**Basics of Engineering EconomyLeland Blank, P. E.Dean EmeritusAmerican University of SharjahUnited Arab EmiratesandProfessor EmeritusIndustrial and Systems EngineeringTexas A&M UniversityAnthony Tarquin, P. E.ProfessorCivil EngineeringUniversity of Texas—EI PasoBrief ContentsChapters1 Foundations of Engineering Economy 12 Factors: How Time and Interest Affect Money 273 Nominal and Effective Interest Rates 594 Present Worth Analysis 805 Annual Worth Analysis 1076 Rate of Return Analysis 1247 Benefit/Cost Analysis and Public Sector Projects 1608 Breakeven, Sensitivity, and Payback Analysis 1829 Replacement and Retention Decisions 21510 Effects of Inflation 23711 Estimating Costs 25912 Depreciation Methods 28713 After-Tax Economic Analysis 312AppendicesA Using Spreadsheets and Microsoft Excel 348B Accounting Reports and Business Ratios 363C Alternative Evaluation that Includes Multiple Attributes and Risk 370D Answers to Problems for Test Review and FE Exam Practice 385Reference Materials 386Interest Factor Tables 388Index 414ivvContentsPreface ixChapter 1Foundations of Engineering Economy 11.1 What is Engineering Economy? 31.2 Performing an Engineering Economy Study 31.3 Interest Rate, Rate of Return, and MARR 51.4 Equivalence 81.5 Simple and Compound Interest 91.6 Terminology and Symbols 141.7 Cash Flows: Their Estimation andDiagramming 161.8 The Rule of 72 201.9 Introduction to Using Spreadsheet Functions 21Summary 23Problems 23Problems for Test Review and FE ExamPractice 25Chapter 2Factors: How Time and InterestAffect Money 272.1 Single-Payment Formulas (FP and PF) 292.2 Uniform Series Formulas(PA, AP, AF, FA) 342.3 Gradient Formulas 372.4 Calculations for Cash FlowsThat are Shifted 412.5 Using Spreadsheets for EquivalencyComputations 45Summary 49Problems 50Problems for Test Review and FE ExamPractice 57Chapter 3Nominal and Effective Interest Rates 593.1 Nominal and Effective Interest RateStatements 613.2 Effective Interest Rate Formulation 633.3 Reconciling Compounding Periods andPayment Periods 653.4 Equivalence Calculations Involving OnlySingle-Amount Factors 663.5 Equivalence Calculations Involving Series withPP CP 683.6 Equivalence Calculations Involving Series withPP CP 703.7 Using Spreadsheets for Effective Interest RateComputations 72Summary 74Problems 74Problems for Test Review and FE ExamPractice 78Chapter 4Present Worth Analysis 804.1 Formulating Alternatives 824.2 Present Worth Analysis of Equal-LifeAlternatives 844.3 Present Worth Analysis of Different-LifeAlternatives 864.4 Capitalized Cost Analysis 894.5 Evaluation of Independent Projects 944.6 Using Spreadsheets forPW Analysis 96Summary 98Problems 99Problems for Test Review and FE ExamPractice 105vi ContentsChapter 5Annual Worth Analysis 1075.1 AW Value Calculations 1095.2 Evaluating Alternatives Basedon Annual Worth 1125.3 AW of a Permanent Investment 1145.4 Using Spreadsheets for AW Analysis 116Summary 118Problems 119Problems for Test Review and FE ExamPractice 122Chapter 6Rate of Return Analysis 1246.1 Interpretation of ROR Values 1266.2 ROR Calculation 1286.3 Cautions when Using the ROR Method 1316.4 Understanding Incremental RORAnalysis 1316.5 ROR Evaluation of Two or More MutuallyExclusive Alternatives 1356.6 Multiple ROR Values 1396.7 Removing Multiple ROR Values by Using aReinvestment Rate 1436.8 Using Spreadsheets for ROR Analysis 147Summary 151Problems 151Problems for Test Review and FE ExamPractice 158Chapter 7Benefit/Cost Analysis and Public SectorProjects 1607.1 Public Versus Private SectorProjects 1627.2 Benefit/Cost Analysis of a SingleProject 1667.3 Incremental B/C Evaluation of Two or MoreAlternatives 1687.4 Using Spreadsheets for B/C Analysis 174Summary 176Problems 176Problems for Test Review and FE ExamPractice 180Chapter 8Breakeven, Sensitivity, andPayback Analysis 1828.1 Breakeven Analysis for a SingleProject 1848.2 Breakeven Analysis BetweenTwo Alternatives 1898.3 Sensitivity Analysis for Variationin Estimates 1928.4 Sensitivity Analysis of Multiple Parameters forMultiple Alternatives 1978.5 Payback Period Analysis 1998.6 Using Spreadsheets for Sensitivity orBreakeven Analysis 201Summary 205Problems 206Problems for Test Review and FE ExamPractice 213Chapter 9Replacement and Retention Decisions 2159.1 Basics of a Replacement Study 2179.2 Economic Service Life 2189.3 Performing a Replacement Study 2209.4 Defender Replacement Value 2249.5 Replacement Study Over a SpecifiedStudy Period 2249.6 Using Spreadsheets for aReplacement Study 228Summary 231Problems 232Problems for Test Review and FE ExamPractice 235Contents viiChapter 10Effects of Inflation 23710.1 Understanding the Impact of Inflation 23910.2 PW Calculations Adjusted for Inflation 24110.3 FW Calculations Adjusted for Inflation 24610.4 AW Calculations Adjusted for Inflation 25010.5 Using Spreadsheets to Adjust for Inflation 252Summary 253Problems 254Problems for Test Review and FE ExamPractice 257Chapter 11Estimating Costs 25911.1 How Cost Estimates Are Made 26111.2 Unit Method 26411.3 Cost Indexes 26611.4 Cost-Estimating Relationships:Cost-Capacity Equations 26911.5 Cost-Estimating Relationships:Factor Method 27111.6 Cost-Estimating Relationships:Learning Curve 27311.7 Indirect Cost (Overhead) Estimation andAllocation 275Summary 281Problems 282Problems for Test Review and FE ExamPractice 285Chapter 12Depreciation Methods 28712.1 Depreciation Terminology 28912.2 Straight Line (SL) Depreciation 29112.3 Declining Balance Depreciation 29212.4 Modified Accelerated Cost Recovery System(MACRS) 29512.5 Switching Between Classical Methods;Relation to MACRS Rates 29912.6 Depletion Methods 30112.7 Using Spreadsheets for DepreciationComputations 303Summary 306Problems 307Problems for Test Review and FE ExamPractice 310Chapter 13After-Tax Economic Analysis 31213.1 Income Tax Terminology andRelations 31413.2 Before-Tax and After-Tax AlternativeEvaluation 31713.3 How Depreciation Can Affect an After-TaxStudy 32013.4 After-Tax Replacement Study 32613.5 Capital Funds and the Cost of Capital 32813.6 Using Spreadsheets for After-TaxEvaluation 33213.7 After-Tax Value-Added Analysis 33513.8 Tax Considerations for InternationalProjects 337Summary 339Problems 340Problems for Test Review and FE ExamPractice 346Appendix AUsing Spreadsheets andMicrosoft Excel© 348A.1 Introduction to Using Excel 348A.2 Organization (Layout) of the Spreadsheet 351A.3 Excel Functions Important to EngineeringEconomy 353A.4 GOAL SEEK—A Simple Tool for Breakevenand Sensitivity Analyses 361A.5 Error Messages 362viii ContentsAppendix BAccounting Reports andBusiness Ratios 363B.1 The Balance Sheet 363B.2 Income Statement and Cost of Goods SoldStatement 364B.3 Business Ratios 366Appendix CAlternative Evaluation that Includes MultipleAttributes and Risk 370C.1 Multiple Attribute Analysis 370C.2 Economic Evaluation with RiskConsidered 376Appendix DAnswers to Problems for Test Review andFE Exam Practice 385Reference Materials 386Interest Factor Tables 388Index 414IndexAAbsolute cell referencing, 349Accelerated write-off, 290, 299,323–26Accountingratios, 366–69statements, 363–65Accuracy of estimates, 263–64Acid-test ratio, 367Activity-based costing (ABC),279–81A/F factor, 35–6After-taxalternative selection, 318cash flow, 317debt versus equity financing, 328and depreciation, 314international, 337–39MARR, 318rate or return, 318WACC, 329–32After-tax replacement analysis,326–28A/G factor, 39. See also Gradients,arithmeticAlternative depreciation system(ADS), 298Alternativesand breakeven analysis,189–91cost, 82defined, 3, 82incremental rate-of-return,131–39independent, 82 (see alsoIndependent projects)infinite life, 89–94, 114–16mutually exclusive, 82, 86–96,112–14, 131–39, 168–74revenue, 82types, 82–83Amortization. See DepreciationAnnual interest rateeffective, 61–65, 72nominal, 61, 72Annual operating costs (AOC), 17,84, 110, 314Annual worthadvantages, 109after-tax analysis, 318, 320of annual operating costs, 110and B/C analysis, 166, 170, 173and breakeven analysis, 189–92equivalent uniform, 110–12, 114evaluation by, 112–18and EVA, 335–37and future worth, 110and incremental rate ofreturn, 139of infinite-life projects, 114–16and inflation, 109, 250–52and present worth, 110and replacement analysis, 218–24,225–28and sensitivity analysis, 193, 197AOC. See Annual operating costsA/P factor, 34–35Arithmetic gradient. See Gradient,arithmeticAttributesevaluating multiple, 370–75weighting, 371–73Average, 379–81Average cost per unit, 188AVERAGE function, Excel,379, 384Average tax rate, 315BBalance sheet, 363–64Base amount, and shifted gradients,38, 39, 43–45Basis, 289B/C. See Benefit/cost ratioBefore-tax rate of return, 128–30and after-taxes, 318Benefit and cost difference, 167Benefit/cost ratiocalculation, 166–68conventional, 167incremental analysis, 168–74independent project evaluation, 173modified, 167for three or more alternatives,171–73Benefitsdirect versus usage costs, 169in public projects, 163–66Bondsand debt financing, 328, 330description, 85interest computation, 85present worth, 85–86rate of return, 130Book depreciation, 289, 295Book valueby declining-balance method, 293defined, 289by double declining balancemethod, 293and EVA, 335–36by MACRS, 295versus market value, 289, 326–28by straight line method, 291Bottom-up approach, 262–63Breakeven analysis. See alsoSensitivity analysisaverage cost per unit, 188description, 182, 184–88fixed costs, 185and make-buy decisions, 190–92PW versus i graph, 149and replacement value, 224versus sensitivity analysis, 192single project, 184–89two alternatives, 189–92Index 415Breakeven point, 185Bundles. See Independent projectsCCapitalcost of (See Cost of capital)debt versus equity, 328recovery and AW, 110Capital budgeting. See IndependentprojectsCapitalized cost, 14, 89–94, 114and annual worth, 114–16computation, 90and present worth, 89–94Capital financingdebt, 7, 328debt versus equity, 328–32equity, 7, 328Capital gain, 321, 326Capital loss 321, 326Capital recoveryin annual worth of costs, 110–12defined, 110and inflation, 250–52and replacement analysis, 218–19Capital recovery factor. See A/P factorCapital recovery for assets. SeeDepreciationCash flowafter tax, 317and EVA, 335before tax, 317conventional series, 139–40defined, 3–4diagramming, 18–20discounted, 80estimating, 16–17, 261–75incremental, 132net, 17, 317nonconventional, 139–40and payback analysis, 199positive net, and ROR, 143–44and public sector projects, 162–63recurring and nonrecurring, 90and replacement analysis, 224revenue versus cost, 82sign test, 139zero, 47, 356, 358Cash flow after taxes (CFAT), 317Cash flow before taxes (CFBT), 317Cash flow diagrams, 18–20Cell references, in Excel, 349Challenger, in replacement analysis,217, 221–24, 326Charts in Excel, 350–51Class life, 298, 337–39Composite rate of return (CRR),143–47Compound amount factorssingle payment (F/P), 29–33uniform series (F/A), 35–36Compound interest, 9–14Compoundingcontinuous, 64–65frequency, 63interperiod, 71–72and simple interest, 9–10Compounding periodcontinuous, 64–65defined, 61–62and payment period, 65–66Constant value dollars, 239, 242Consultant’s perspective, 217Continuous compounding, 64–65Contracts, types, 166Conventional benefit/cost ratio, 167Conventional cash flow series,139–40Conventional gradient, 38Cost, life-cycle, 89Cost alternative, 82, 133, 135Cost-capacity equations, 269–71Cost centers, 276, 279Cost depletion. See DepletionCost driver, 279–81Cost-estimating relationships,269–75Cost estimationapproaches, 262cost-capacity method, 269–71cost indexes, 266–69factor method, 271–73and inflation, 7, 87, 239learning curve, 275unit method, 264–65Cost indexes, 266–69Cost of capitaland debt-equity mix, 330for debt financing, 328, 332defined, 328for equity financing, 328and MARR, 6–7, 328weighted average, 329–32Cost-of-goods-sold, 278, 364–65Cost of invested capital, 335Cost(s)and alternative evaluation, 82,133, 135and annual worth, 110, 218–19of asset ownership, 110direct, estimating, 261–75fixed, 185–88indirect, estimating, 275–81of invested capital, 335–37life-cycle, 89linear, 185nonlinear, 187in public projects, 163sign convention, 18, 166sunk, 217variable, 185–88Cumulative cash flow sign test, 139Current assets, 363Current liabilities, 363Current ratio, 366DDB function, Excel, 293, 303–5, 353DDB function, Excel, 293, 303–5,353–54Debt capital, 6, 328–32Debt-equity mix, 329Debt financingon balance sheet, 363cost of, 329–32and inflation, 246leveraging, 330–31Debt ratio, 367Decision makingattributes, 370–71under certainty, 376engineering economy role, 3under risk, 376–84Declining balance depreciation,292–95, 338, 353Decreasing gradients, 38Defender, in replacement analysis,217, 220–28Deflation, 241Delphi method, 371416 IndexDepletion, 301–2Depreciationaccelerated, 290, 299, 323–26alternative system (ADS), 298book, 289, 295class life, 298, 337–39declining balance, 292–95, 296,338, 353defined, 289double declining balance, 293,296, 299, 353and EVA, 335–37half-year convention, 290, 295and income taxes, 320–26MACRS, 295–98and Excel functions, 299, 360recovery period for, 295, 298present worth of, 299recapture, 320–21recovery rate, 290, 306straight line, 291–92, 298straight line alternative, 298switching methods, 299–300, 360Descartes’ rule, 139Design stages, 89, 263Design-to-cost approach, 262–63Direct benefits, 169–70Direct costs, 261–75Disbenefits, 163, 167–68Discount rate, 80, 164Discounted cash flow, 14, 80Discounted payback, 199Discrete cash flows, compound interest factors (tables), 388–413Dollars, today versus future, 239–41Do-nothing alternative, 4, 82and B/C analysis, 169–71and independent projects, 94–96and rate of return, 135, 137–38Double declining balance, 293–95in Excel, 293, 353–54in switching, 299–300, 360and taxes, 324Dumping, 241EEconomic service life (ESL),218–20, 223, 230Economic value added (EVA),335–37Effective interest rateand compounding frequency, 65–66for continuous compounding,64–65defined, 63and nominal rate, 61–62EFFECT function, Excel, 72–74, 354Effective tax rate, 314, 318Efficiency ratios, 366End-of-period convention, 17–18Engineering economydefined, 3role in decision-making, 3terminology and symbols, 14–20Engineering News Record, 268Equal-service alternatives, 84,86–87, 109, 132Equity financing, 328–32cost of, 329, 332Equivalence, 8–9compounding period versuspayment period, 65–66, 68,70–71Equivalent uniform annual cost, 107.See also Annual worthEquivalent uniform annual worth.See Annual worthEstimationaccuracy, 263–64of cash flow, 3–4, 261–64of doubling time, 20–21of interest rates, 240and sensitivity analysis, 192–98before and after tax MARR, 318before and after tax ROR, 318using cost-estimating relations,269–75Evaluation criteria, 4Excel. See also Spreadsheets;specific functionsafter-tax analysis, 332–35and B/C analysis, 174–76and breakeven analysis, 203–5charts, 350–51and depreciation, 303–6error messages, 362functions listing, 353–61Goal Seek, Excel, 203, 361–62imbedded function, 118and inflation, 252–53introduction, 21–23and rate of return, 147–51and sensitivity analysis, 201–3spreadsheet layout, 351–53Expected value, 379–81Expenses, 314, 364. See also Costestimation; Cost(s)Experience curve, 275External rate of return, 143–44. Seealso Rate of returnFF/A factor, 35–36.Face value, of bonds, 85Factor method estimation, 271–73Factorscapital recovery, 34gradientarithmetic, 37–39, 43–44geometric, 39–41, 44notation, 30, 39for shifted series, 41–45single payment, 29–33sinking fund, 36tabulated values, 388–413uniform-series, 34–37Factory cost, 278, 365Financial worth of corporations, 336Financing. See Debt financing;Equity financingFirst cost, 17, 84, 289Fiscal year, 363Fixed assets, 363Fixed costs, 185–89Fixed percentage method. SeeDeclining balancedepreciationF/P factor, 29Future worthcalculation, 89, 110evaluation by, 89, 166and inflation, 246–49of shifted series, 42FV function, Excel, 22, 46, 354–55GGains and losses. See Capital gain;Capital lossGeneral depreciation system(GDS), 298Index 417Goal Seek, Excel, 361–62for breakeven, 203–5for replacement value, 230–31Gradient, arithmeticbase amount, 38, 43conventional, 37–39decreasing, 38factors, 37, 39, 40shifted, 43–45Gradient, geometricbase amount, 39factors, 39–41shifted, 44Graduated tax rates, 314–17Gross income, 301, 314HHalf-year convention, 290, 295,305–6Highly leveraged corporations,330–31Hurdle rate. See Minimum attractiverate of returnHyperinflation, 250IIncomegross, 314net, 335as revenue, 17, 314, 364taxable, 314, 316, 335–36Income statement, 364–65Income tax, 314–39average tax rate, 315and cash flow, 317–20corporate, 315defined, 314and depreciation, 320–26effective rates, 314, 318individual taxpayers, 316–17international, 337–39present worth of, 324–26and rate of return, 318rates, 314–17and replacement studies,326–28tax savings, 318Incremental benefit/cost analysis,168–74Incremental cash flow, 132–35Incremental costsand benefit/cost analysis, 168–69definition, 132–33and rate-of-return, 135–39Incremental rate of return analysis,135–39, 320Independent projectsB/C evaluation of, 173bundles, 95formation, 82–83PW evaluation of, 94–98ROR evaluation of, 135Indexing, income taxes, 314Indirect costsactivity-based costing, 279–81definition, 261, 276factor method, 271–73rates, 276–77Infinite life, 89–94, 114–16, 162Inflation, 237–53assumption in PW and AW, 87, 109and capital recovery, 250–52definition, 7, 239and future worth, 246–50high, 250and interest rates, 240and MARR, 249and present worth, 241–46Initial investment. See First costInstallation costs, in depreciation, 289Intangible factors, 4. See alsoMultiple attribute evaluation;Noneconomic factorsInterestcompound, 10–14defined, 5interperiod, 71rate (See Interest rate)simple, 9–10, 12–14Interest period, 5Interest rate. See also Effective interest ratecontinuous compounding, 64–65definition, 5inflation-adjusted, 240inflation free (real), 240, 247IRR function, 22, 49, 129,148–51, 355–56market, 240multiple, 139–43nominal versus effective, 61–65for public sector, 164unknown, 21, 30on unrecovered balance, 126Interest tables, 388–413Internal rate of return. See Rate ofreturnInternational aspectsafter taxes, 337–39contracts, 166cost estimation, 263deflation, 241depreciation, 289, 291, 337–39hyperinflation, 250Inventory turnover ratio, 368Invested capital, cost of, 335–36Investment(s). See also First costextra, 132–35permanent, 89–90, 114–16safe, 6–7IPMT function, Excel, 355IRR function, Excel, 22, 49, 129,148–51, 355–56LLand, 290Lang factors, 271Least common multiple (LCM)and annual worth, 109, 139and future worth, 89and incremental cash flow, 132, 134and incremental rate of return,132, 135, 137–39and independent projects, 94–95and present worth, 86–88Learning curve, 273–75Leveraging, 330–331Liabilities, 363–64Life. See LivesLife cycle, and annual worth, 109Life cycle costs, 89Likert scale, 373Livescommon multiple, 86–88, 109equal, 84, 132finite, 93, 116independent projects, 94–95minimum cost, 218–20perpetual, 89–94, 114–16and rate of return, 132–35418 IndexLives—Cont.recovery, in depreciation, 289unequal, 86–88, 93, 109unknown, 20, 22, 30, 357useful, 289MMACRS (Modified Accelerated CostRecovery System), 295–99depreciation rates, 296and Excel functions, 305, 360–61PW of, depreciation, 299, 305–6recovery period, 298straight line alternative, 298switching, 299U.S., required, 291, 295Maintenance and operating (M&O)costs, 3, 167, 314. See alsoAnnual operating costsMake-or-buy decisions, 112, 183, 191Manufacturing progress function, 275Marginal tax rates, 314Market interest rate. See Interest rateMarket valueand depreciation, 289in ESL analysis, 217estimating, 217in replacement analysis, 221–24as salvage value, 86MARR. See Minimum attractive rateof returnMarshall & Swift, 266, 268Mean, 379Measure of worth, 5, 192Minimum attractive rate of returnafter-tax, 318definition, 6establishing, 7, 328–29as hurdle rate, 7and independent projects, 94inflation-adjusted, 249in PW and AW analysis, 84,86, 112and rate of return, 131–39in sensitivity analysis, 192before tax, 7, 84, 318and WACC, 329–30M&O costs. See Annual operatingcosts; Maintenance andoperating costsModified benefit/cost ratio, 167Most likely estimate, 197, 376Multiple alternativesbenefit/cost analysis, 168–74independent, 94–96rate of return analysis, 135–39Multiple attribute evaluation,370–75Multiple rates of returndefinition, 139determining, 139–43removing, 143–47Municipal bonds, 85–86Mutually exclusive alternativesannual worth analysis, 112–16benefit/cost analysis, 168–74capitalized cost analysis, 89–94formation of, 82–83future worth analysis, 89present worth analysis, 84–89rate of return analysis, 135–39NNet cash flow, 17, 199, 317Net investment procedure, 144–47Net present value. See NPV function,Excel; Present worthNet profit after taxes (NPAT),335–36Net worth, 363–64NOMINAL function, Excel,72–73, 357Nominal interest rate, 61–63annual, 63and effective rates, 63–65Nonconventional cash flow series,139–40Noneconomic factors, 4No-return payback, 199Norstrom’s criterion, 139NPER function, Excel, 22, 46, 357and annual worth, 115and unknown n, 22, 46–48NPV function, Excel, 97–98, 357for arithmetic gradients, 69imbedding in PMT, 48, 118,228–30and present worth, 97–98in PV vs. i graphs, 149and shifting, 46–48OOne-year-later replacement analysis,221–24Operating costs. See Annual operating costs; Cost estimationOptimistic estimate, 197–98Order of magnitude estimates, 263Overhead rates. See Indirect costsOwner’s equity, 363P, QP/A factor, 34–35, 38Payback analysis 199–201limitations, 199, 206Payment periodof bonds, 85defined, 66relative to compounding period,65–72Payout period. See Payback analysisPercentage depletion. See DepletionPermanent investments, 89, 114. Seealso Capitalized costPersonal property, 290, 298Pessimistic estimate, 197–98P/F factor, 29.P/G factor, 37–38. See alsoGradients, arithmeticPlanning horizon. See Study periodPlant costs, 271–73PMT function, Excel, 22, 35, 358and annual worth, 46–48, 111,116–18and capital recovery, 116and economic service life, 228–30imbedded with NPV function, 48,118, 228–30and shifted series, 47–48Point estimates, 17, 376Power law and sizing model, 269Present worth, 84–98and annual worth, 110arithmetic gradient, 38assumptions, 84, 86of bonds, 85of depreciation, 299for equal lives, 84geometric gradient, 39–40of income taxes, 324and independent projects, 94–96Index 419and inflation, 241–46and life cycle cost, 89and multiple interest rates,140–44and rate of return, 135–39and sensitivity analysis, 192–95in shifted series, 43single-payment factor, 29for unequal lives, 86–89versus i graph, 149Present worth factorsgradient, 37–40single-payment, 29–30uniform-series, 34–35Probabilitydefined, 377and expected value, 379–81Probability distribution, 377Productive hour rate method, 278Profit, 185–87Profitability index, 124. See alsoRate of returnProfitability ratios, 366Profit-and-loss statement. SeeIncome statementProject net-investment, 144–47Property class, 298Public sector projects, 162–66and annual worth, 114–16benefit/cost analysis, 166–74BOT contracts, 166capitalized cost, 89–94Purchasing power, 246–48PV function, Excel, 22, 35, 358and NPV function, 97–98, 358and present worth, 45, 86, 97and single payment, 32and uniform series presentworth, 35PW vs. i graph, 149Quick ratio, 367RRandom samples, 377Random variable, 377–84classification, 377expected value, 379–81probability distribution of, 377standard deviation, 382–84Rank and rate technique, 374RATE function, Excel, 22, 129,147–48, 359Rate of depreciationdeclining balance, 292–93MACRS, 295–96straight line, 291Rate of return (ROR), 124–51after-tax, 318–20and annual worth, 139on bonds, 130cautions, 131composite, 143–44on debt and equity capital, 330–31defined, 5, 126external, 143on extra investment, 135–39incremental, 131–33and independent projects, 136internal, 126,143minimum attractive (see Minimumattractive rate of return)and MIRR function, Excel, 150multiple, 139–47and mutually exclusive alternatives,135–39ranking inconsistency, 132and reinvestment rate, 144and sensitivity analysis, 195–96Ratios, accounting, 366–69Real interest rate, 240, 247Real property, 290, 296Recaptured depreciationdefinition, 320in replacement study, 326–28and taxes, 320–23Recovery perioddefined, 289effect on taxes, 323–24, 326MACRS, 296, 298Recovery rate. See Rate ofdepreciationReinvestment rate, 144Replacement analysis, 215–31after-tax, 326–28before-tax, 220–24cash flow approach, 224consultant’s viewpoint, 217depreciation recapture, 326–28economic service life, 218–20first costs, 217market value, 217, 221opportunity cost (conventional)approach, 224and study periods, 221,224–26, 228sunk costs, 217Replacement value, 224, 230Retained earnings, 364Retirement life. See Economicservice lifeReturn on assets ratio, 368Return on invested capital, 144Return on investment (ROI), 5, 124.See also Rate of returnReturn on sales ratio, 367Revenue alternative, 82, 133, 135, 169Riskand debt-equity mix, 330–31and decision making, 376and payback analysis, 201and variation in estimates, 376Rule of 72, 20–21Rule of 100, 21Rule of signscash flow, 139–41cumulative cash flow, 139, 142SSafe investment, 6–7Sales, return on, 367Salvage valuein B/C analysis, 166and capital recovery, 110–11and depreciation, 290, 291,293, 295and market value, 86, 112, 222in replacement analysis, 219–22Sample, 377average, 379–81expected value, 379standard deviation, 382Savings, tax, 318Scatter charts. See xy Excel chartsSensitivity analysis. See alsoBreakeven analysis; GoalSeek, Excelapproach, 192of one parameter, 192–95of several parameters, 195–96with three estimates, 197–98420 IndexService life. See Economic service lifeShifted gradients, 43–45Shifted series, 41–45Sign changes, 139–40Simple cash flow series, 139Simple interest, 9, 12–14Single-payment compound amountfactor (F/P), 29Single payment factors, 29–33Single-payment present worth factor(P/F), 29Single-value estimates, 17, 376Sinking fund (A/F) factor, 35–36SLN function, Excel, 291,303–4, 359Solvency ratios, 366Solver tool, Excel, 96, 195Spreadsheet analysis. See also Excelafter-tax, 332–35annual worth, 116–18, 333–34B/C analysis, 174–76breakeven analysis, 203–5depreciation, 303–6effective interest, 72–74equivalency computations, 45–49EVA, 336–37Excel functions, 22, 353–62inflation, 252–53layout, 351–53present worth, 96–98, 333–34rate of return, 147–51, 333–35replacement analysis, 228–31sensitivity analysis, 201–3Standard deviation, 382–84STDEV function, Excel, 382, 384Stocks, 328, 330–31Straight line alternative, inMACRS, 298Straight line depreciation,291–92, 299Straight line rate, 291, 293Study periodAW evaluation, 109, 112equal service, 86, 95FW analysis, 89independent projects, 95PW evaluation, 86replacement analysis, 220–21,224–26Sunk cost, 217Survivor, in multiple-alternativeanalysis, 135–39, 168–73Switching, depreciation methods,299–300, 305TTax depreciation, 289Taxable income, 314–26and CFAT, 317–18and depreciation, 322, 324–25negative, 318Taxes, 314–39. See also After-tax;Economic value added;Income tax; Taxable incomeTerminology, 14–15Time placement of dollars, 17–20, 239Time value of money, 4–5Top down approach, 262–63Total cost relation, 185–88. See alsoBreakeven analysisTrade-in value, 218, 224, 290. See alsoMarket value; Salvage valueUUniform distribution, 377Uniform gradient. See Gradient,arithmeticUniform percentage method. SeeDeclining balance depreciationUniform seriescompounding period and paymentperiod, 65–72description, 14factors, 34–37shifted, 41–45Unit method, 264–65Unrecovered balance, 126, 144V–YValue added analysis. See Economicvalue added (EVA)Value engineering, 263Variable. See Random variableVariable costs, 185–86VDB function, Excel, 305–6, 360for MACRS rates, 296, 305–6Weighted attribute method, 370–75Weighted average cost of capital(WACC), 329–32xy Excel charts, 149, 202, 229, 305,334, 350–51Year(s). See also Half-year conventioncash flow diagrams, 18–20end-of-period conGlossary of Terms and SymbolsTerm Symbol DescriptionAnnual amount or worth A or AW Equivalent uniform annual worth of all cash inflows andoutflows over estimated life.Annual operating cost AOC Estimated annual costs to maintain and support an alternative.Average X Measure of central tendency; average of sample values.Benefit/cost ratio B/C Ratio of a project’s benefi ts to costs expressed in PW,AW, or FW terms.Bond dividend I Dividend (interest) paid periodically on a bond.Book value BV Remaining capital investment in an asset after depreciation isaccounted for.Breakeven point QBE Quantity at which revenues and costs are equal, or twoalternatives are equivalent.Capital recovery CR Equivalent annual cost of owning an asset plusthe required return on the initial investment.Capitalized cost CC or P Present worth of an alternative that will last forever(or a long time).Cash fl ow CF Actual cash amounts which are receipts (inflow) anddisbursements (outflow).Cash flow before CFBT or Cash flow amount before relevant taxes or after taxesor after taxes CFAT are applied.Composite rate i Unique rate of return when a reinvestment rate c isof return applied to a multiple-rate cash flow series.Compounding frequency m Number of times interest is compounded per period (year).Cost estimating C2 or CT Relations that use design variables and changing costsrelationships over time to estimate current and future costs.Cost of capital WACC Interest rate paid for the use of capital funds; includes bothdebt and equity funds. For debt and equity considered, itis weighted average cost of capital.Debt-equity mix D-E Percentages of debt and equity investment capitalused by a corporation to fund projects.Depreciation D Reduction in the value of assets using specifi c models andrules; there are book and tax depreciation methods.Depreciation rate dt Annual rate for reducing the value of assets usingdepreciation.Economic service life ESL or n Number of years at which the AW of costs is a minimum.Expenses E All corporate costs incurred in transacting business.First cost P Total initial cost—purchase, construction, setup, etc.Future amount or F or FW Amount at some future date considering time value ofworth money.(Continued)Term Symbol DescriptionGradient, arithmetic G Uniform change ( or ) in cash fl ow each time period.Gradient, geometric g Constant rate of change ( or ) each time period.Gross income GI Income from all sources for corporations or individuals.Inflation rate f Rate that refl ects changes in the value of currency over time.Interest Simple interest is based on the principal only; compoundingaccrues interest on principal plus all accumulated interest.Interest rate i or r Interest expressed as a percentage of the original amountper time period; nominal (r) and effective (i) rates.Interest rate, if Interest rate adjusted to take infl ation into account.inflation-adjustedLife (estimated) n Number of years or periods over which an alternative orasset will be used; the evaluation time.Measure of worth Varies Value, such as PW, AW, i**

*, B/C, used to judge economic viability. Minimum attractive MARR Minimum value of the rate of return for an alternative to rate of return be financially viable. Net cash fl ow NCF Resulting net amount of cash that fl ows in or out during a time period. Net present value NPV Another name for the present worth, PW. Payback period n p Number of years to recover the initial investment and a stated rate of return. Present amount P or PW Amount of money at the current time or a time denoted as or worth present. Random variable X Parameter or characteristic that can take on any one of several values; discrete and continuous. Rate of return i*or ROR Compound interest rate on unpaid or unrecovered balancessuch that the final amount results in a zero balance.Recovery period n Number of years to completely depreciate an asset.Salvage value S Expected trade-in or market value when an asset is tradedor disposed of.Standard deviation s Measure of dispersion or spread about the expected valueor average.Study period n Specified number of years over which an evaluation takes place.Taxable income TI Amount upon which income taxes are based.Tax rate T Decimal rate, usually graduated, used to calculate corporateor individual taxes.Tax rate, effective Te Single-figure tax rate incorporating several rates and bases.Time t Indicator for a time period.Value added EVA Economic value added refl ects net profi t after taxes (NPAT)after removing cost of invested capital during the year.Format for Commonly Used Spreadsheet Functions on Excel©Present worth:PV(i%,n,A,F) for constant A seriesNPV(i%,second_cell:last_cell) first_cell for varying cash flow seriesFuture worth:FV(i%,n,A,P) for constant A seriesAnnual worth:PMT(i%,n,P,F) for single amounts with no A seriesNumber of periods (years):NPER(i%,A,P,F) for constant A series(Note: The PV, FV, and PMT functions change the sense of the sign. Place a minus in front of the functionto retain the same sign.)Rate of return:RATE(n,A,P,F) for constant A seriesIRR(first_cell:last_cell) for varying cash flow seriesInterest rate:EFFECT(r%,m) for nominal r, compounded m times per periodNOMINAL(i%,m) for effective i, compounded m times per yearDepreciation:SLN(P,S,n) Straight line depreciation for each periodDDB(P,S,n,t,d) Double declining balance depreciation forperiod t at rate dDB(P,S,n,t) Declining balance, rate determined by thefunctionVDB(P,S,n, start_period, Switch from declining balance to straightend_period, factor) line depreciationVDB(P,0,n,MAX(0,t 1.5), MACRS depreciation for period t

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