are shown in Figure 18. The negative cash outfl ow P occurs now. The with-drawals(positive cash infl ow) for the A1 series occur at the end of years 1 through 5, and A2A2 = $3000A1 = $20001 2 3 4 5 6YearA rental company spent $2500 on a new air compressor 7 years ago. The annual rental incomefrom the compressor has been $750. The $100 spent on maintenance the fi rst year has in-creasedeach year by $25. The company plans to sell the compressor at the end of next year for$150. Construct the cash fl ow diagram from the companys perspective and indicate where thepresent worth now is located.SolutionLet now be time t0. The incomes and costs for years 7 through 1 (next year) are tabulatedbelow with net cash fl ow computed using Equation [1.5]. The net cash fl ows (one negative,eight positive) are diagrammed in Figure 19 . Present worth P is located at year 0.End of Year Income Cost Net Cash Flow7 $ 0 $2500 $25006 750 100 6505 750 125 6254 750 150 6003 750 175 5752 750 200 5501 750 225 5250 750 250 5001 750150 275 625EXAMPLE 1.11Figure 19Cash fl ow diagram, Example 1.11.$625$525 $500$625$575$650$600$550P = ? 7 6 5 4 3 2 1 0 1$2500Yearoccurs in years 6 through 8.0 7 8i = 8.5%P = ?Figure 18Cash fl ow diagram with two different A series, Example 1.10. 38. 1.7 Economic Equivalence 191.7 Economic EquivalenceEconomic equivalence is a fundamental concept upon which engineering economy computationsare based. Before we delve into the economic aspects, think of the many types of equivalency wemay utilize daily by transferring from one scale to another. Some example transfers betweenscales are as follows:Length:12 inches1 foot 3 feet1 yard 39.370 inches1 meter100 centimeters1 meter 1000 meters1 kilometer 1 kilometer0.621 milePressure:1 atmosphere1 newton/meter 210 3 pascal1 kilopascalOften equivalency involves two or more scales. Consider the equivalency of a speed of 110 kilo-metersper hour