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 |  موضوع: كتاب Basics of Engineering Economy الإثنين 18 أكتوبر 2021, 12:21 am | |
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أخواني في الله
أحضرت لكم كتاب
Basics of Engineering Economy
Leland Blank, P. E.
Dean Emeritus
American University of Sharjah
United Arab Emirates
and
Professor Emeritus
Industrial and Systems Engineering
Texas A&M University
Anthony Tarquin, P. E.
Professor
Civil Engineering
University of Texas—EI Paso
و المحتوى كما يلي :
Brief Contents
Chapters
1 Foundations of Engineering Economy 1
2 Factors: How Time and Interest Affect Money 27
3 Nominal and Effective Interest Rates 59
4 Present Worth Analysis 80
5 Annual Worth Analysis 107
6 Rate of Return Analysis 124
7 Benefit/Cost Analysis and Public Sector Projects 160
8 Breakeven, Sensitivity, and Payback Analysis 182
9 Replacement and Retention Decisions 215
10 Effects of Inflation 237
11 Estimating Costs 259
12 Depreciation Methods 287
13 After-Tax Economic Analysis 312
Appendices
A Using Spreadsheets and Microsoft Excel 348
B Accounting Reports and Business Ratios 363
C Alternative Evaluation that Includes Multiple Attributes and Risk 370
D Answers to Problems for Test Review and FE Exam Practice 385
Reference Materials 386
Interest Factor Tables 388
Index 414
ivv
Contents
Preface ix
Chapter 1
Foundations of Engineering Economy 1
1.1 What is Engineering Economy? 3
1.2 Performing an Engineering Economy Study 3
1.3 Interest Rate, Rate of Return, and MARR 5
1.4 Equivalence 8
1.5 Simple and Compound Interest 9
1.6 Terminology and Symbols 14
1.7 Cash Flows: Their Estimation and
Diagramming 16
1.8 The Rule of 72 20
1.9 Introduction to Using Spreadsheet Functions 21
Summary 23
Problems 23
Problems for Test Review and FE Exam
Practice 25
Chapter 2
Factors: How Time and Interest
Affect Money 27
2.1 Single-Payment Formulas (FP and PF) 29
2.2 Uniform Series Formulas
(PA, AP, AF, FA) 34
2.3 Gradient Formulas 37
2.4 Calculations for Cash Flows
That are Shifted 41
2.5 Using Spreadsheets for Equivalency
Computations 45
Summary 49
Problems 50
Problems for Test Review and FE Exam
Practice 57
Chapter 3
Nominal and Effective Interest Rates 59
3.1 Nominal and Effective Interest Rate
Statements 61
3.2 Effective Interest Rate Formulation 63
3.3 Reconciling Compounding Periods and
Payment Periods 65
3.4 Equivalence Calculations Involving Only
Single-Amount Factors 66
3.5 Equivalence Calculations Involving Series with
PP CP 68
3.6 Equivalence Calculations Involving Series with
PP CP 70
3.7 Using Spreadsheets for Effective Interest Rate
Computations 72
Summary 74
Problems 74
Problems for Test Review and FE Exam
Practice 78
Chapter 4
Present Worth Analysis 80
4.1 Formulating Alternatives 82
4.2 Present Worth Analysis of Equal-Life
Alternatives 84
4.3 Present Worth Analysis of Different-Life
Alternatives 86
4.4 Capitalized Cost Analysis 89
4.5 Evaluation of Independent Projects 94
4.6 Using Spreadsheets for
PW Analysis 96
Summary 98
Problems 99
Problems for Test Review and FE Exam
Practice 105vi Contents
Chapter 5
Annual Worth Analysis 107
5.1 AW Value Calculations 109
5.2 Evaluating Alternatives Based
on Annual Worth 112
5.3 AW of a Permanent Investment 114
5.4 Using Spreadsheets for AW Analysis 116
Summary 118
Problems 119
Problems for Test Review and FE Exam
Practice 122
Chapter 6
Rate of Return Analysis 124
6.1 Interpretation of ROR Values 126
6.2 ROR Calculation 128
6.3 Cautions when Using the ROR Method 131
6.4 Understanding Incremental ROR
Analysis 131
6.5 ROR Evaluation of Two or More Mutually
Exclusive Alternatives 135
6.6 Multiple ROR Values 139
6.7 Removing Multiple ROR Values by Using a
Reinvestment Rate 143
6.8 Using Spreadsheets for ROR Analysis 147
Summary 151
Problems 151
Problems for Test Review and FE Exam
Practice 158
Chapter 7
Benefit/Cost Analysis and Public Sector
Projects 160
7.1 Public Versus Private Sector
Projects 162
7.2 Benefit/Cost Analysis of a Single
Project 166
7.3 Incremental B/C Evaluation of Two or More
Alternatives 168
7.4 Using Spreadsheets for B/C Analysis 174
Summary 176
Problems 176
Problems for Test Review and FE Exam
Practice 180
Chapter 8
Breakeven, Sensitivity, and
Payback Analysis 182
8.1 Breakeven Analysis for a Single
Project 184
8.2 Breakeven Analysis Between
Two Alternatives 189
8.3 Sensitivity Analysis for Variation
in Estimates 192
8.4 Sensitivity Analysis of Multiple Parameters for
Multiple Alternatives 197
8.5 Payback Period Analysis 199
8.6 Using Spreadsheets for Sensitivity or
Breakeven Analysis 201
Summary 205
Problems 206
Problems for Test Review and FE Exam
Practice 213
Chapter 9
Replacement and Retention Decisions 215
9.1 Basics of a Replacement Study 217
9.2 Economic Service Life 218
9.3 Performing a Replacement Study 220
9.4 Defender Replacement Value 224
9.5 Replacement Study Over a Specified
Study Period 224
9.6 Using Spreadsheets for a
Replacement Study 228
Summary 231
Problems 232
Problems for Test Review and FE Exam
Practice 235Contents vii
Chapter 10
Effects of Inflation 237
10.1 Understanding the Impact of Inflation 239
10.2 PW Calculations Adjusted for Inflation 241
10.3 FW Calculations Adjusted for Inflation 246
10.4 AW Calculations Adjusted for Inflation 250
10.5 Using Spreadsheets to Adjust for Inflation 252
Summary 253
Problems 254
Problems for Test Review and FE Exam
Practice 257
Chapter 11
Estimating Costs 259
11.1 How Cost Estimates Are Made 261
11.2 Unit Method 264
11.3 Cost Indexes 266
11.4 Cost-Estimating Relationships:
Cost-Capacity Equations 269
11.5 Cost-Estimating Relationships:
Factor Method 271
11.6 Cost-Estimating Relationships:
Learning Curve 273
11.7 Indirect Cost (Overhead) Estimation and
Allocation 275
Summary 281
Problems 282
Problems for Test Review and FE Exam
Practice 285
Chapter 12
Depreciation Methods 287
12.1 Depreciation Terminology 289
12.2 Straight Line (SL) Depreciation 291
12.3 Declining Balance Depreciation 292
12.4 Modified Accelerated Cost Recovery System
(MACRS) 295
12.5 Switching Between Classical Methods;
Relation to MACRS Rates 299
12.6 Depletion Methods 301
12.7 Using Spreadsheets for Depreciation
Computations 303
Summary 306
Problems 307
Problems for Test Review and FE Exam
Practice 310
Chapter 13
After-Tax Economic Analysis 312
13.1 Income Tax Terminology and
Relations 314
13.2 Before-Tax and After-Tax Alternative
Evaluation 317
13.3 How Depreciation Can Affect an After-Tax
Study 320
13.4 After-Tax Replacement Study 326
13.5 Capital Funds and the Cost of Capital 328
13.6 Using Spreadsheets for After-Tax
Evaluation 332
13.7 After-Tax Value-Added Analysis 335
13.8 Tax Considerations for International
Projects 337
Summary 339
Problems 340
Problems for Test Review and FE Exam
Practice 346
Appendix A
Using Spreadsheets and
Microsoft Excel 348
A.1 Introduction to Using Excel 348
A.2 Organization (Layout) of the Spreadsheet 351
A.3 Excel Functions Important to Engineering
Economy 353
A.4 GOAL SEEK—A Simple Tool for Breakeven
and Sensitivity Analyses 361
A.5 Error Messages 362viii Contents
Appendix B
Accounting Reports and
Business Ratios 363
B.1 The Balance Sheet 363
B.2 Income Statement and Cost of Goods Sold
Statement 364
B.3 Business Ratios 366
Appendix C
Alternative Evaluation that Includes Multiple
Attributes and Risk 370
C.1 Multiple Attribute Analysis 370
C.2 Economic Evaluation with Risk
Considered 376
Appendix D
Answers to Problems for Test Review and
FE Exam Practice 385
Reference Materials 386
Interest Factor Tables 388
Index 414
Index
A
Absolute cell referencing, 349
Accelerated write-off, 290, 299,
323–26
Accounting
ratios, 366–69
statements, 363–65
Accuracy of estimates, 263–64
Acid-test ratio, 367
Activity-based costing (ABC),
279–81
A/F factor, 35–6
After-tax
alternative selection, 318
cash flow, 317
debt versus equity financing, 328
and depreciation, 314
international, 337–39
MARR, 318
rate or return, 318
WACC, 329–32
After-tax replacement analysis,
326–28
A/G factor, 39. See also Gradients,
arithmetic
Alternative depreciation system
(ADS), 298
Alternatives
and breakeven analysis,
189–91
cost, 82
defined, 3, 82
incremental rate-of-return,
131–39
independent, 82 (see also
Independent projects)
infinite life, 89–94, 114–16
mutually exclusive, 82, 86–96,
112–14, 131–39, 168–74
revenue, 82
types, 82–83
Amortization. See Depreciation
Annual interest rate
effective, 61–65, 72
nominal, 61, 72
Annual operating costs (AOC), 17,
84, 110, 314
Annual worth
advantages, 109
after-tax analysis, 318, 320
of annual operating costs, 110
and B/C analysis, 166, 170, 173
and breakeven analysis, 189–92
equivalent uniform, 110–12, 114
evaluation by, 112–18
and EVA, 335–37
and future worth, 110
and incremental rate of
return, 139
of infinite-life projects, 114–16
and inflation, 109, 250–52
and present worth, 110
and replacement analysis, 218–24,
225–28
and sensitivity analysis, 193, 197
AOC. See Annual operating costs
A/P factor, 34–35
Arithmetic gradient. See Gradient,
arithmetic
Attributes
evaluating multiple, 370–75
weighting, 371–73
Average, 379–81
Average cost per unit, 188
AVERAGE function, Excel,
379, 384
Average tax rate, 315
B
Balance sheet, 363–64
Base amount, and shifted gradients,
38, 39, 43–45
Basis, 289
B/C. See Benefit/cost ratio
Before-tax rate of return, 128–30
and after-taxes, 318
Benefit and cost difference, 167
Benefit/cost ratio
calculation, 166–68
conventional, 167
incremental analysis, 168–74
independent project evaluation, 173
modified, 167
for three or more alternatives,
171–73
Benefits
direct versus usage costs, 169
in public projects, 163–66
Bonds
and debt financing, 328, 330
description, 85
interest computation, 85
present worth, 85–86
rate of return, 130
Book depreciation, 289, 295
Book value
by declining-balance method, 293
defined, 289
by double declining balance
method, 293
and EVA, 335–36
by MACRS, 295
versus market value, 289, 326–28
by straight line method, 291
Bottom-up approach, 262–63
Breakeven analysis. See also
Sensitivity analysis
average cost per unit, 188
description, 182, 184–88
fixed costs, 185
and make-buy decisions, 190–92
PW versus i graph, 149
and replacement value, 224
versus sensitivity analysis, 192
single project, 184–89
two alternatives, 189–92Index 415
Breakeven point, 185
Bundles. See Independent projects
C
Capital
cost of (See Cost of capital)
debt versus equity, 328
recovery and AW, 110
Capital budgeting. See Independent
projects
Capitalized cost, 14, 89–94, 114
and annual worth, 114–16
computation, 90
and present worth, 89–94
Capital financing
debt, 7, 328
debt versus equity, 328–32
equity, 7, 328
Capital gain, 321, 326
Capital loss 321, 326
Capital recovery
in annual worth of costs, 110–12
defined, 110
and inflation, 250–52
and replacement analysis, 218–19
Capital recovery factor. See A/P factor
Capital recovery for assets. See
Depreciation
Cash flow
after tax, 317
and EVA, 335
before tax, 317
conventional series, 139–40
defined, 3–4
diagramming, 18–20
discounted, 80
estimating, 16–17, 261–75
incremental, 132
net, 17, 317
nonconventional, 139–40
and payback analysis, 199
positive net, and ROR, 143–44
and public sector projects, 162–63
recurring and nonrecurring, 90
and replacement analysis, 224
revenue versus cost, 82
sign test, 139
zero, 47, 356, 358
Cash flow after taxes (CFAT), 317
Cash flow before taxes (CFBT), 317
Cash flow diagrams, 18–20
Cell references, in Excel, 349
Challenger, in replacement analysis,
217, 221–24, 326
Charts in Excel, 350–51
Class life, 298, 337–39
Composite rate of return (CRR),
143–47
Compound amount factors
single payment (F/P), 29–33
uniform series (F/A), 35–36
Compound interest, 9–14
Compounding
continuous, 64–65
frequency, 63
interperiod, 71–72
and simple interest, 9–10
Compounding period
continuous, 64–65
defined, 61–62
and payment period, 65–66
Constant value dollars, 239, 242
Consultant’s perspective, 217
Continuous compounding, 64–65
Contracts, types, 166
Conventional benefit/cost ratio, 167
Conventional cash flow series,
139–40
Conventional gradient, 38
Cost, life-cycle, 89
Cost alternative, 82, 133, 135
Cost-capacity equations, 269–71
Cost centers, 276, 279
Cost depletion. See Depletion
Cost driver, 279–81
Cost-estimating relationships,
269–75
Cost estimation
approaches, 262
cost-capacity method, 269–71
cost indexes, 266–69
factor method, 271–73
and inflation, 7, 87, 239
learning curve, 275
unit method, 264–65
Cost indexes, 266–69
Cost of capital
and debt-equity mix, 330
for debt financing, 328, 332
defined, 328
for equity financing, 328
and MARR, 6–7, 328
weighted average, 329–32
Cost-of-goods-sold, 278, 364–65
Cost of invested capital, 335
Cost(s)
and alternative evaluation, 82,
133, 135
and annual worth, 110, 218–19
of asset ownership, 110
direct, estimating, 261–75
fixed, 185–88
indirect, estimating, 275–81
of invested capital, 335–37
life-cycle, 89
linear, 185
nonlinear, 187
in public projects, 163
sign convention, 18, 166
sunk, 217
variable, 185–88
Cumulative cash flow sign test, 139
Current assets, 363
Current liabilities, 363
Current ratio, 366
D
DB function, Excel, 293, 303–5, 353
DDB function, Excel, 293, 303–5,
353–54
Debt capital, 6, 328–32
Debt-equity mix, 329
Debt financing
on balance sheet, 363
cost of, 329–32
and inflation, 246
leveraging, 330–31
Debt ratio, 367
Decision making
attributes, 370–71
under certainty, 376
engineering economy role, 3
under risk, 376–84
Declining balance depreciation,
292–95, 338, 353
Decreasing gradients, 38
Defender, in replacement analysis,
217, 220–28
Deflation, 241
Delphi method, 371416 Index
Depletion, 301–2
Depreciation
accelerated, 290, 299, 323–26
alternative system (ADS), 298
book, 289, 295
class life, 298, 337–39
declining balance, 292–95, 296,
338, 353
defined, 289
double declining balance, 293,
296, 299, 353
and EVA, 335–37
half-year convention, 290, 295
and income taxes, 320–26
MACRS, 295–98
and Excel functions, 299, 360
recovery period for, 295, 298
present worth of, 299
recapture, 320–21
recovery rate, 290, 306
straight line, 291–92, 298
straight line alternative, 298
switching methods, 299–300, 360
Descartes’ rule, 139
Design stages, 89, 263
Design-to-cost approach, 262–63
Direct benefits, 169–70
Direct costs, 261–75
Disbenefits, 163, 167–68
Discount rate, 80, 164
Discounted cash flow, 14, 80
Discounted payback, 199
Discrete cash flows, compound interest factors (tables), 388–413
Dollars, today versus future, 239–41
Do-nothing alternative, 4, 82
and B/C analysis, 169–71
and independent projects, 94–96
and rate of return, 135, 137–38
Double declining balance, 293–95
in Excel, 293, 353–54
in switching, 299–300, 360
and taxes, 324
Dumping, 241
E
Economic service life (ESL),
218–20, 223, 230
Economic value added (EVA),
335–37
Effective interest rate
and compounding frequency, 65–66
for continuous compounding,
64–65
defined, 63
and nominal rate, 61–62
EFFECT function, Excel, 72–74, 354
Effective tax rate, 314, 318
Efficiency ratios, 366
End-of-period convention, 17–18
Engineering economy
defined, 3
role in decision-making, 3
terminology and symbols, 14–20
Engineering News Record, 268
Equal-service alternatives, 84,
86–87, 109, 132
Equity financing, 328–32
cost of, 329, 332
Equivalence, 8–9
compounding period versus
payment period, 65–66, 68,
70–71
Equivalent uniform annual cost, 107.
See also Annual worth
Equivalent uniform annual worth.
See Annual worth
Estimation
accuracy, 263–64
of cash flow, 3–4, 261–64
of doubling time, 20–21
of interest rates, 240
and sensitivity analysis, 192–98
before and after tax MARR, 318
before and after tax ROR, 318
using cost-estimating relations,
269–75
Evaluation criteria, 4
Excel. See also Spreadsheets;
specific functions
after-tax analysis, 332–35
and B/C analysis, 174–76
and breakeven analysis, 203–5
charts, 350–51
and depreciation, 303–6
error messages, 362
functions listing, 353–61
Goal Seek, Excel, 203, 361–62
imbedded function, 118
and inflation, 252–53
introduction, 21–23
and rate of return, 147–51
and sensitivity analysis, 201–3
spreadsheet layout, 351–53
Expected value, 379–81
Expenses, 314, 364. See also Cost
estimation; Cost(s)
Experience curve, 275
External rate of return, 143–44. See
also Rate of return
F
F/A factor, 35–36.
Face value, of bonds, 85
Factor method estimation, 271–73
Factors
capital recovery, 34
gradient
arithmetic, 37–39, 43–44
geometric, 39–41, 44
notation, 30, 39
for shifted series, 41–45
single payment, 29–33
sinking fund, 36
tabulated values, 388–413
uniform-series, 34–37
Factory cost, 278, 365
Financial worth of corporations, 336
Financing. See Debt financing;
Equity financing
First cost, 17, 84, 289
Fiscal year, 363
Fixed assets, 363
Fixed costs, 185–89
Fixed percentage method. See
Declining balance
depreciation
F/P factor, 29
Future worth
calculation, 89, 110
evaluation by, 89, 166
and inflation, 246–49
of shifted series, 42
FV function, Excel, 22, 46, 354–55
G
Gains and losses. See Capital gain;
Capital loss
General depreciation system
(GDS), 298Index 417
Goal Seek, Excel, 361–62
for breakeven, 203–5
for replacement value, 230–31
Gradient, arithmetic
base amount, 38, 43
conventional, 37–39
decreasing, 38
factors, 37, 39, 40
shifted, 43–45
Gradient, geometric
base amount, 39
factors, 39–41
shifted, 44
Graduated tax rates, 314–17
Gross income, 301, 314
H
Half-year convention, 290, 295,
305–6
Highly leveraged corporations,
330–31
Hurdle rate. See Minimum attractive
rate of return
Hyperinflation, 250
I
Income
gross, 314
net, 335
as revenue, 17, 314, 364
taxable, 314, 316, 335–36
Income statement, 364–65
Income tax, 314–39
average tax rate, 315
and cash flow, 317–20
corporate, 315
defined, 314
and depreciation, 320–26
effective rates, 314, 318
individual taxpayers, 316–17
international, 337–39
present worth of, 324–26
and rate of return, 318
rates, 314–17
and replacement studies,
326–28
tax savings, 318
Incremental benefit/cost analysis,
168–74
Incremental cash flow, 132–35
Incremental costs
and benefit/cost analysis, 168–69
definition, 132–33
and rate-of-return, 135–39
Incremental rate of return analysis,
135–39, 320
Independent projects
B/C evaluation of, 173
bundles, 95
formation, 82–83
PW evaluation of, 94–98
ROR evaluation of, 135
Indexing, income taxes, 314
Indirect costs
activity-based costing, 279–81
definition, 261, 276
factor method, 271–73
rates, 276–77
Infinite life, 89–94, 114–16, 162
Inflation, 237–53
assumption in PW and AW, 87, 109
and capital recovery, 250–52
definition, 7, 239
and future worth, 246–50
high, 250
and interest rates, 240
and MARR, 249
and present worth, 241–46
Initial investment. See First cost
Installation costs, in depreciation, 289
Intangible factors, 4. See also
Multiple attribute evaluation;
Noneconomic factors
Interest
compound, 10–14
defined, 5
interperiod, 71
rate (See Interest rate)
simple, 9–10, 12–14
Interest period, 5
Interest rate. See also Effective interest rate
continuous compounding, 64–65
definition, 5
inflation-adjusted, 240
inflation free (real), 240, 247
IRR function, 22, 49, 129,
148–51, 355–56
market, 240
multiple, 139–43
nominal versus effective, 61–65
for public sector, 164
unknown, 21, 30
on unrecovered balance, 126
Interest tables, 388–413
Internal rate of return. See Rate of
return
International aspects
after taxes, 337–39
contracts, 166
cost estimation, 263
deflation, 241
depreciation, 289, 291, 337–39
hyperinflation, 250
Inventory turnover ratio, 368
Invested capital, cost of, 335–36
Investment(s). See also First cost
extra, 132–35
permanent, 89–90, 114–16
safe, 6–7
IPMT function, Excel, 355
IRR function, Excel, 22, 49, 129,
148–51, 355–56
L
Land, 290
Lang factors, 271
Least common multiple (LCM)
and annual worth, 109, 139
and future worth, 89
and incremental cash flow, 132, 134
and incremental rate of return,
132, 135, 137–39
and independent projects, 94–95
and present worth, 86–88
Learning curve, 273–75
Leveraging, 330–331
Liabilities, 363–64
Life. See Lives
Life cycle, and annual worth, 109
Life cycle costs, 89
Likert scale, 373
Lives
common multiple, 86–88, 109
equal, 84, 132
finite, 93, 116
independent projects, 94–95
minimum cost, 218–20
perpetual, 89–94, 114–16
and rate of return, 132–35418 Index
Lives—Cont.
recovery, in depreciation, 289
unequal, 86–88, 93, 109
unknown, 20, 22, 30, 357
useful, 289
M
MACRS (Modified Accelerated Cost
Recovery System), 295–99
depreciation rates, 296
and Excel functions, 305, 360–61
PW of, depreciation, 299, 305–6
recovery period, 298
straight line alternative, 298
switching, 299
U.S., required, 291, 295
Maintenance and operating (M&O)
costs, 3, 167, 314. See also
Annual operating costs
Make-or-buy decisions, 112, 183, 191
Manufacturing progress function, 275
Marginal tax rates, 314
Market interest rate. See Interest rate
Market value
and depreciation, 289
in ESL analysis, 217
estimating, 217
in replacement analysis, 221–24
as salvage value, 86
MARR. See Minimum attractive rate
of return
Marshall & Swift, 266, 268
Mean, 379
Measure of worth, 5, 192
Minimum attractive rate of return
after-tax, 318
definition, 6
establishing, 7, 328–29
as hurdle rate, 7
and independent projects, 94
inflation-adjusted, 249
in PW and AW analysis, 84,
86, 112
and rate of return, 131–39
in sensitivity analysis, 192
before tax, 7, 84, 318
and WACC, 329–30
M&O costs. See Annual operating
costs; Maintenance and
operating costs
Modified benefit/cost ratio, 167
Most likely estimate, 197, 376
Multiple alternatives
benefit/cost analysis, 168–74
independent, 94–96
rate of return analysis, 135–39
Multiple attribute evaluation,
370–75
Multiple rates of return
definition, 139
determining, 139–43
removing, 143–47
Municipal bonds, 85–86
Mutually exclusive alternatives
annual worth analysis, 112–16
benefit/cost analysis, 168–74
capitalized cost analysis, 89–94
formation of, 82–83
future worth analysis, 89
present worth analysis, 84–89
rate of return analysis, 135–39
N
Net cash flow, 17, 199, 317
Net investment procedure, 144–47
Net present value. See NPV function,
Excel; Present worth
Net profit after taxes (NPAT),
335–36
Net worth, 363–64
NOMINAL function, Excel,
72–73, 357
Nominal interest rate, 61–63
annual, 63
and effective rates, 63–65
Nonconventional cash flow series,
139–40
Noneconomic factors, 4
No-return payback, 199
Norstrom’s criterion, 139
NPER function, Excel, 22, 46, 357
and annual worth, 115
and unknown n, 22, 46–48
NPV function, Excel, 97–98, 357
for arithmetic gradients, 69
imbedding in PMT, 48, 118,
228–30
and present worth, 97–98
in PV vs. i graphs, 149
and shifting, 46–48
O
One-year-later replacement analysis,
221–24
Operating costs. See Annual operating costs; Cost estimation
Optimistic estimate, 197–98
Order of magnitude estimates, 263
Overhead rates. See Indirect costs
Owner’s equity, 363
P, Q
P/A factor, 34–35, 38
Payback analysis 199–201
limitations, 199, 206
Payment period
of bonds, 85
defined, 66
relative to compounding period,
65–72
Payout period. See Payback analysis
Percentage depletion. See Depletion
Permanent investments, 89, 114. See
also Capitalized cost
Personal property, 290, 298
Pessimistic estimate, 197–98
P/F factor, 29.
P/G factor, 37–38. See also
Gradients, arithmetic
Planning horizon. See Study period
Plant costs, 271–73
PMT function, Excel, 22, 35, 358
and annual worth, 46–48, 111,
116–18
and capital recovery, 116
and economic service life, 228–30
imbedded with NPV function, 48,
118, 228–30
and shifted series, 47–48
Point estimates, 17, 376
Power law and sizing model, 269
Present worth, 84–98
and annual worth, 110
arithmetic gradient, 38
assumptions, 84, 86
of bonds, 85
of depreciation, 299
for equal lives, 84
geometric gradient, 39–40
of income taxes, 324
and independent projects, 94–96Index 419
and inflation, 241–46
and life cycle cost, 89
and multiple interest rates,
140–44
and rate of return, 135–39
and sensitivity analysis, 192–95
in shifted series, 43
single-payment factor, 29
for unequal lives, 86–89
versus i graph, 149
Present worth factors
gradient, 37–40
single-payment, 29–30
uniform-series, 34–35
Probability
defined, 377
and expected value, 379–81
Probability distribution, 377
Productive hour rate method, 278
Profit, 185–87
Profitability index, 124. See also
Rate of return
Profitability ratios, 366
Profit-and-loss statement. See
Income statement
Project net-investment, 144–47
Property class, 298
Public sector projects, 162–66
and annual worth, 114–16
benefit/cost analysis, 166–74
BOT contracts, 166
capitalized cost, 89–94
Purchasing power, 246–48
PV function, Excel, 22, 35, 358
and NPV function, 97–98, 358
and present worth, 45, 86, 97
and single payment, 32
and uniform series present
worth, 35
PW vs. i graph, 149
Quick ratio, 367
R
Random samples, 377
Random variable, 377–84
classification, 377
expected value, 379–81
probability distribution of, 377
standard deviation, 382–84
Rank and rate technique, 374
RATE function, Excel, 22, 129,
147–48, 359
Rate of depreciation
declining balance, 292–93
MACRS, 295–96
straight line, 291
Rate of return (ROR), 124–51
after-tax, 318–20
and annual worth, 139
on bonds, 130
cautions, 131
composite, 143–44
on debt and equity capital, 330–31
defined, 5, 126
external, 143
on extra investment, 135–39
incremental, 131–33
and independent projects, 136
internal, 126,143
minimum attractive (see Minimum
attractive rate of return)
and MIRR function, Excel, 150
multiple, 139–47
and mutually exclusive alternatives,
135–39
ranking inconsistency, 132
and reinvestment rate, 144
and sensitivity analysis, 195–96
Ratios, accounting, 366–69
Real interest rate, 240, 247
Real property, 290, 296
Recaptured depreciation
definition, 320
in replacement study, 326–28
and taxes, 320–23
Recovery period
defined, 289
effect on taxes, 323–24, 326
MACRS, 296, 298
Recovery rate. See Rate of
depreciation
Reinvestment rate, 144
Replacement analysis, 215–31
after-tax, 326–28
before-tax, 220–24
cash flow approach, 224
consultant’s viewpoint, 217
depreciation recapture, 326–28
economic service life, 218–20
first costs, 217
market value, 217, 221
opportunity cost (conventional)
approach, 224
and study periods, 221,
224–26, 228
sunk costs, 217
Replacement value, 224, 230
Retained earnings, 364
Retirement life. See Economic
service life
Return on assets ratio, 368
Return on invested capital, 144
Return on investment (ROI), 5, 124.
See also Rate of return
Return on sales ratio, 367
Revenue alternative, 82, 133, 135, 169
Risk
and debt-equity mix, 330–31
and decision making, 376
and payback analysis, 201
and variation in estimates, 376
Rule of 72, 20–21
Rule of 100, 21
Rule of signs
cash flow, 139–41
cumulative cash flow, 139, 142
S
Safe investment, 6–7
Sales, return on, 367
Salvage value
in B/C analysis, 166
and capital recovery, 110–11
and depreciation, 290, 291,
293, 295
and market value, 86, 112, 222
in replacement analysis, 219–22
Sample, 377
average, 379–81
expected value, 379
standard deviation, 382
Savings, tax, 318
Scatter charts. See xy Excel charts
Sensitivity analysis. See also
Breakeven analysis; Goal
Seek, Excel
approach, 192
of one parameter, 192–95
of several parameters, 195–96
with three estimates, 197–98420 Index
Service life. See Economic service life
Shifted gradients, 43–45
Shifted series, 41–45
Sign changes, 139–40
Simple cash flow series, 139
Simple interest, 9, 12–14
Single-payment compound amount
factor (F/P), 29
Single payment factors, 29–33
Single-payment present worth factor
(P/F), 29
Single-value estimates, 17, 376
Sinking fund (A/F) factor, 35–36
SLN function, Excel, 291,
303–4, 359
Solvency ratios, 366
Solver tool, Excel, 96, 195
Spreadsheet analysis. See also Excel
after-tax, 332–35
annual worth, 116–18, 333–34
B/C analysis, 174–76
breakeven analysis, 203–5
depreciation, 303–6
effective interest, 72–74
equivalency computations, 45–49
EVA, 336–37
Excel functions, 22, 353–62
inflation, 252–53
layout, 351–53
present worth, 96–98, 333–34
rate of return, 147–51, 333–35
replacement analysis, 228–31
sensitivity analysis, 201–3
Standard deviation, 382–84
STDEV function, Excel, 382, 384
Stocks, 328, 330–31
Straight line alternative, in
MACRS, 298
Straight line depreciation,
291–92, 299
Straight line rate, 291, 293
Study period
AW evaluation, 109, 112
equal service, 86, 95
FW analysis, 89
independent projects, 95
PW evaluation, 86
replacement analysis, 220–21,
224–26
Sunk cost, 217
Survivor, in multiple-alternative
analysis, 135–39, 168–73
Switching, depreciation methods,
299–300, 305
T
Tax depreciation, 289
Taxable income, 314–26
and CFAT, 317–18
and depreciation, 322, 324–25
negative, 318
Taxes, 314–39. See also After-tax;
Economic value added;
Income tax; Taxable income
Terminology, 14–15
Time placement of dollars, 17–20, 239
Time value of money, 4–5
Top down approach, 262–63
Total cost relation, 185–88. See also
Breakeven analysis
Trade-in value, 218, 224, 290. See also
Market value; Salvage value
U
Uniform distribution, 377
Uniform gradient. See Gradient,
arithmetic
Uniform percentage method. See
Declining balance depreciation
Uniform series
compounding period and payment
period, 65–72
description, 14
factors, 34–37
shifted, 41–45
Unit method, 264–65
Unrecovered balance, 126, 144
V–Y
Value added analysis. See Economic
value added (EVA)
Value engineering, 263
Variable. See Random variable
Variable costs, 185–86
VDB function, Excel, 305–6, 360
for MACRS rates, 296, 305–6
Weighted attribute method, 370–75
Weighted average cost of capital
(WACC), 329–32
xy Excel charts, 149, 202, 229, 305,
334, 350–51
Year(s). See also Half-year convention
cash flow diagrams, 18–20
end-of-period con
Glossary of Terms and Symbols
Term Symbol Description
Annual amount or worth A or AW Equivalent uniform annual worth of all cash inflows and
outflows 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 is
accounted for.
Breakeven point QBE Quantity at which revenues and costs are equal, or two
alternatives are equivalent.
Capital recovery CR Equivalent annual cost of owning an asset plus
the 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) and
disbursements (outflow).
Cash flow before CFBT or Cash flow amount before relevant taxes or after taxes
or after taxes CFAT are applied.
Composite rate i Unique rate of return when a reinvestment rate c is
of 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 costs
relationships over time to estimate current and future costs.
Cost of capital WACC Interest rate paid for the use of capital funds; includes both
debt and equity funds. For debt and equity considered, it
is weighted average cost of capital.
Debt-equity mix D-E Percentages of debt and equity investment capital
used by a corporation to fund projects.
Depreciation D Reduction in the value of assets using specifi c models and
rules; there are book and tax depreciation methods.
Depreciation rate dt Annual rate for reducing the value of assets using
depreciation.
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 of
worth money.
(Continued)
Term Symbol Description
Gradient, 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; compounding
accrues interest on principal plus all accumulated interest.
Interest rate i or r Interest expressed as a percentage of the original amount
per time period; nominal (r) and effective (i) rates.
Interest rate, i
f Interest rate adjusted to take infl ation into account.
inflation-adjusted
Life (estimated) n Number of years or periods over which an alternative or
asset 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 balances
such 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 traded
or disposed of.
Standard deviation s Measure of dispersion or spread about the expected value
or 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 corporate
or individual taxes.
Tax rate, effective T
e 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 series
NPV(i%,second_cell:last_cell) first_cell for varying cash flow series
Future worth:
FV(i%,n,A,P) for constant A series
Annual worth:
PMT(i%,n,P,F) for single amounts with no A series
Number 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 function
to retain the same sign.)
Rate of return:
RATE(n,A,P,F) for constant A series
IRR(first_cell:last_cell) for varying cash flow series
Interest rate:
EFFECT(r%,m) for nominal r, compounded m times per period
NOMINAL(i%,m) for effective i, compounded m times per year
Depreciation:
SLN(P,S,n) Straight line depreciation for each period
DDB(P,S,n,t,d) Double declining balance depreciation for
period t at rate d
DB(P,S,n,t) Declining balance, rate determined by the
function
VDB(P,S,n, start_period, Switch from declining balance to straight
end_period, factor) line depreciation
VDB(P,0,n,MAX(0,t 1.5), MACRS depreciation for period t
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