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12e
Managerial Economics
Mark Hirschey
University of Kansas
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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Managerial Economics, 12th Edition
© 2009, 2006 South-Western, a part of Cengage Learning
Mark Hirschey
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Dedication
For Christine—I still do.
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About the Author
Mark Hirschey, Ph.D. (University of Wisconsin-Madison), is the Anderson W. Chandler
Professor of Business at the University of Kansas, where he teaches undergraduate and
graduate courses in managerial economics and finance. Professor Hirschey is president of
the Association of Financial Economists and member of several professional organizations.
He has published articles in the American Economic Review, Review of Economics and Statistics,
Journal of Business, Journal of Business and Economic Statistics, Journal of Finance, Journal of
Financial Economics, Journal of Industrial Economics, and other leading academic journals.
He is editor of Advances in Financial Economics, and past editor of Managerial and Decision
Economics. Professor Hirschey is also author of Fundamentals of Managerial Economics and
Investments: Analysis & Behavior.
vii
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Brief Contents
Preface
xxiii
Part 1: Overview of Managerial Economics
1
1. Nature and Scope of Managerial Economics 3
2. Economic Optimization 23
3. Demand and Supply 77
Part 2: Demand Analysis and Estimation
111
4. Demand Analysis 113
5. Demand Estimation 161
6. Forecasting 199
Part 3: Production and Competitive Markets
7.
8.
9.
10.
11.
Part 4: Imperfect Competition
12.
13.
14.
15.
455
Monopoly and Monopsony 457
Monopolistic Competition and Oligopoly 501
Game Theory and Competitive Strategy 549
Pricing Practices 585
Part 5: Long-Term Investment Decisions
16.
17.
18.
19.
243
Production Analysis and Compensation Policy 245
Cost Analysis and Estimation 289
Linear Programming 331
Competitive Markets 379
Performance and Strategy in Competitive Markets 413
629
Risk Analysis 631
Capital Budgeting 671
Organization Structure and Corporate Governance 713
Government in the Market Economy 747
Appendix A: Compounding and the Time Value of Money 787
Appendix B: Interest Factor Tables 803
Appendix C: Statistical Tables 811
Selected Figures for End of Chapter Problems 817
Index
825
ix
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Contents
Part 1: Overview of Managerial Economics
Chapter 1: Nature and Scope of Managerial
Economics
3
How is Managerial Economics Useful?
3
Evaluating Choice Alternatives, 3 • Making
the Best Decision, 5
5
Theory of the Firm
6
Expected Value Maximization, 6 • Constraints
and the Theory of the Firm, 7 • Limitations of the
Theory of the Firm, 8
9
Business Versus Economic Profit, 9 • Variability
of Business Profits, 10
Managerial Application: 1.2 The World Is
Turning to Capitalism and Democracy
Why do Profits Vary Among Firms?
9
12
Disequilibrium Profit Theories, 12 • Compensatory
Profit Theories, 12 • Role of Profits in the
Economy, 13
Managerial Application: 1.3 Google on Social
Responsibility
13
Role of Business in Society
14
Why Firms Exist, 14 • Social Responsibility
of Business, 15
Managerial Application 1.4: The Internet
Revolution
Structure of this Text
Chapter 2: Economic Optimization
23
Economic Optimization Process
23
Optimal Decisions, 23 • Maximizing the Value
of the Firm, 24
Revenue Relations
Managerial Application 1.1: Business Ethics
Profit Measurement
1
25
Price and Total Revenue, 25 • Marginal Revenue,
28 • Revenue Maximization Example, 29
Managerial Application 2.1: The Ethics of Greed
Versus Self-Interest
25
Managerial Application 2.2: Do Firms
Really Optimize?
30
Cost Relations
30
Total Cost, 30 • Marginal and Average Cost, 32
• Average Cost Minimization Example, 33
Profit Relations
34
Total and Marginal Profit, 34 • Profit Maximization
Example, 35
Managerial Application 2.3: Market-Based
Management
34
Incremental Concept in Economic Analysis
38
Marginal Versus Incremental Concept, 38
• Incremental Profits, 38 • Incremental Concept
Example, 40
Managerial Application 2.4: Behavioral Economics
39
16
Summary
41
16
Questions
42
Development of Topics, 17
Self-Test Problems and Solutions
43
Summary
18
Problems
48
Questions
19
Case Study: Is Coca-Cola the “Perfect” Business?
19
Case Study: Spreadsheet Analysis of the EOQ
at the Neighborhood Pharmacy, Inc.
53
Selected References
22
Selected References
54
xi
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xii
Contents
Appendix 2A: Math Analysis for Managers
55
Properties of Real Numbers
55
Demand Curve
Transitive Property, 55 • Commutative
Properties, 55 • Associative Properties, 56
• Distributive Properties, 56 • Inverse Properties, 56
• Exponents and Radicals, 56
Equations
Equivalent Operations, 57 • Linear Equations, 58
• Quadratic Equations, 58 • Multiplicative
Equations, 58 • Exponential Functions, 58
• Logarithmic Functions, 59
Managerial Application 3.2: ISP Customers Learn
About Demand and Supply
84
Basis for Supply
85
How Output Prices Affect Supply, 85 • Other
Factors That Influence Supply, 86
Concept of a Marginal
60
Rules for Differentiating a Function
62
Constants, 62 • Powers, 63 • Sums and
Differences, 63 • Products, 64 • Quotients, 65
• Logarithmic Functions, 65 • Function
of a Function (Chain Rule), 66
68
Partial Derivative Concept, 68 • Maximizing
Multivariate Functions, 69
Constrained Optimization
81
Demand Curve Determination, 81 • Relation
Between the Demand Curve and
Demand Function, 82
57
Appendix 2B: Multivariate Optimization
and the Lagrangian Technique
Determinants of Demand, 79 • Industry Demand
Versus Firm Demand, 80
70
Role of Constraints, 71 • Lagrangian
Multipliers, 72
Problem
76
Chapter 3: Demand and Supply
77
Basis for Demand
77
Direct Demand, 77 • Derived Demand, 78
Market Supply Function
86
Determinants of Supply, 86 • Industry Supply
Versus Firm Supply, 87
Managerial Application 3.3: The Import Supply
Battle in the U.S. Auto Industry
88
Supply Curve
89
Supply Curve Determination, 89 • Relation
Between Supply Curve and Supply Function, 89
Managerial Application 3.4: MBA Demand
and Supply
92
Market Equilibrium
93
Surplus and Shortage, 93 • Comparative Statics:
Changing Demand, 95 • Comparative Statics:
Changing Supply, 97 • Comparative Statics:
Changing Demand and Supply, 98
Summary
99
Questions
99
Self-Test Problems and Solutions
100
Problems
103
Managerial Application 3.1: How the
Internet Affects Demand and Supply
79
Case Study: Spreadsheet Analysis of Demand
and Supply for Sunbest Orange Juice
107
Market Demand Function
79
Selected References
109
Part 2: Demand Analysis and Estimation
Chapter 4: Demand Analysis
113
Utility Theory
113
111
Basic Characteristics, 118• Perfect Substitutes
and Perfect Complements, 120
Budget Constraints
Basic Assumptions, 113 • Utility Functions, 114
• Marginal Utility, 115 • Law of Diminishing
Marginal Utility, 116
Managerial Application 4.1: Odd-number
Pricing Riddle
118
Indifference Curves
118
120
Characteristics of Budget Constraints, 120
• Effects of Changing Income and Changing
Prices, 123 • Income and Substitution
Effects, 124
Individual Demand
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xiii
Price–Consumption Curve, 124
• Income–Consumption Curve, 127
• Engle Curves, 127
Managerial Application 4.2: Relationship Marketing 130
Optimal Consumption
130
134
Elasticity Concept, 134 • Point Elasticity, 134
• Arc Elasticity, 135
Price Elasticity Of Demand
135
139
Elasticity Varies Along a Linear Demand
Curve, 139 • Price Elasticity and Price
Changes,140
Price Elasticity and Optimal Pricing Policy
143
165
Graphing the Market Demand Curve, 165
• Evaluating Market Demand, 166
168
Changing Nature of Demand Relations, 168
• Interplay of Demand and Supply, 168
• Shifts in Demand and Supply, 169
• Simultaneous Relations, 171
171
What is a Statistical Relation?, 171
• Specifying the Regression Model, 174
• Least Squares Method, 175
Managerial Application 5.2: Market
Experiments on the Web
172
Managerial Application 5.3:Lies, Damn Lies,
and Government Statistics
177
Measures of Regression Model Significance
177
Standard Error of the Estimate, 177 • Goodness
of Fit, 179 • F Statistic, 180
Optimal Price Formula, 143 • Optimal Pricing
Policy Example, 144
Judging Variable Significance
Managerial Application 4.3: Haggling in the
Car Business
143
Cross-Price Elasticity of Demand
145
Cross-Price Elasticity Formula, 145
• Substitutes and Complements, 146
Income Elasticity of Demand
Simple Market Demand Curve Estimation
Regression Analysis
Price Elasticity Formula, 135 • Price Elasticity
and Total Revenue, 137
Price Elasticity and Marginal Revenue
163
Identification Problem
Marginal Utility and Consumer Choice, 130
• Marginal Rate of Substitution, 131
• Utility Maximization, 133
Demand Sensitivity Analysis: Elasticity
Managerial Application 5.1: Sampling
Technology for TV Advertising
146
Income Elasticity Formula, 146 • Normal Versus
Inferior Goods, 147
181
Two-Tail t Tests, 181 • One-Tail t Tests, 184
Managerial Application 5.4: Spreadsheet
and Statistical Software for the PC
182
Summary
185
Questions
186
Self-Test Problems and Solutions
186
Managerial Application 4.4: What's in a Name?
148
Problems
191
Summary
148
Questions
149
Case Study: Demand Estimation for
Mrs. Smyth’s Pies
195
Self-Test Problems and Solutions
150
Selected References
198
Problems
155
Chapter 6: Forecasting
199
Case Study: Optimal Level of Advertising
158
Selected References
159
Forecasting Applications
199
Chapter 5: Demand Estimation
161
Interview and Experimental Methods
161
Consumer Interviews, 161 • Market
Experiments, 162
Simple Demand Curve Estimation
Simple Linear Demand Curves, 162 • Using
Simple Linear Demand Curves, 164
162
Macroeconomic Applications, 199
• Microeconomic Applications, 200
• Forecast Techniques, 200
Managerial Application 6.1: Economic
Forecasting: The Art and the Science
201
Qualitative Analysis
202
Expert Opinion, 202 • Survey
Techniques, 202
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xiv
Contents
Trend Analysis and Projection
203
Trends in Economic Data, 203 • Linear Trend
Analysis, 203 • Growth Trend Analysis, 206
• Linear and Growth Trend Comparison, 208
Managerial Application 6.2: Prediction
Markets: The IEM
209
Business Cycle
210
What is the Business Cycle?, 210 •
Economic Indicators, 212 • Economic
Recessions, 213 • Sources of Forecast
Information, 215
Managerial Application 6.4: How Good Is Your
Forecasting Ability?
221
Judging Forecast Reliability
225
Tests of Predictive Capability, 225 • Correlation
Analysis, 225 • Sample Mean Forecast Error
Analysis, 225
Choosing the Best Forecast Technique
Managerial Application 6.3: The Stock
Market and the Business Cycle
216
Exponential Smoothing
217
Exponential Smoothing Concept, 217
• One-Parameter (Simple) Exponential
Smoothing, 217 • Two-Parameter (Holt)
Exponential Smoothing, 218 • Three-Parameter
(Winters) Exponential Smoothing, 219
• Practical Use of Exponential
Smoothing, 219
Econometric Forecasting
Advantages of Econometric Methods, 220
• Single-Equation Models, 222 • MultipleEquation Systems, 223
226
Data Requirements, 226 • Time Horizon
Considerations, 226 • Role of
Judgment, 228
Summary
228
Questions
229
Self-Test Problems and Solutions
230
Problems
234
Case Study: Forecasting Global
Performance for a Mickey Mouse Organization
238
Selected References
241
220
Part 3: Production and Competitive Markets
Chapter 7: Production Analysis and
Compensation Policy
245
Production Functions
245
Properties of Production Functions, 245
• Returns to Scale and Returns
to a Factor, 246
Total, Marginal, and Average Product
251
261
Budget Lines, 261 • Expansion Path, 262
• Illustration of Optimal Input
Proportions, 263
Optimal Levels of Multiple Inputs
264
Optimal Employment and Profit
Maximization, 264 • Illustration of Optimal
Levels of Multiple Inputs, 265
Diminishing Returns to a Factor Concept, 251
• Illustration of Diminishing Returns to
a Factor, 252
Managerial Application 7.1: Efficiency Wages
252
Input Combination Choice
253
Production Isoquants, 253 • Input Factor
Substitution, 255 • Marginal Rate of Technical
Substitution, 256 • Rational Limits of Input
Substitution, 257
Managerial Application 7.2: An
Inconvenient Truth About Minimum Wages
258
Marginal Revenue Product, 258 • Optimal Level
of a Single Input, 259 • Illustration of Optimal
Employment, 260
Optimal Combination of Multiple Inputs
248
Total Product, 248 • Marginal and Average
Product, 248
Law of Diminishing Returns to a Factor
Marginal Revenue Product and Optimal
Employment
243
Managerial Application 7.3: What’s Wrong
with Manufacturing?
265
Returns to Scale
266
Output Elasticity and Returns to Scale, 266
• Returns to Scale Estimation, 267
Productivity Measurement
258
Economic Productivity, 269 • Causes of
Productivity Growth, 270
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xv
Managerial Application 7.4: CEO Compensation
269
Summary
271
Questions
272
Self-Test Problems and Solutions
273
Problems
276
Case Study: Worker Productivity Among Giant
U.S. Corporations
280
Selected References
283
Managerial Application 8.4: Bigger Isn’t
Always Better
310
Economies of Scope
313
Economies of Scope Concept, 313 • Exploiting
Scope Economies, 313
Cost-Volume-Profit Analysis
314
Cost-Volume-Profit Charts, 314 • Degree of
Operating Leverage, 315
Summary
318
Questions
319
285
Self-Test Problems and Solutions
320
285
Problems
322
Constrained Cost Minimization
287
Problem
288
Case Study: Estimating Hospitalization
Costs for Regional Hospitals
326
Selected References
329
Chapter 8: Cost Analysis and Estimation
289
Economic and Accounting Costs
289
Chapter 9: Linear Programming
331
Basic Assumptions
331
Appendix 7A: A Constrained Optimization
Approach to Developing the Optimal Input
Combination Relationships
Constrained Production Maximization
Historical Versus Current Costs, 289
• Opportunity Costs, 290
Role of Time in Cost Analysis
291
Incremental Versus Sunk Cost, 291
• How is the Operating Period Defined?, 292
Managerial Application 8.1: GE’s “20-70-10” Plan
292
Short-Run Cost Curves
293
Short-Run Cost Categories, 293
• Short-Run Cost Relations, 294
Managerial Application 8.2: Gaps in GAAP?
296
Long-Run Cost Curves
296
Long-Run Total Costs, 297 • Economies of
Scale, 297 • Cost Elasticities and Economies
of Scale, 299 • Long-Run Average Costs, 299
Managerial Application 8.3: What’n Heck is a FASB? 301
Minimum Efficient Scale
302
Competitive Implications of Minimum Efficient
Scale, 302 • Transportation Costs and MES, 302
Firm Size and Plant Size
303
332
Production Planning for a Single Product
333
Production Processes, 333 • Production
Isoquants, 334 • Least-Cost Input
Combinations, 336 • Optimal Input Combinations
with Limited Resources, 337
Managerial Application 9.2: LP: More Than a
Visual Approach
340
Production Planning for Multiple Products
340
Objective Function Specification, 340 • Constraint
Equation Specification, 341 • Nonnegativity
Requirement, 341
Graphic Specification and Solution
342
Analytic Expression, 342 • Graphing the
Feasible Space, 342 • Graphing the Objective
Function, 344 • Graphic Solution, 345
346
Algebraic Specification, 346 • Algebraic
Solution, 348
309
Learning Curve Concept, 309 • Learning Curve
Example, 310 • Strategic Implications of the
Learning Curve Concept, 312
Managerial Application 9.1: Karmarkar’s LP
Breakthrough
Algebraic Specification and Solution
Multiplant Economies and Diseconomies of
Scale, 303 • Economics of Multiplant Operation
An Example, 304 • Plant Size and Flexibility, 308
Learning Curves
Inequality Constraints, 331 • Linearity
Assumption, 332
Managerial Application 9.3: LP on the PC!
351
Dual in Linear Programming
352
Duality Concept, 352 • Shadow Prices, 352
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xvi
Contents
Dual Specification
353
Dual Objective Function, 353 • Dual Constraints,
353 • Dual Slack Variables, 354
Solving the Dual Problem
Competitive Market Equilibrium
396
Balance of Supply and Demand, 396 • Normal
Profit Equilibrium, 397
355
Dual Solution, 355 • Using the Dual Solution
to Solve the Primal, 356
Managerial Application 10.4: The Enron Debacle
398
Summary
398
Questions
399
Managerial Application 9.4: It’s a RIOT
on the Internet!
358
Self-Test Problems and Solutions
400
Summary
358
Problems
405
Questions
359
Self-Test Problems and Solutions
360
Case Study: Profitability Effects of Firm Size
for DJIA Companies
409
Problems
367
Selected References
411
Case Study: A LP Pension Funding Model
372
Chapter 11: Performance and Strategy
in Competitive Markets
413
Competitive Market Efficiency
413
Appendix 9A: Rules for Forming the Dual Linear
Programming Problem
375
Primal Problem
375
Dual Problem
376
Selected References
377
Chapter 10: Competitive Markets
Competitive Environment
Why Is it Called Perfect Competition?, 413
• Deadweight Loss Problem, 415 • Deadweight
Loss Illustration, 416
379
Managerial Application 11.1: The Wal-Mart
Phenomenon
418
379
Market Failure
418
Structural Problems, 418
• Incentive Problems, 419
What Is Market Structure?, 379 • Vital Role of
Potential Entrants, 380
Role for Government
Factors that Shape the Competitive
Environment
380
Product Differentiation, 380 • Production
Methods, 382 • Entry and Exit Conditions, 382
Managerial Application 10.1: Benefits From
Free Trade
Competitive Market Characteristics
381
Managerial Application 11.2: Corn Growers
Discover Oil!
421
383
Subsidy and Tax Policy
421
Subsidy Policy, 422 • Deadweight Loss
from Taxes, 422
Basic Features, 383 • Examples of Competitive
Markets, 383
Tax Incidence and Burden
Managerial Application 10.2: Is the Stock
Market Perfectly Competitive?
384
Profit Maximization in Competitive Markets
385
Profit Maximization Imperative, 385 • Role of
Marginal Analysis, 385
Marginal Cost and Firm Supply
389
Competitive Market Supply Curve
392
392
Market Supply with a Fixed Number
of Competitors, 393 • Market Supply
with Entry and Exit, 393
424
Role of Elasticity, 424 • Tax Cost–Sharing
Example, 426
Managerial Application 11.3: Measuring
Economic Profits
428
Price Controls
429
Price Floors, 429
• Price Ceilings, 431
Short-Run Firm Supply Curve, 389 • Long-Run
Firm Supply Curve, 391
Managerial Application 10.3: Dot.com
419
• How Government Influences Competitive
Markets, 419 • Broad Social
Considerations, 420
Business Profit Rates
432
Return on Stockholders’ Equity, 432
• Typical Profit Rates, 433
Managerial Application 11.4: Wonderful
Businesses
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xvii
Market Structure and Profit Rates
435
Profit Rates in Competitive Markets, 435
• Mean Reversion in Profit Rates, 435
Competitive Market Strategy
437
Short-Run Firm Performance, 437
Long-Run Firm Performance
438
Summary
438
Questions
440
Self-Test Problems and Solutions
441
Problems
447
Case Study: The Most Profitable S&P 500
Companies
451
Selected References
454
Part 4: Imperfect Competition
455
Chapter 12: Monopoly and Monopsony
457
Summary
485
Monopoly Market Characteristics
457
Questions
486
Self-Test Problems and Solutions
486
Basic Features, 457 • Examples of Monopoly, 458
Managerial Application 12.1: The NCAA Cartel
460
Problems
493
Profit Maximization Under Monopoly
460
Case Study: Effect of R&D on Tobin’s q
497
Selected References
500
Chapter 13: Monopolistic Competition
and Oligopoly
501
Contrast Between Monopolistic Competition
and Oligopoly
501
Price–Output Decisions, 460 • Role of Marginal
Analysis, 462
Social Costs of Monopoly
464
Monopoly Underproduction, 464 • Deadweight Loss
from Monopoly, 464
Social Benefits of Monopoly
468
Economies of Scale, 468 • Invention and
Innovation, 468
Monopoly Regulation
Monopolistic Competition
469
Dilemma of Natural Monopoly, 469 • Utility
Price and Profit Regulation, 471 • Utility Price
and Profit Regulation Example, 473
• Problems with Utility Price and Profit
Regulation, 475
Managerial Application 12.2: Is Ticketmaster a
Monopoly?
470
Monopsony
475
Buyer Power, 475 • Bilateral Monopoly
Illustration, 476
Antitrust Policy
479
Managerial Application 13.1: Dell’s Price War
with Dell
504
Managerial Application 13.2: Intel: Running
Fast to Stay in Place
507
Monopolistic Competition Process
507
Short-Run Monopoly Equilibrium, 507
• Long-Run High-Price/Low-Output
Equilibrium, 508 • Long-Run
Low-Price/High-Output Equilibrium, 510
510
Oligopoly Market Characteristics, 511
• Examples of Oligopoly, 511
479
Managerial Application 12.4: Price Fixing by the
Insurance Cartel
482
Competitive Strategy in Monopoly Markets
482
Market Niches, 482 • Information Barriers to
Competitive Strategy, 483
503
Monopolistic Competition Characteristics, 503
• Monopolistic Competition Price–Output
Decisions, 505
Oligopoly
Overview of Antitrust Law, 480 • Sherman and
Clayton Acts, 480 • Antitrust Enforcement, 481
Managerial Application 12.3: Is This Why
They Call it “Hardball”?
Monopolistic Competition, 501 • Oligopoly, 502
• Dynamic Nature of Competition, 503
Cartels and Collusion
512
Overt and Covert Agreements, 512 • Enforcement
Problems, 513
Oligopoly Output-Setting Models
Cournot Ogopoly, 513
• Stackelberg Oligopoly, 516
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513
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xviii
Contents
Oligopoly Price-Setting Models
519
561
Auction Types, 561 • Public Policy
Applications, 562
Bertrand Oligopoly: Identical Products, 519
• Bertrand Oligopoly: Differentiated Products,
520 • Sweezy Oligopoly, 523 • Oligopoly Model
Comparison, 524
Managerial Application 13.3: Contestable Airline
Passenger Service Markets
525
Market Structure Measurement
525
Economic Census, 525 • NAICS System, 526
Census Measures of Market Concentration
Game Theory and Auction Strategy
Managerial Application 14.3: Wrigley's Success
Formula
563
Competitive Strategy
563
Competitive Advantage, 563 • When Large
Size Is a Disadvantage, 565
Pricing Strategies
527
Concentration Ratios, 527
• Herfindahl–Hirschmann Index, 529
• Limitations of Census Information, 531
565
Limit Pricing, 565 • Network Externalities, 567
• Market Penetration Pricing, 567
Managerial Application 14.4: Network
Switching Costs
568
Nonprice Competition
568
Managerial Application 13.4: Horizontal
Merger Guidelines
534
Summary
534
Questions
536
Self-Test Problems and Solutions
536
Summary
Problems
540
Questions
574
Self-Test Problems and Solutions
574
Advantages of Nonprice Competition, 568
• Optimal Level of Advertising, 569
• Optimal Advertising Example, 571
573
Case Study: Market Structure Analysis at
Columbia Drugstores, Inc.
545
Problems
577
Selected References
548
Chapter 14: Game Theory and
Competitive Strategy
Case Study: Time Warner, Inc., Is Playing
Games with Stockholders
582
549
Selected References
584
Game Theory Basics
549
Chapter 15: Pricing Practices
585
Pricing Rules-of-Thumb
585
Types of Games, 549 • Role of Interdependence,
550 • Strategic Considerations, 551
Managerial Application 14.1: Asymmetric
Information
551
Prisoner’s Dilemma
552
Classic Riddle, 552 • Business Application, 553
• Broad Implications, 554
Nash Equilibrium
555
Nash Equilibrium Concept, 555 • Nash
Bargaining, 556
Infinitely Repeated Games
Managerial Application 15.1: Markup Pricing
Technology
587
Markup Pricing and Profit Maximization
587
Optimal Markup on Cost, 587 • Optimal
Markup on Price, 588 • Why Do Optimal
Markups Vary?, 589
Price Discrimination
557
Role of Reputation, 557 • Product Quality
Games, 558
559
Finitely Repeated Games
559
590
Profit-Making Criteria, 590 • Degrees of Price
Discrimination, 591
Price Discrimination Example
Managerial Application 14.2: The Market
for Lemons
Uncertain Final Period, 559 • End-of-Game
Problem, 560 • First-Mover Advantages, 561
Competitive Markets, 585 • Imperfectly
Competitive Markets, 586
592
Price–Output Determination, 593 • One-Price
Alternative, 594
Managerial Application 15.2: Do Colleges Price
Discriminate?
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
593
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Contents
xix
Two-Part Pricing
597
One-Price Policy and Consumer Surplus, 597
• Capturing Consumer Surplus with Two-Part
Pricing, 599 • Consumer Surplus and Bundle
Pricing, 599
Multiple-Product Pricing
600
Demand Interrelations, 600 • Production
Interrelations, 601
Joint Products
602
Joint Products in Variable Proportions, 602
• Joint Products in Fixed Proportions, 602
Managerial Application 15.3: 10¢ for a Gallon
of Gas in Dayton, Ohio
605
Joint Product Pricing Example
604
Joint Products without Excess By-Product, 604
• Joint Production with Excess By-Product
(Dumping), 607
Managerial Application 15.4: Why Some
Price Wars Never End
609
Summary
610
Questions and Answers
611
Self-Test Problems and Solutions
611
Problems
613
Case Study: Pricing Practices in the
Denver, Colorado, Newspaper Market
617
Selected References
619
Appendix 15A: Transfer Pricing
620
Transfer Pricing Problem, 620 • Products
Without External Markets, 620 • Products with
Competitive External Markets, 621 • Products
with Imperfectly Competitive External
Markets, 622
Global Transfer Pricing Example
Profit Maximization for an Integrated Firm, 622
• Transfer Pricing with No External Market, 623
• Competitive External Market with Excess
Internal Demand, 624 • Competitive
External Market withExcess Internal
Supply, 625
Problem
Part 5: Long-Term Investment Decisions
Chapter 16: Risk Analysis
Concepts of Risk and Uncertainty
631
631
Economic Risk and Uncertainty, 631 • General
Risk Categories, 632 • Special Risks of Global
Operations, 633
Probability Concepts
633
Probability Distribution, 634 • Expected Value, 635
• Absolute Risk Measurement, 637 • Relative Risk
Measurement, 639 • Other Risk Measures, 639
Managerial Application 16.1: Behavioral Finance
634
Standard Normal Concept
640
Utility Theory and Risk Analysis
Possible Risk Attitudes, 643 • Relation Between
Money and Its Utility, 643
626
629
Adjusting the Valuation Model for Risk
644
Basic Valuation Model, 644 • Certainty
Equivalent Adjustments, 645 • Certainty
Equivalent Adjustment Example, 647
• Risk-Adjusted Discount Rates, 648
• Risk-Adjusted Discount Rate Example, 649
Managerial Application 16.3: Stock
Option Backdating Scandal
645
Decision Trees and Computer Simulation
650
Decision Trees, 650 • Computer Simulation, 651
• Computer Simulation Example, 652
Managerial Application 16.4: Internet Fraud
654
Summary
655
Questions
656
Self-Test Problems and Solutions
657
642
Problems
661
642
Case Study: Stock-Price Beta Estimation for
Google, Inc.
665
Selected References
669
Normal Distribution, 640 • Standardized
Variables, 641 • Use of the Standard Normal
Concept: An Example, 641
Managerial Application 16.2: Why Are
Lotteries Popular?
622
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xx
Contents
Chapter 17: Capital Budgeting
671
Capital Budgeting Process
671
What Is Capital Budgeting?, 671 • Project
Classification Types, 672
Steps in Capital Budgeting
672
Sequence of Project Valuation, 672 • Cash Flow
Estimation, 673 • Incremental Cash Flow
Evaluation, 673
Cash Flow Estimation Example
674
Project Description, 674 • Cash Flow Estimation
and Analysis, 675
677
Net Present-Value Analysis, 677 • Profitability
Index or Benefit/Cost Ratio Analysis, 680 • Internal
Rate of Return Analysis, 680 • Payback
Period Analysis, 681
713
What Is Organization Structure?, 713
• Optimal Design Is Dynamic, 714
Transaction Cost Theory of the Firm
715
716
Sources of Conflict Within Firms, 716 • Risk
Management Problems, 717 • Investment
Horizon Problems, 719 • Information
Asymmetry Problems, 719
Managerial Application 18.1: Organization
Design at GE
717
Organization Design
720
Resolving Unproductive Conflict Within Firms, 720
• Centralization Versus Decentralization, 721
Decision Management and Control
682
Decision Rule Conflict Problem, 682 • Reasons
for Decision Rule Conflict, 684 • Ranking
Reversal Problem, 684, • Making the Correct
Investment Decision, 687
722
Assigning Decision Rights, 722 • Decision
Process, 723
Corporate Governance
724
Role Played by Boards of Directors, 724 • Corporate
Governance Inside the Firm, 726
Managerial Application 17.2: Is the Sun Setting
on Japan’s Vaunted MOF?
683
Cost of Capital
687
Component Cost of Debt Financing, 687
• Component Cost of Equity Financing, 688
• Weighted-Average Cost of Capital, 691
Managerial Application 17.3: Federal Government
Support for R&D
Organization Structure
Nature of Firms, 715 • Coase Theorem, 716
674
Project Selection
713
The Firm’s Agency Problem
Managerial Application 17.1: Market-Based
Capital Budgeting
Capital Budgeting Decision Rules
Chapter 18: Organization Structure
and Corporate Governance
Managerial Application 18.2: Company
Information on the Internet
725
Ownership Structure as a Corporate
Governance Mechanism
727
Dimensions of Ownership Structure, 727
• Is Ownership Structure Endogenous?, 731
688
Managerial Application 17.4: Capital Allocation
at Berkshire Hathaway, Inc.
693
Optimal Capital Budget
693
Managerial Application 18.3: Sarbanes–Oxley
727
Managerial Application 18.4: Institutional
Investors Are Corporate Activists
732
Agreements and Alliances Among Firms
732
Franchising, 732 • Strategic Alliances, 733
Investment Opportunity Schedule, 693
• Marginal Cost of Capital, 695
• Postaudit, 695
Legal and Ethical Environment
734
Sarbanes–Oxley Act, 734 • Business Ethics, 735
Summary
696
Summary
735
Questions
696
Questions
737
Self-Test Problems and Solutions
697
Self-Test Problems and Solutions
738
Problems
701
Problems
740
Case Study: Sophisticated NPV Analysis
at Level 3 Communications, Inc.
706
Case Study: Do Boards of Directors Make Good
Corprate Watchdogs?
743
Selected References
710
Selected References
746
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Contents
xxi
Chapter 19: Government in the Market
Economy
747
Externalities
747
Negative Externalities, 747 • Positive
Externalities, 748
Managerial Application 19.1: “Tobacco” Ethics
750
Solving Externalities
750
Government Solutions, 750 • Market
Solutions, 751
Public Goods
752
Regulatory Reform in the New
Millennium
767
Promoting Competition in Electric Power
Generation, 767 • Fostering Competition in
Telecommunications, 767 • Reforming
Environmental Regulation, 768
• Improving Regulation of Health
and Safety, 768
Managerial Application 19.4: Price Controls for
Pharmaceutical Drugs
769
Health Care Reform
769
Managed Competition, 769 • Outlook for Health
Care Reform, 771
Rivalry and Exclusion, 752 • Free Riders
and Hidden Preferences, 753
Managerial Application 19.2: Political
Corruption
Summary
772
755
Questions
773
Optimal Allocation of Social Resources
756
Self-Test Problems and Solutions
774
Problems
779
Pareto Improvement, 756 • Marginal Social Costs
and Benefits, 756
Benefit–Cost Methology
758
Benefit–Cost Concepts, 758 • Social Rate of
Discount, 759
Benefit–Cost Criteria
760
Social Net Present-Value, 760 • Benefit–Cost
Ratio, 762 • Social Internal Rate of Return, 763
• Limitations of Benefit–Cost Analysis, 764
Additional Methods for Improving Public
Management
764
Cost-Effectiveness Analysis, 764
• Privatization, 765
Managerial Application 19.3: Free Trade
Helps Everyone
Case Study: Oh Lord, Won't You Buy Me a
Mercedes-Benz (Factory)?
784
Selected References
786
Appendix A: Compounding and the
Time Value of Money
787
Appendix B: Interest Factor Tables
803
Appendix C: Statistical Tables
811
Selected Check Figures for End-of-Chapter
Problems
817
Index
823
765
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May not be copied, scanned, or duplicated, in whole or in part.
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Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Preface
Billy Beane, general manager of Major League Baseball’s Oakland A’s had a problem:
How can a small-market club with a tight budget consistently win in the Major Leagues?
He decided on a simple, but uncommon approach. Beane focused on signing the most
effective baseball players based on their proven ability to help teams win, not on basis
of their unrealized potential. In baseball, conventional wisdom says to sign big, strong,
and fast hitters; and pitchers able to throw the baseball 95 mph. Beane defied tradition
by fielding a team comprised of hitters with high on-base percentage, and pitchers who
throw strikes and get lots of ground outs. Read Michael Lewis’s Moneyball to get the
blow-by-blow account on how Beane built winning teams of young affordable players
and inexpensive castoff veterans.
You might wonder why Warren Buffett and Charlie Munger, chairman and vicechairman Berkshire Hathaway, Inc., enthusiastically recommend Moneyball to their friends
and stockholders. Why would two of the most successful business managers and investors
of all time actively promote a book about baseball? The answer is simple: Beane’s
management of the Oakland A’s shows how successful one can become simply by being
rational and focusing on the most useful data available. That’s just common sense, but in
baseball common sense is rarely employed. Common sense is sometimes uncommon in
business too.
Economic concepts show how to apply common sense to understand business and
solve managerial problems. Economic intuition is really useful. It helps managers decide
on which products to produce, costs to consider, and prices to charge. It also helps them
decide on the best hiring policy and the most effective style of organization. Students and
future managers need to learn these things. The topics covered in managerial economics
are powerful tools that can be used to make them more effective and their careers more
satisfying. By studying managerial economics, those seeking to further their business
careers learn how to more effectively collect, organize and analyze information.
A key feature of this book is its depiction of the firm as a cohesive organization.
Effective management involves an integration of the accounting, finance, marketing,
personnel, and production functions. This integrative approach demonstrates that
important managerial decisions are interdisciplinary in the truest sense of the word. Over
the years, I have come to appreciate that students find understanding of the business firm
as a unified whole, rather than a series of unrelated parts, as one of the most valuable
lessons of managerial economics.
Although both microeconomic and macroeconomic relations have implications
for managerial decision making, this book concentrates on microeconomic topics.
Following development of the economic model of the firm, the vital role of profits
is examined. Because economic decision making often requires an elementary
understanding of optimization techniques and statistical relations, those basic concepts
are described early in the text. Because demand for a firm’s products plays a crucial role
xxiii
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xxiv
Preface
in determining its profitability and ongoing success, demand analysis and estimation is
an essential area of study. An important part of this study is an investigation of the
basic forces of demand and supply. This naturally leads to discussion of economic
forecasting and methods for assessing forecast reliability. Production theory and cost
analysis are then explored as means for understanding the economics of resource
allocation and employment.
Once the internal workings of a successful firm are understood, attention can turn
toward consideration of the firm’s external economic environment. Market structure
analysis provides the foundation for studying the external economic environment
and for defining an effective competitive strategy. The role of government in the
market economy, including the constraints it imposes on business, requires a careful
examination of regulation and antitrust law. Risk analysis and capital budgeting
are also shown as methods for introducing marginal analysis into the long-range
strategic planning and control process. Finally, given government’s increasing role in
managing demand and supply for basic services, such as education and health care,
the use of economic principles to understand and improve public management is also
considered.
Managerial Economics, 12th Edition, takes a practical problem-solving approach. The
focus is on the economics—not the mathematics—of the managerial decision process.
Quantitative tools are sometimes employed, but the emphasis is on economic intuition.
CHANGES IN THE 12TH EDITION
Managerial Economics and Fundamentals of Managerial Economics defined the field, and
continue to play an important role in shaping the teaching of managerial economics.
Both are published to help students use basic economic concepts to understand and
improve the managerial decision-making process. Despite sharing a common objective,
Managerial Economics and Fundamentals of Managerial Economics use slightly different
methods. Managerial Economics features an intuitive calculus-based treatment of economic
theory and analysis; Fundamental of Managerial Economics uses an intuitive noncalculusbased approach.
Students and instructors will find that Managerial Economics, 12th Edition provides an
efficient calculus-based introduction and guide to the optimization process. Chapter 2,
Economic Optimization, illustrates how the concept of a derivative can be used as a
practical tool to understand and apply marginal analysis. Multivariate Optimization and
the Lagrangian Technique, Appendix 2B, examines the optimization process for equations
with three or more variables. Such techniques are especially helpful when managers
face constrained optimization problems, or decision situations with limited alternatives.
Throughout the text, a wide variety of problems describing real-world decisions can be
solved using such techniques.
Like Fundamentals of Managerial Economics, students and instructors will find that
Managerial Economics, 12th Edition provides an intuitive guide to marginal analysis and
basic economic relations. Although differential calculus is an obviously helpful tool for
understanding the process of economic optimization, it is important that students not let
mathematical manipulation get in the way of their basic grasp of economic concepts. The
concept of a marginal can also be described graphically in an intuitive noncalculus-based
approach. Once students learn to grasp the importance of marginal revenue and marginal
cost concepts, the process of economic optimization becomes intuitively obvious.
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Preface
xxv
Although those using a non-calculus based approach can safely skip parts of Chapter 2
and Appendix 2B, all other material is fully and completely assessable. With practice
using a wide variety of problems and examples throughout the text, all students are able
to gain a simple, practical understanding of how economics can be used to understand
and improve managerial decisions. I’ve used both calculus-based and noncalculus-based
approaches in my own MBA classes. Both work.
Of course, the environment in which managerial decisions are made is constantly
changing. To maintain its value as an educational resource, a textbook must be enhanced
and updated. This revision of Managerial Economics contains a number of important
additions and improvements. Every chapter has been thoroughly revised and refined
in response to valuable suggestions provided by students and their instructors. The
following section highlights some of most important changes.
Content
•
•
•
•
•
•
Chapter 2 has been completely rewritten to clarify key economic concepts and the
intuition of marginal analysis. A new Appendix 2A, Math Analysis for Managers, has
also been added to help students that might benefit from a quick review of basic math
concepts.
Chapter 4, Demand Analysis, gives expanded coverage of economic principles used to
understand the underpinnings of demand at the individual and market levels. This
material gives an essential theoretical backdrop for subsequent analysis of demand
estimation and pricing practices.
Chapter 7, Production Analysis and Compensation Policy, now delves more deeply into
important labor market issues that confront both employers and their employees.
This material provided the background for expanded class discussion of a variety of
related issues, such as minimum wage policy, imperfectly competitive labor markets,
and internal labor markets.
Chapter 9, Linear Programming, is new. Linear programming is an especially useful
tool for addressing problems encountered in a number of business, engineering,
financial, and scientific applications. This chapter illustrates how linear
programming can be used to quickly and easily solve real-world decision
problems.
Chapter 14, Game Theory and Competitive Strategy, has been extensively revised
to make clear essential game theory concepts and show how firms use these ideas
to improve decision making when payoffs depend on actions taken by others.
Chapter 15, Pricing Practices, has been expanded to include discussion of two-part
pricing practices that are often featured in markets for distinctive goods and services.
Transfer pricing practices for competitive and imperfectly competitive markets has
been added in a new appendix to the chapter.
Learning Aids
• Each chapter incorporates a wide variety of simple numerical examples and detailed
practical illustrations of chapter concepts. These features portray the valuable use and
real-world implications of covered material.
• Each chapter includes four short Managerial Applications boxes to show current
examples of how the concepts introduced in managerial economics apply to
real-world situations. New Managerial Applications based on articles from the
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May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
xxvi
Preface
•
•
•
•
•
Internet or Barron’s, Business Week, Forbes, Fortune, and The Wall Street Journal are
provided. This feature stimulates student interest and offers a popular basis for
classroom discussion.
The book incorporates several new regression-based illustrations of chapter concepts
using actual company data, or hypothetical data adapted from real-world situations.
Like all aspects of the text, this material is self-contained and intuitive.
Effective managers must be sensitive to the special challenges posed by an
increasingly global marketplace. To increase student awareness of such issues,
a number of examples, Managerial Applications, and case studies that relate to
global business topics are featured.
Each chapter is accompanied by a case study that provides in-depth treatment of
chapter concepts. To meet the needs of all instructors and their students, these case
studies are written to allow, but do not require, a computer-based approach. These
case studies are fully self-contained and especially helpful to instructors who wish
to more fully incorporate the use of basic spreadsheet and statistical software in their
courses.
370 new end-of-chapter questions and problems are provided, after having been
subject to necessary revision and class testing. Questions are designed to give
students the opportunity to grasp basic concepts on an intuitive level and express
their understanding in a nonquantitative fashion. Problems cover a wide variety of
decision situations and illustrate the role of economic analysis from within a simple
numerical framework.
Each chapter includes two self-test problems with detailed solutions to show students
how economic tools and techniques can be used to solve practical business problems.
These self-test problems are a proven study aid that greatly enhances the learning
value of end-of-chapter questions and problems.
Ancillary Package
Managerial Economics, 12th Edition, is supported by the most comprehensive ancillary
package available in managerial economics to make teaching and learning the material
both easy and enjoyable.
Instructor’s Manual The Instructor’s Manual offers learning suggestions, plus detailed
answers and solutions for all chapter questions and problems. Case study data are also
provided to adopters with the Instructor’s Manual.
Study Guide The Study Guide furnishes a detailed line summary of major concepts for
each chapter, a brief discussion of important economic relations as they are covered in
the text, and an expanded set of 190 solved problems. This completely new edition has
undergone extensive class testing and analysis. Based on the comments of students and
instructors alike, this new study guide is highly recommended as a valuable learning
resource.
Test Bank A comprehensive Test Bank is also provided that offers a variety of multiplechoice questions, one-step, and multistep problems for every chapter. Full solutions are
included, of course. With nearly 1,000 questions and problems, the Test Bank is a valuable
tool for exam preparation.
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May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Preface
xxvii
Acknowledgments
A number of people have aided in the preparation of Managerial Economics, 12th Edition.
Helpful suggestions and constructive comments have been received from a great number
of instructors and students who have used previous editions. Numerous reviewers
have also provided insights and assistance in clarifying difficult material. Among those
who have been especially helpful in the development of this edition are: Barry Keating,
University of Notre Dame; Stephen Conroy, University of San Diego; Xu Wang, Texas
A&M University; Michael Brandl, University of Texas—Austin; Neil Garston, California
State University—Los Angeles; Albert Okunade, University of Memphis; David Carr,
University of South Dakota; Steven Rock, Western Illinois University; Mel Borland,
Western Kentucky University; Tom Staley, San Francisco State University.
I am also indebted to the South-Western staff and would like to give special thanks
to Mike Roche for 20 years of editorial and marketing contributions. Amy Ray for her
help on this edition and the many editions of the book she has worked on through the
years. Michelle Kunkler for conceptualizing the new look and feel. Betty Jung and Brian
Joyner for working to promote the new edition to professors, students, and the Cengage
Learning sales force. And to Lysa Oeters and her team at Integra for making the 12th
edition a reality. Christine Hauschel read the entire manuscript, gave numerous helpful
suggestions, and helped make the revision process lots of fun. Chris deserves a special
word of thanks (Thanks!).
Every effort has been made to minimize errors in the book. However, errors do
occasionally slip through despite diligent efforts to provide an error-free package of text
and ancillary materials. Readers are invited to correspond with me directly concerning
any corrections or other suggestions.
Finally, more than ever before, it is obvious that economic efficiency is an
essential ingredient in the successful management of both business and public-sector
organizations. Like any dynamic area of study, the field of managerial economics
continues to undergo profound change in response to the challenges imposed by a rapidly
evolving environment. It is exciting to participate in these developments. I sincerely hope
that Managerial Economics, 12th Edition, contributes to a better understanding of the
usefulness of economic theory.
For students, I hope it makes $ense.
Mark Hirschey
mhirschey@ku.edu
March 2008
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Licensed to: iChapters User
Appendix A
Compounding and the Time Value
of Money
The concepts of compound growth and the time value of money are widely used in
all aspects of business and economics. Compounding is the principle that underlies
growth, whether it is growth in value, growth in sales, or growth in assets. The time
value of money—the fact that a dollar received in the future is worth less than a dollar
in hand today—also plays an important role in managerial economics. Cash flows
occurring in different periods must be adjusted to their value at a common point in time
to be analyzed and compared. Because of the importance of these concepts in economic
analysis, thorough understanding of the material on future (compound) and present
values in the appendix is important for the study of managerial economics.
FUTURE VALUE (OR COMPOUND VALUE)
Suppose that you deposit $100 in a bank savings account that pays 5 percent interest
compounded annually. How much will you have at the end of 1 year? Let us define terms
as follows:
PV Present value of your account, or the beginning amount, $100;
i Interest rate the bank pays you 5 percent per year, or, expressed in decimal terms, 0.05;
I Dollars of interest earned during the year;
FVN Future value, or ending amount, of your account at the end of N years. Whereas
PV is the value now, at the present time, FVN is the value N years into the future,
after compound interest has been earned. Note also that FV0 is the future value
zero years into the future, which is the present, so FV0 PV.
In our example, N 1, so FVN FV1, and it is calculated as follows:
FV 1 PV I
PV PV i
PV(1 i)
A.1
We can now use Equation (A.1) to find how much the account is worth at the end of 1 year:
FV 1 $100(1 0.05) $100(1.05) $105
787
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788
Appendix A: Compounding and the Time Value of Money
Your account earned $5 of interest (I $5), so you have $105 at the end of the year.
Now suppose that you leave your funds on deposit for 5 years; how much will you have
at the end of the fifth year? The answer is $127.63; this value is worked out in Table A.1.
Notice that the Table A.1 value for FV2, the value of the account at the end of year 2, is
equal to
FV 2 FV 1(1 i) PV(1 i)(1 i) PV(1 i) 2
FV3, the balance after 3 years, is
FV 3 FV 2(1 i) PV(1 i) 3
In general, FVn, the future value at the end of N years, is found as
FV N PV(1 i ) N
A.2
Applying Equation (A.2) in the case of a 5-year account that earns 5 percent per year gives
PV 5 $100(1.05) 5
$100(1.2763)
$127.63
which is the same as the value in Table A.1.
If an electronic calculator is handy, it is easy enough to calculate (1 i)N directly.1
However, tables have been constructed for values of (1 i)N for wide ranges of i and N, as
Table A.2 illustrates. Table B.1 in Appendix B contains a more complete set of compound
value interest factors. Interest compounding can occur over periods of time different
from 1 year. Thus, although compounding is often on an annual basis, it can be quarterly,
semiannually, monthly, or for any other period.
The term future value interest factor (FVIFi,N) equals (1 i)N. Therefore, Equation (A.2)
may be written as FVN PV(FVIFi,N). One needs only to go to an appropriate interest
table to find the proper interest factor. For example, the correct interest factor for our
Table A.1 Compound Interest Calculations
1
Year
Beginning
Amount, PV
1
$100.00
1.05
$105.00
2
105.00
1.05
110.25
3
110.25
1.05
115.76
4
115.76
1.05
121.55
5
121.55
1.05
127.63
ⴛ
(1 ⴙ i)
ⴝ
Ending
Amount, FVn
For example, to calculate (1 i)N for I 5 percent 0.05 and N 5 years, simply multiply (1 i) (1.05)
times (1.05); multiple this product by (1.05); and so on:
(1 i)N (1.05)(1.05)(1.05)(1.05)(1.05) (1.05)5 1.2763
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Appendix A: Compounding and the Time Value of Money
789
Table A.2 Future Value of $1 at the End of n Periods: FVIFi,n ⴝ (1 ⴙ i)n
Period
(n)
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
0
1
2
3
4
5
1.0000
1.0100
1.0201
1.0303
1.0406
1.0510
1.0000
1.0200
1.0404
1.0612
1.0824
1.1041
1.0000
1.0300
1.0609
1.0927
1.1255
1.1593
1.0000
1.0400
1.0816
1.1249
1.1699
1.2167
1.0000
1.0500
1.1025
1.1576
1.2155
1.2763
1.0000
1.0600
1.1236
1.1910
1.2625
1.3382
1.0000
1.0700
1.1449
1.2250
1.3108
1.4026
1.0000
1.0800
1.1664
1.2597
1.3605
1.4693
1.0000
1.0900
1.1881
1.2950
1.4116
1.5386
1.0000
1.1000
1.2100
1.3310
1.4641
1.6105
6
7
8
9
10
1.0615
1.0721
1.0829
1.0937
1.1046
1.1262
1.1487
1.1717
1.1951
1.2190
1.1941
1.2299
1.2668
1.3048
1.3439
1.2653
1.3159
1.3686
1.4233
1.4802
1.3401
1.4071
1.4775
1.5513
1.6289
1.4185
1.5036
1.5938
1.6895
1.7908
1.5007
1.6058
1.7182
1.8385
1.9672
1.5869
1.7138
1.8509
1.9990
2.1589
1.6771
1.8280
1.9926
2.1719
2.3674
1.7716
1.9487
2.1436
2.3579
2.5937
11
12
13
14
15
1.1157
1.1268
1.1381
1.1495
1.1610
1.2434
1.2682
1.2936
1.3195
1.3459
1.3842
1.4258
1.4685
1.5126
1.5580
1.5395
1.6010
1.6651
1.7317
1.8009
1.7103
1.7959
1.8856
1.9799
2.0789
1.8983
2.0122
2.1329
2.2609
2.3966
2.1049
2.2522
2.4098
2.5785
2.7590
2.3316
2.5182
2.7196
2.9372
3.1722
2.5804
2.8127
3.0658
3.3417
3.6425
2.8531
3.1384
3.4523
3.7975
4.1772
5-year, 5 percent illustration can be found in Table A.2. Simply look down the Period
column to 5, then across this row to the 5 percent column to find the interest factor,
1.2763. Then, using this interest factor, we find the value of $100 after 5 years as FVN PV(FVIFi,N) $100(1.2763) $127.63, which is identical to the value obtained by the long
method in Table A.1.
Graphic View of the Compounding Process: Growth
Figure A.1 shows how $1 (or any other initial quantity) grows over time at various rates
of interest. The higher the rate of interest, the faster the rate of growth. The interest rate
is, in fact, the growth rate: If a sum is deposited and earns 5 percent, then the funds
on deposit grow at the rate of 5 percent per period. Similarly, the sales of a firm or the
gross domestic product (GDP) of a country might be expected to grow at a constant rate.
Projections of future sales or GDP could be obtained using the compound value method.
Future value curves could be drawn for any interest rate, including fractional rates. In
Figure A.1, we have plotted curves for 0 percent, 5 percent, and 10 percent, using the data
from Table A.2.
PRESENT VALUE
Suppose that you are offered the alternative of receiving either $127.63 at the end of 5 years
or X dollars today. There is no question that the $127.63 will be paid in full (perhaps the
payer is the U.S. government). Having no current need for the money, you would deposit
it in a bank account that pays 5 percent interest. (Five percent is your opportunity cost, or the
rate of interest you could earn on alternative investments of equal risk.) What value of X
will make you indifferent between X dollars today or the promise of $127.63 5 years hence?
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Appendix A: Compounding and the Time Value of Money
Figure A.1
Relations Among Future Value Interest Factors, Interest Rates, and Time
The future value interest factor rises with increases in the interest rate and in the number of periods
for interest compounding.
Table A.1 shows that the initial amount of $100 growing at 5 percent a year yields
$127.63 at the end of 5 years. Thus, you should be indifferent in your choice between $100
today and $127.63 at the end of 5 years. The $100 is the present value, or PV, of $127.63
due in 5 years when the applicable interest rate is 5 percent. Therefore, if X is anything
less than $100, you would prefer the promise of $127.63 in 5 years to X dollars today.
In general, the present value of a sum due N years in the future is the amount that, if it
were invested today, would grow to equal the future sum over a period of N years. Because
$100 would grow to $127.63 in 5 years at a 5 percent interest rate, $100 is the present value
of $127.63 due 5 years in the future when the appropriate interest rate is 5 percent.
Finding present values (or discounting, as it is commonly called) is simply the reverse
of compounding, and Equation (A.2) can readily be transformed into a present value
formula:
FV N PV(1i) N
which, when solved for PV, gives
[
FV N
1
PV ______
FV N ______
(1i) N
(1i) N
]
Tables have been constructed for the term in brackets for various values of i and N; Table
A.3 is an example. For a more complete table, see Table B.2 in Appendix B. For the case
being considered, look down the 5 percent column in Table A.3 to the fifth row. The
figure shown there, 0.7835, is the present value interest factor (PVIFi,N) used to determine
the present value of $127.63 payable in 5 years, discounted at 5 percent
PV FV 5(PVIF i,N)
$127.63(0.7835)
$100
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791
Graphic View of the Discounting Process
Figure A.2 shows how the interest factors for discounting decrease as the discounting
period increases. The curves in the figure were plotted with data taken from Table A.3;
they show that the present value of a sum to be received at some future date decreases
(1) as the payment date is extended further into the future and (2) as the discount rate
increases. If relatively high discount rates apply, funds due in the future are worth very
little today. Even at relatively low discount rates, the present values of funds due in the
distant future are quite small. For example, $1 due in 10 years is worth about 614 today
if the discount rate is 5 percent. It is worth only 254 today at a 15 percent discount rate.
Similarly, $1 due in 5 years at 10 percent is worth 624 today, but at the same discount rate,
$1 due in 10 years is worth only 394 today.
FUTURE VALUE VERSUS PRESENT VALUE
Notice that Equation (A.2), the basic equation for compounding, was developed from
the logical sequence set forth in Table A.1; the equation merely presents in mathematical
form the steps outlined in the table. The present value interest factor (PVIF i,N) in
Equation (A.3), the basic equation for discounting or finding present values, was found
as the reciprocal of the future value interest factor (FVIFi,N) for the same i, N combination:
1
PVIF i,N _______
FVIF i,N
A.3
For example, the future value interest factor for 5 percent over 5 years is seen in Table
A.2 to be 1.2763. The present value interest factor for 5 percent over 5 years must be the
reciprocal of 1.2763
1 0.7835
PVIF 5%,5 yrs ______
1.2763
Table A.3 Present Values of $1 Due at the End of n Periods
[
1
1 _____
PVIFi,n ______
(1i)
(1i) n
]
n
Period
(n)
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
15%
1
2
3
4
5
.9901
.9803
.9706
.9610
.9515
.9804
.9612
.9423
.9238
.9057
.9709
.9426
.9151
.8885
.8626
.9615
.9246
.8890
.8548
.8219
.9524
.9070
.8638
.8227
.7835
.9434
.8900
.8396
.7921
.7473
.9346
.8734
.8163
.7629
.7130
.9259
.8573
.7938
.7350
.6806
.9174
.8417
.7722
.7084
.6499
.9091
.8264
.7513
.6830
.6209
.8929
.7972
.7118
.6355
.5674
.8772
.7695
.6750
.5921
.5194
.8696
.7561
.6575
.5718
.4972
6
7
8
9
10
.9420
.9327
.9235
.9143
.9053
.8880
.8706
.8535
.8368
.8203
.8375
.8131
.7894
.7664
.7441
.7903
.7599
.7307
.7026
.6756
.7462
.7107
.6768
.6446
.6139
.7050
.6651
.6274
.5919
.5584
.6663
.6227
.5820
.5439
.5083
.6302
.5835
.5403
.5002
.4632
.5963
.5470
.5019
.4604
.4224
.5645
.5132
.4665
.4241
.3855
.5066
.4523
.4039
.3606
.3220
.4556
.3996
.3506
.3075
.2697
.4323
.3759
.3269
.2843
.2472
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792
Appendix A: Compounding and the Time Value of Money
Figure A.2
Relations Among Present Value Interest Factors, Interest Rates, and Time
The present value interest factor falls with increases in the interest rate and in the number of periods
prior to payment.
The PVIFi,N found in this manner does, of course, correspond with the PVIFi,N shown in
Table A.3.
The reciprocal relation between present value and future value permits us to find
present values in two ways—by multiplying or by dividing. Thus, the present value of
$1,000 due in 5 years and discounted at 5 percent may be found as
[ ]
1
PV FV N ____
1 i
N
FV N(PVIF i,N) $1,000(0.7835) $ 783.50
or as
FV N
FV N
$1,000
PV _______
_______
______ $783.50
(1 i) N FVIF i,N 1.2763
To conclude this comparison of present and future values, compare Figures A.1 and A.2.2
FUTURE VALUE OF AN ANNUITY
An annuity is defined as a series of payments of a fixed amount for a specified number of periods.
Each payment occurs at the end of the period.3 For example, a promise to pay $1,000 a
year for 3 years is a 3-year annuity. If you were to receive such an annuity and were to
deposit each annual payment in a savings account paying 4 percent interest, how much
2
Notice that Figure A.2 is not a mirror image of Figure A.1. The curves in Figure A.1 approach 4 as n
increases; in Figure A.2 the curves approach zero, not −4.
3 Had the payment been made at the beginning of the period, each receipt would simply have been shifted
back 1 year. The annuity would have been called an annuity due; the one in the present discussion, with
payments made at the end of each period, is called a regular annuity or, sometimes, a deferred annuity.
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Appendix A: Compounding and the Time Value of Money
793
would you have at the end of 3 years? The answer is shown graphically as a time line in
Figure A.3. The first payment is made at the end of year 1, the second at the end of year 2,
and the third at the end of year 3. The last payment is not compounded at all, the second
payment is compounded for 1 year, and the first is compounded for 2 years. When the
future values of each of the payments are added, their total is the sum of the annuity. In
the example, this total is $3,121.60.
Expressed algebraically, with SN defined as the future value, R as the periodic receipt,
N as the length of the annuity, and FVIFAi,N as the future value interest factor for an
annuity, the formula for SN is
S N R(1 i) N1 R(1 i) N2 · · · R(1 i) 1 R(1 i) 0
R[(1 i) N1 (1 i) N2 · · · (1 i) 1 (1 i) 0]
N
R
N
∑
t1
(1 i) Nt
or R
∑(1 i)t 1
t1
R(FVIFAi,N)
A.4
The expression in parentheses, FVIFAi,N, has been calculated for various combinations of
i and N.4 An illustrative set of these annuity interest factors is given in Table A.4.5 To find
the answer to the 3-year, $1,000 annuity problem, simply refer to Table A.4, look down the
4 percent column to the row of the third period, and multiply the factor 3.1216 by $1,000.
The answer is the same as the one derived by the long method illustrated in Figure A.3:
S N R(FVIFAi,N)
S 3 $1,000(3.1216) $3,121.60
Figure A.3
Time Line for an Annuity: Future Value (i = 4%)
When the interest rate is 4%, the future value of $1,000 annuity to be paid over 3 years
is $3,121.60.
4
The third equation is simply a shorthand expression in which sigma (Σ) signifies sum up or add the
N
values of N factors. The symbol
∑ simply says, “Go through the following process: Let t 1 and find
t=1
the first factor. Then let t 2 and find the second factor. Continue until each individual factor has been
found, and then add these individual factors to find the value of the annuity.”
5 The equation given in Table A.4 recognizes that the FVIFA factor is the sum of a geometric progression.
The proof of this equation is given in most algebra texts. Notice that it is easy to use the equation to
develop annuity factors. This is especially useful if you need the FVIFA for some interest rate not given
in the tables (for example, 6.5 percent).
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Appendix A: Compounding and the Time Value of Money
Table A.4 Future Value of an Annuity of $1 per Period for n Periods
n
FVIFAi, n ∑(1 i)t1
t1
(1 i) n–1
________
i
Number
of
Periods
1%
2%
3%
4%
5%
6%
7%
8%
1
2
3
4
5
1.0000
2.0100
3.0301
4.0604
5.1010
1.0000
2.0200
3.0604
4.1216
5.2040
1.0000
2.0300
3.0909
4.1836
5.3091
1.0000
2.0400
3.1216
4.2465
5.4163
1.0000
2.0500
3.1525
4.3101
5.5256
1.0000
2.0600
3.1836
4.3746
5.6371
1.0000
2.0700
3.2149
4.4399
5.7507
1.0000
2.0800
3.2464
4.5061
5.8666
6
7
8
9
10
6.1520
7.2135
8.2857
9.3685
10.4622
6.3081
7.4343
8.5830
9.7546
10.9497
6.4684
7.6625
8.8923
10.1591
11.4639
6.6330
7.8983
9.2142
10.5828
12.0061
6.8019
8.1420
9.5491
11.0266
12.5779
6.9753
8.3938
9.8975
11.4913
13.1808
7.1533
8.6540
10.2598
11.9780
13.8164
7.3359
8.9228
10.6366
12.4876
14.4866
Notice that for all positive interest rates, the FVIFAi,N for the sum of an annuity is always
equal to or greater than the number of periods the annuity runs.6
PRESENT VALUE OF AN ANNUITY
Suppose that you were offered the following alternatives: a 3-year annuity of $1,000 per
year or a lump-sum payment today. You have no need for the money during the next
3 years, so if you accept the annuity, you would simply deposit the receipts in a savings
account paying 4 percent interest. How large must the lump-sum payment be to make
it equivalent to the annuity? The time line shown in Figure A.4 will help explain the
problem.
The present value of the first receipt is R[1/(1 i)], the second is R[1/(1 i)]2, and so
on. Designating the present value of an annuity of N years as AN and the present value
interest factor for an annuity as PVIFAi,N, we may write the following equation:
6
It is worth noting that the entry for each period t in Table A.4 equals the sum of the entries in Table A.2
up to the period N − 1. For example, the entry for Period 3 under the 4 percent column in Table A.4 is
equal to 1.000 1.0400 1.0816 3.1216.
Also, had the annuity been an annuity due, with payments received at the beginning rather than
at the end of each period, the three payments would have occurred at t 0, t 1, and t 2. To find the
future value of an annuity due, look up the FVIFAi,N for N 1 years, then subtract 1.0 from the amount
to get the FVIFAi,N for the annuity due. In the example, the annuity due FVIFAi,N is 4.2465 − 1.0 3.2465
versus 3.1216 for a regular annuity. Because payments on an annuity due come earlier, it is a little more
valuable than a regular annuity.
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Appendix A: Compounding and the Time Value of Money
Figure A.4
795
Time Line for an Annuity: Present Value (i 4%)
When the interest rate is 4%, the present value of a $1,000 annuity to be paid over 3 years is
$2,775.10.
1 1 R ____
1 2 . . . R ____
1
AN R ____
1i
1i
1i
( ) ( )
( )
1 _______
1 . . . _______
1
R _______
(1 i) 1 (1 i) 2
(1 i) N
(
N
)
N
1
∑______
(1 i) t
R
t1
R(PVIFAi,N)
A.5
Again, tables have been worked out for PVIFAi,N, the term in parentheses in Equation
(A.5), as Table A.5 illustrates; a more complete listing is found in Table B.4 in Appendix
B. From Table A.5, the PVIFAi,N for a 3-year, 4 percent annuity is found to be 2.7751.
Table A.5 Present Value of an Annuity of $1 per Period for n Periods
n
PVIFAi,n ∑ (1 + i)t ______
1
1
1_______
(1 i) n
_________
i
t1
Period
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
2
3
4
5
0.9901
1.9704
2.9410
3.9020
4.8534
0.9804
1.9416
2.8839
3.8077
4.7135
0.9709
1.9135
2.8286
3.7171
4.5797
0.9615
1.8861
2.7751
3.6299
4.4518
0.9524
1.8594
2.7232
3.5460
4.3295
0.9434
1.8334
2.6730
3.4651
4.2124
0.9346
1.8080
2.6243
3.3872
4.1002
0.9259
1.7833
2.5771
3.3121
3.9927
0.9174
1.7591
2.5313
3.2397
3.8897
0.9091
1.7355
2.4869
3.1699
3.7908
6
7
8
9
10
5.7955
6.7282
7.6517
8.5660
9.4713
5.6014
6.4720
7.3255
8.1622
8.9826
5.4172
6.2303
7.0197
7.7861
8.5302
5.2421
6.0021
6.7327
7.4353
8.1109
5.0757
5.7864
6.4632
7.1078
7.7217
4.9173
5.5824
6.2098
6.8017
7.3601
4.7665
5.3893
5.9713
6.5152
7.0236
4.6229
5.2064
5.7466
6.2469
6.7101
4.4859
5.0330
5.5348
5.9952
6.4177
4.3553
4.8684
5.3349
5.7590
6.1446
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796
Appendix A: Compounding and the Time Value of Money
Multiplying this factor by the $1,000 annual receipt gives $2,775.10, the present value of
the annuity. This figure is identical to the long-method answer shown in Figure A.4:
AN R(PVIFAi,N)
A3 $1,000(2.7751)
$2,775.10
Notice that the entry for each period N in Table A.5 is equal to the sum of the entries in
Table A.3 up to and including period N. For example, the PVIFA for 4 percent, three periods
as shown in Table A.5, could have been calculated by summing values from Table A.3:
0.9615 0.9246 0.8890 2.7751
Notice also that for all positive interest rates, PVIFAi,N for the present value of an annuity is
always less than the number of periods.7
PRESENT VALUE OF AN UNEVEN SERIES OF RECEIPTS
The definition of an annuity includes the words fixed amount—in other words, annuities
involve situations in which cash flows are identical in every period. Although many
managerial decisions involve constant cash flows, some important decisions are
concerned with uneven cash flows. Consequently, it is necessary to deal with varying
payment streams.
The PV of an uneven stream of future income is found as the sum of the PVs of the
individual components of the stream. For example, suppose that we are trying to find the
PV of the stream of receipts shown in Table A.6, discounted at 6 percent. As shown in the
table, we multiply each receipt by the appropriate PVIFi,N, then sum these products to obtain
the PV of the stream, $1,413.24. Figure A.5 gives a graphic view of the cash-flow stream.
Table A.6 Present Value of an Uneven Stream of Receipts (i = 6%)
Year
Stream of
Receipts
1
2
3
4
5
6
7
$100
200
200
200
200
0
1,000
ⴛ
PVIFi,n
ⴝ
0.9434
0.8900
0.8396
0.7921
0.7473
0.7050
0.6651
PV of Individual
Receipts
$94.34
178.00
167.92
158.42
149.46
0
665.10
PV Sum $1,413.24
7
To find the PVIFAi,N for an annuity due, look up the PVIFAi,N for N − 1 periods, then add 1.0 to this
amount to obtain the PVIFAi,N for the annuity due. In the example, the PVIFAi,N for a 4 percent, 3-year
annuity due is 1.8861 1.0 2.8861.
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Appendix A: Compounding and the Time Value of Money
Figure A.5
797
Time Line for an Uneven Cash Flow Stream (i 6%)
The PV of the receipts shown in Table A.6 and Figure A.5 can also be found by using
the annuity equation; the steps in this alternative solution process are as follows:
• Step 1: Find PV of $100 due in 1 year:
$100(0.9434) $94.34
• Step 2: Recognize that a $200 annuity will be received during years 2 through 5.
Thus, we can determine the value of a 5-year annuity, subtract from it the value
of a 1-year annuity, and have the remaining value of a 4-year annuity whose first
payment is due in 2 years. This result is achieved by subtracting the PVIFA for a
1-year, 6 percent annuity from the PVIFA for a 5-year annuity and then multiplying
the difference by $200:
PV of the Annuity (PVIFA6%,5 yrs PVIFA6%,1 yr)($200)
(4.2124 0.9434)($200)
$653.80
Thus, the present value of the annuity component of the uneven stream is $653.80.
• Step 3: Find the PV of the $1,000 due in year 7:
$1,000(0.6651) $665.10
• Step 4: Sum the components:
$94.34 $653.80 $665.10 $1,413.24
Either of the two methods can be used to solve problems of this type. However, the
alternative (annuity) solution is easier if the annuity component runs for many years. For
example, the alternative solution would be clearly superior for finding the PV of a stream
consisting of $100 in year 1, $200 in years 2 through 29, and $1,000 in year 30.
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798
Appendix A: Compounding and the Time Value of Money
ANNUAL PAYMENTS FOR ACCUMULATION OF A FUTURE SUM
Suppose that you want to know the amount of money that must be deposited at 5 percent
for each of the next 5 years in order to have $10,000 available to pay off a debt at the end
of the fifth year. Dividing both sides of Equation (A.4) by FVIFA we obtain
SN
R ________
FVIFAi,N
Looking up the future value of an annuity interest factor for 5 years at 5 percent in Table
A.4 and dividing this figure into $10,000 gives
$10,000
R _______ $1,810
5.5256
Thus, if $1,810 is deposited each year in an account paying 5 percent interest, at the end
of 5 years the account will have accumulated to $10,000.
ANNUAL RECEIPTS FROM AN ANNUITY
Suppose that on September 1, 2007, you received an inheritance of $7,500. The
money is to be used for your education and is to be spent during the academic years
beginning September 2008, 2009, and 2010. If you place the money in a bank account
paying 6 percent annual interest and make three equal withdrawals at each of the
specified dates, how large can each withdrawal be so as to leave you with exactly a
zero balance after the last one has been made?
The solution requires application of the present value of an annuity formula, Equation
(A.5). Here, however, we know that the present value of the annuity is $7,500, and the
problem is to find the three equal annual payments when the interest rate is 6 percent.
This calls for dividing both sides
AN
R _________
PVIFAi,N
of Equation (A.5) by PVIFAi,N to derive Equation (A.7):
The interest factor is found in Table A.5 to be 2.6730, and substituting this value into
Equation (A.7), the three annual withdrawals are calculated to be $2,806:
$7,500
R ______ $2,806
2.6730
This particular calculation is used frequently to set up insurance and pension-plan benefit
schedules and to find the periodic payments necessary to retire a loan within a specified
period. For example, if you want to retire in three equal annual payments a $7,500 bank
loan accruing interest at 6 percent on the unpaid balance, each payment would be $2,806.
In this case, the bank is acquiring an annuity with a present value of $7,500.
DETERMINING INTEREST RATES
We can use the basic equations developed earlier to determine the interest rates implicit
in financial contracts.
Example 1. A bank offers to lend you $1,000 if you sign a note to repay $1,610.50 at the
end of 5 years. What rate of interest are you paying? To solve the problem, recognize that
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Appendix A: Compounding and the Time Value of Money
799
$1,000 is the PV of $1,610.50 due in 5 years, and solve Equation (A.3) for the present value
interest factor (PVIFi, N).
[
]
1
PV FV N _______
FV N(PVIF i,N)
(1 i) N
$1,000 $1,610.50(PVIF i,5 yrs)
$1,000/$1,610.50 0.6209 PVIF i,5 yrs
A.3
Now, go to Table A.3 and look across the row for year 5 until you find 0.6209. It is in the
10 percent column, so you would be paying a 10 percent rate of interest.
Example 2. A bank offers to lend you $100,000 to buy a house. You must sign a mortgage
calling for payments of $8,882.73 at the end of each of the next 30 years, equivalent to
roughly $740.23 per month. What interest rate is the bank charging you?
1. Recognize that $100,000 is the PV of a 30-year, $8,882.73 annuity:
30
$100,000 PV 1
∑ $8,882.73 [ ______
$8,882.73(PVIFAi,30 yrs)
(1 i) t ]
t1
2. Solve for PVIFAi,30 yrs
PVIFAi,30 yrs $100,000/$8,882.73 11.2578
3. Turn to Table B.4 in Appendix B, because Table A.5 does not cover a 30-year period.
Looking across the row for 30 periods, find 11.2578 under the column for 8 percent.
Therefore, the rate of interest on this mortgage is 8 percent.
SEMIANNUAL AND OTHER COMPOUNDING PERIODS
All of the examples thus far have assumed that returns were received once a year,
or annually. Suppose, however, that you put your $1,000 in a bank that offers to
pay 6 percent interest compounded semiannually. How much will you have at the
end of 1 year? Semiannual compounding means that interest is actually paid every
6 months, a fact taken into account in the tabular calculations in Table A.7. Here the
annual interest rate is divided by two, but twice as many compounding periods are
used because interest is paid twice a year. Comparing the amount on hand at the end
of the second 6-month period, $1,060.90, with what would have been on hand under
annual compounding, $1,060, shows that semiannual compounding is better from the
standpoint of the saver. This result occurs because you earn interest on interest more
frequently.
Throughout the economy, different types of investments use different compounding
periods. For example, bank and savings and loan accounts generally pay interest
quarterly, some bonds pay interest semiannually, and other bonds pay interest annually.
Thus, if we are to compare securities with different compounding periods, we need to
put them on a common basis. This need has led to the development of the terms nominal,
or stated, interest rate and effective annual, or annual percentage rate (APR). The stated, or
nominal, rate is the quoted rate; thus, in our example the nominal rate is 6 percent. The
annual percentage rate is the rate that would have produced the final compound value,
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
800
Appendix A: Compounding and the Time Value of Money
Table A.7 Compound Interest Calculations with Semiannual Compounding
Beginning
Amount ( PV )
ⴛ
(1 ⴙ i/2)
ⴝ
Ending
Amount, FVn
Period 1
$1,000.00
(1.03)
$1,030.00
Period 2
$1,030.00
(1.03)
$1,060.00
$1,060.90, under annual rather than semiannual compounding. In this case, the effective
annual rate is 6.09 percent:
$1,000(1 i) $1,060.90
$1,060.90
i _________ 1 0.0609 6.09%
$1,000
Thus, if one bank offered 6 percent with semiannual compounding, whereas another
offered 6.09 percent with annual compounding, they would both be paying the same
effective rate of interest. In general, we can determine the effective annual rate of interest,
given the nominal rate, as follows:
• Step 1: Find the FV of $1 at the end of 1 year, using the equation
(
in
FV 1 1 ___
M
)
M
Here in is the nominal rate, and M is the number of compounding periods per year.
• Step 2: Subtract 1.0 from the result in Step 1; then multiply by 100. The final result is
the effective annual rate.
Example. Find the effective annual rate if the nominal rate is 6 percent, compounded
semiannually:
0.06 1.0
Effective Annual Rate 1 ____
2
(1.03) 2 1.0
(
)
2
1.0609 1.0
0.0609
6.09%
The points made about semiannual compounding can be generalized as follows. When
compounding periods are more frequent than once a year, use a modified version of
Equation (A.2):
FV N PV(1 i) N
i MN
FV N PV 1 ___
M
(
)
A.2a
Here M is the number of times per year compounding occurs. When banks compute daily
interest, the value of M is set at 365, and Equation (A.2a) is applied.
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Appendix A: Compounding and the Time Value of Money
801
The interest tables can be used when compounding occurs more than once a year.
Simply divide the nominal, or stated, interest rate by the number of times compounding
occurs, and multiply the years by the number of compounding periods per year. For
example, to find the amount to which $1,000 will grow after 6 years with semiannual
compounding and a stated 8 percent interest rate, divide 8 percent by 2 and multiply
the 6 years by 2. Then look in Table A.2 under the 4 percent column and in the row for
Period 12. You will find an interest factor of 1.6010. Multiplying this by the initial $1,000
gives a value of $1,601, the amount to which $1,000 will grow in 6 years at 8 percent
compounded semiannually. This compares with $1,586.90 for annual compounding.
The same procedure applies in all of the cases covered—compounding, discounting,
single payments, and annuities. To illustrate semiannual discounting in finding the
present value of an annuity, consider the case described in the section “Present Value of
an Annuity”—$1,000 a year for 3 years, discounted at 4 percent. With annual discounting,
the interest factor is 2.7751, and the present value of the annuity is $2,775.10. For
semiannual discounting, look under the 2 percent column and in the Period 6 row of
Table A.5 to find an interest factor of 5.6014. This is now multiplied by half of $1,000, or
the $500 received each 6 months, to get the present value of the annuity, $2,800.70. The
payments come a little more rapidly—the first $500 is paid after only 6 months (similarly
with other payments)—so the annuity is a little more valuable if payments are received
semiannually rather than annually.
SUMMARY
Managerial decisions often require determining the
present value of a stream of future cash flows. Also,
we often need to know the amount to which an initial
quantity will grow during a specified time period, and
at other times we must calculate the interest rate built
into a financial contract. The basic concepts involved in
these processes are called compounding and the time
value of money.
equation. The term [1/(1 i)N]is the present value
interest factor, PVIFi, N.
•
Future Value of an Annuity: An annuity is
defined as a series of constant or equal payments
of R dollars per period. The sum, or future value
of an annuity, is given the symbol SN, and it is
found as follows:
SN R
The key procedures covered in this appendix are
summarized here
•
•
Future Value: FVN PV(1 i)N, where FVN is the
future value of an initial amount, PV, compounded
at the rate of i percent for N periods. The term
(1 i)N is the future value interest factor, FVIFi, N.
Values for FVIF are contained in tables.
Present Value: PV FVN[1/(1 i)N]. This equation
is simply a transformation of the future value
[
]
N
[
N
∑
(1 i) t 1 . The term ∑ (1 i) t 1
t1
t1
]
is the
future value interest factor for an annuity, FVIFAi, N.
•
Present Value of an Annuity: The present value of an
annuity is identified by the symbol AN, and it
[
is found as follows: AN R
[∑
N
]
N
∑ (1/1 i)t
t1
]
. The term
(1/1 i) t PVIFA i,N is the present value
t1
interest factor for an annuity.
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Appendix B
Interest Factor Tables
Table B.1 Future Value of $1: FVIFi,n (1 i )n
Period
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
1.0100
1.0201
1.0303
1.0406
1.0510
1.0615
1.0721
1.0829
1.0937
1.1046
1.1157
1.1268
1.1381
1.1495
1.1610
1.1726
1.1843
1.1961
1.2081
1.2202
1.2324
1.2447
1.2572
1.2697
1.2824
1.2953
1.3082
1.3213
1.3345
1.3478
1.4889
1.6446
1.8167
1.0200
1.0404
1.0612
1.0824
1.1041
1.1262
1.1487
1.1717
1.1951
1.2190
1.2434
1.2682
1.2936
1.3195
1.3459
1.3728
1.4002
1.4282
1.4568
1.4859
1.5157
1.5460
1.5769
1.6084
1.6406
1.6734
1.7069
1.7410
1.7758
1.8114
2.2080
2.6916
3.2810
1.0300
1.0609
1.0927
1.1255
1.1593
1.1941
1.2299
1.2668
1.3048
1.3439
1.3842
1.4258
1.4685
1.5126
1.5580
1.6047
1.6528
1.7024
1.7535
1.8061
1.8603
1.9161
1.9736
2.0328
2.0938
2.1566
2.2213
2.2879
2.3566
2.4273
3.2620
4.3839
5.8916
1.0400
1.0816
1.1249
1.1699
1.2167
1.2653
1.3159
1.3686
1.4233
1.4802
1.5395
1.6010
1.6651
1.7317
1.8009
1.8730
1.9479
2.0258
2.1068
2.1911
2.2788
2.3699
2.4647
2.5633
2.6658
2.7725
2.8834
2.9987
3.1187
3.2434
4.8010
7.1067
10.519
1.0500
1.1025
1.1576
1.2155
1.2763
1.3401
1.4071
1.4775
1.5513
1.6289
1.7103
1.7959
1.8856
1.9799
2.0789
2.1829
2.2920
2.4066
2.5270
2.6533
2.7860
2.9253
3.0715
3.2251
3.3864
3.5557
3.7335
3.9201
4.1161
4.3219
7.0400
11.467
18.679
1.0600
1.1236
1.1910
1.2625
1.3382
1.4185
1.5036
1.5938
1.6895
1.7908
1.8983
2.1022
2.1329
2.2609
2.3966
2.5404
2.6928
2.8543
3.0256
3.2071
3.3996
3.6035
3.8197
4.0489
4.2919
4.5494
4.8223
5.1117
5.4184
5.7435
10.285
18.420
32.987
1.0700
1.1449
1.2250
1.3108
1.4026
1.5007
1.6058
1.7182
1.8385
1.9672
2.1049
2.2522
2.4098
2.5785
2.7590
2.9522
3.1588
3.3799
3.6165
3.8697
4.1406
4.4304
4.7405
5.0724
5.4274
5.8074
6.2139
6.6488
7.1143
7.6123
14.974
29.457
57.946
1.0800
1.1664
1.2597
1.3605
1.4693
1.5869
1.7138
1.8509
1.9990
2.1589
2.3316
2.5182
2.7196
2.9372
3.1722
3.4259
3.7000
3.9960
4.3157
4.6610
5.0338
5.4365
5.8715
6.3412
6.8485
7.3964
7.9881
8.6271
9.3173
10.062
21.724
46.901
101.25
1.0900
1.1881
1.2950
1.4116
1.5386
1.6771
1.8280
1.9926
2.1719
2.3674
2.5804
2.8127
3.0658
3.3417
3.6425
3.9703
4.3276
4.7171
5.1417
5.6044
6.1088
6.6586
7.2579
7.9111
8.6231
9.3992
10.245
11.167
12.172
13.267
31.409
74.357
176.03
1.1000
1.2100
1.3310
1.4641
1.6105
1.7716
1.9487
2.1436
2.3579
2.5937
2.8531
3.1384
3.4523
3.7975
4.1772
4.5950
5.0545
5.5599
6.1159
6.7275
7.4002
8.1403
8.9543
9.8497
10.834
11.918
13.110
14.421
15.863
17.449
45.259
117.39
304.48
803
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
804
Appendix B: Interest Factor Tables
Table B.1 Future Value of $1: FVIFi,n (1 i)n (continued)
Period
12%
14%
15%
16%
18%
20%
24%
28%
32%
36%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
1.1200
1.2544
1.4049
1.5735
1.7623
1.9738
2.2107
2.4760
2.7731
3.1058
3.4785
3.8960
4.3635
4.8871
5.4736
6.1304
6.8660
7.6900
8.6128
9.6463
10.803
12.100
13.552
15.178
17.000
19.040
21.324
23.883
26.749
29.959
93.050
289.00
897.59
1.1400
1.2996
1.4815
1.6890
1.9254
2.1950
2.5023
2.8526
3.2519
3.7072
4.2262
4.8179
5.4924
6.2613
7.1379
8.1372
9.2765
10.575
12.055
13.743
15.667
17.861
20.361
23.212
26.461
30.166
34.389
39.204
44.693
50.950
188.88
700.23
2595.9
1.1500
1.3225
1.5209
1.7490
2.0114
2.3131
2.6600
3.0590
3.5179
4.0456
4.6524
5.3502
6.1528
7.0757
8.1371
9.3576
10.761
12.375
14.231
16.366
18.821
21.644
24.891
28.625
32.918
37.856
43.535
50.065
57.575
66.211
267.86
1083.6
4383.9
1.1600
1.3456
1.5609
1.8106
2.1003
2.4364
2.8262
3.2784
3.8030
4.4114
5.1173
5.9360
6.8858
7.9875
9.2655
10.748
12.467
14.462
16.776
19.460
22.574
26.186
30.376
35.236
40.874
47.414
55.000
63.800
74.008
85.849
378.72
1670.7
7370.1
1.1800
1.3924
1.6430
1.9388
2.2878
2.6996
3.1855
3.7589
4.4355
5.2338
6.1759
7.2876
8.5994
10.147
11.973
14.129
16.672
19.673
23.214
27.393
32.323
38.142
45.007
53.108
62.668
73.948
87.259
102.96
121.50
143.37
750.37
3927.3
20555.
1.2000
1.4400
1.7280
2.0736
2.4883
2.9860
3.5832
4.2998
5.1598
6.1917
7.4301
8.9161
10.699
12.839
15.407
18.488
22.186
26.623
31.948
38.337
46.005
55.206
66.247
79.496
95.396
114.47
137.37
164.84
197.81
237.37
1469.7
9100.4
56347.
1.2400
1.5376
1.9066
2.3642
2.9316
3.6352
4.5077
5.5895
6.9310
8.5944
10.657
13.214
16.386
20.319
25.195
31.242
38.740
48.038
59.567
73.864
91.591
113.57
140.83
174.63
216.54
268.51
332.95
412.86
511.95
634.81
5455.9
46890.
*
1.2800
1.6384
2.0972
2.6844
3.4360
4.3980
5.6295
7.2058
9.2234
11.805
15.111
19.342
24.758
31.691
40.564
51.923
66.461
85.070
108.89
139.37
178.40
228.35
292.30
374.14
478.90
612.99
784.63
1004.3
1285.5
1645.5
19426.
*
*
1.3200
1.7424
2.3000
3.0360
4.0075
5.2899
6.9826
9.2170
12.166
16.059
21.198
27.982
36.937
48.756
64.358
84.953
112.13
148.02
195.39
257.91
340.44
449.39
593.19
783.02
1033.5
1364.3
1800.9
2377.2
3137.9
4142.0
66520.
*
*
1.3600
1.8496
2.5155
3.4210
4.6526
6.3275
8.6054
11.703
15.916
21.646
29.439
40.037
54.451
74.053
100.71
136.96
186.27
253.33
344.53
468.57
637.26
866.67
1178.6
1602.9
2180.0
2964.9
4032.2
5483.8
7458.0
10143.
*
*
*
*FVIF 99,999.
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Appendix B: Interest Factor Tables
805
Table B.2 Present Value of $1: PVIFi,n 1/(1 i)n 1/FVIFi,n
Period
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
35
40
45
50
55
.9901
.9803
.9706
.9610
.9515
.9420
.9327
.9235
.9143
.9053
.8963
.8874
.8787
.8700
.8613
.8528
.8444
.8360
.8277
.8195
.8114
.8034
.7954
.7876
.7798
.7720
.7644
.7568
.7493
.7419
.7059
.6717
.6391
.6080
.5785
.9804
.9612
.9423
.9238
.9057
.8880
.8706
.8535
.8368
.8203
.8043
.7885
.7730
.7579
.7430
.7284
.7142
.7002
.6854
.6730
.6598
.6468
.6342
.6217
.6095
.5976
.5859
.5744
.5631
.5521
.5000
.4529
.4102
.3715
.3365
.9709
.9426
.9151
.8885
.8626
.8375
.8131
.7894
.7664
.7441
.7224
.7014
.6810
.6611
.6419
.6232
.6050
.5874
.5703
.5537
.5375
.5219
.5067
.4919
.4776
.4637
.4502
.4371
.4243
.4120
.3554
.3066
.2644
.2281
.1968
.9615
.9246
.8890
.8548
.8219
.7903
.7599
.7307
.7026
.6756
.6496
.6246
.6006
.5775
.5553
.5339
.5134
.4936
.4746
.4564
.4388
.4220
.4057
.3901
.3751
.3607
.3468
.3335
.3207
.3083
.2534
.2083
.1712
.1407
.1157
.9524
.9070
.8638
.8227
.7835
.7462
.7107
.6768
.6446
.6139
.5847
.5568
.5303
.5051
.4810
.4581
.4363
.4155
.3957
.3769
.3589
.3418
.3256
.3101
.2953
.2812
.2678
.2551
.2429
.2314
.1813
.1420
.1113
.0872
.0683
.9434
.8900
.8396
.7921
.7473
.7050
.6651
.6274
.5919
.5584
.5268
.4970
.4688
.4423
.4173
.3936
.3714
.3503
.3305
.3118
.2942
.2775
.2618
.2470
.2330
.2198
.2074
.1956
.1846
.1741
.1301
.0972
.0727
.0543
.0406
.9346
.8734
.8163
.7629
.7130
.6663
.6227
.5820
.5439
.5083
.4751
.4440
.4150
.3878
.3624
.3387
.3166
.2959
.2765
.2584
.2415
.2257
.2109
.1971
.1842
.1722
.1609
.1504
.1406
.1314
.0937
.0668
.0476
.0339
.0242
.9259
.8573
.7938
.7350
.6806
.6302
.5835
.5403
.5002
.4632
.4289
.3971
.3677
.3405
.3152
.2919
.2703
.2502
.2317
.2145
.1987
.1839
.1703
.1577
.1460
.1352
.1252
.1159
.1073
.0994
.0676
.0460
.0313
.0213
.0145
.9174
.8417
.7722
.7084
.6499
.5963
.5470
.5019
.4604
.4224
.3875
.3555
.3262
.2992
.2745
.2519
.2311
.2120
.1945
.1784
.1637
.1502
.1378
.1264
.1160
.1064
.0976
.0895
.0822
.0754
.0490
.0318
.0207
.0134
.0087
.9091
.8264
.7513
.6830
.6209
.5645
.5132
.4665
.4241
.3855
.3505
.3186
.2897
.2633
.2394
.2176
.1978
.1799
.1635
.1486
.1351
.1228
.1117
.1015
.0923
.0839
.0763
.0693
.0630
.0573
.0356
.0221
.0137
.0085
.0053
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
806
Appendix B: Interest Factor Tables
Table B.2 Present Value of $1: PVIFi,n 1/(1 i ) n 1/FVIFi,n (continued)
Period
12%
14%
15%
16%
18%
20%
24%
28%
32%
36%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
35
40
45
50
55
.8929
.7972
.7118
.6355
.5674
.5066
.4523
.4039
.3606
.3220
.2875
.2567
.2292
.2046
.1827
.1631
.1456
.1300
.1161
.1037
.0926
.0826
.0738
.0659
.0588
.0525
.0469
.0419
.0374
.0334
.0189
.0107
.0061
.0035
.0020
.8772
.7695
.6750
.5921
.5194
.4556
.3996
.3506
.3075
.2697
.2366
.2076
.1821
.1597
.1401
.1229
.1078
.0946
.0829
.0728
.0638
.0560
.0491
.0431
.0378
.0331
.0291
.0255
.0224
.0196
.0102
.0053
.0027
.0014
.0007
.8969
.7561
.6575
.5718
.4972
.4323
.3759
.3269
.2843
.2472
.2149
.1869
.1625
.1413
.1229
.1069
.0929
.0808
.0703
.0611
.0531
.0462
.0402
.0349
.0304
.0264
.0230
.0200
.0174
.0151
.0075
.0037
.0019
.0009
.0005
.8621
.7432
.6407
.5523
.4761
.4104
.3538
.3050
.2630
.2267
.1954
.1685
.1452
.1252
.1079
.0930
.0802
.0691
.0596
.0514
.0443
.0382
.0329
.0284
.0245
.0211
.0182
.0157
.0135
.0116
.0055
.0026
.0013
.0006
.0003
.8475
.7182
.6086
.5158
.4371
.3704
.3139
.2660
.2255
.1911
.1619
.1372
.1163
.0985
.0835
.0708
.0600
.0508
.0431
.0365
.0309
.0262
.0222
.0188
.0160
.0135
.0115
.0097
.0082
.0070
.0030
.0013
.0006
.0003
.0001
.8333
.6944
.5787
.4823
.4091
.3349
.2791
.2326
.1938
.1615
.1346
.1122
.0935
.0779
.0649
.0541
.0451
.0376
.0313
.0261
.0217
.0181
.0151
.0126
.0105
.0087
.0073
.0061
.0051
.0042
.0017
.0007
.0003
.0001
*
.8065
.6504
.5245
.4230
.3411
.2751
.2218
.1789
.1443
.1164
.0938
.0757
.0610
.0492
.0397
.0320
.0258
.0208
.0168
.0135
.0109
.0088
.0071
.0057
.0046
.0037
.0030
.0024
.0020
.0016
.0005
.0002
.0001
*
*
.7813
.6104
.4768
.3725
.2910
.2274
.1776
.1388
.1084
.0847
.0662
.0517
.0404
.0316
.0247
.0193
.0150
.0118
.0092
.0072
.0056
.0044
.0034
.0027
.0021
.0016
.0013
.0010
.0008
.0006
.0002
.0001
*
*
*
.7576
.5739
.4348
.3294
.2495
.1890
.1432
.1085
.0822
.0623
.0472
.0357
.0271
.0205
.0155
.0118
.0089
.0068
.0051
.0039
.0029
.0022
.0017
.0013
.0010
.0007
.0006
.0004
.0003
.0002
.0001
*
*
*
*
.7353
.5407
.3975
.2923
.2149
.1580
.1162
.0854
.0628
.0462
.0340
.0250
.0184
.0135
.0099
.0073
.0054
.0039
.0029
.0021
.0016
.0012
.0008
.0006
.0005
.0003
.0002
.0002
.0001
.0001
*
*
*
*
*
* The factor is zero to four decimal places.
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Appendix B: Interest Factor Tables
807
Table B.3 Future Value of an Annuity of $1 for n Periods
n
FVIFAi,n ∑
(1 i)t 1
t1
(1 i) n 1
__________
i
Number
of
Periods
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
1.0000
2.0100
3.0301
4.0604
5.1010
6.1520
7.2135
8.2857
9.3685
10.462
11.566
12.682
13.809
14.947
16.096
17.257
18.430
19.614
20.810
22.019
23.239
24.471
25.716
26.973
28.243
29.525
30.820
32.129
33.450
34.784
48.886
64.463
81.669
1.0000
2.0200
3.0604
4.1216
5.2040
6.3081
7.4343
8.5830
9.7546
10.949
12.168
13.412
14.680
15.973
17.293
18.639
20.012
21.412
22.840
24.297
25.783
27.299
28.845
30.421
32.030
33.670
35.344
37.051
38.792
40.568
60.402
84.579
114.05
1.0000
2.0300
3.0909
4.1836
5.3091
6.4684
7.6625
8.8923
10.159
11.463
12.807
14.192
15.617
17.086
18.598
20.156
21.761
23.414
25.116
26.870
28.676
30.536
32.452
34.426
36.459
38.553
40.709
42.930
45.218
47.575
75.401
112.79
163.05
1.0000
2.0400
3.1216
4.2465
5.4163
6.6330
7.8983
9.2142
10.582
12.006
13.486
15.025
16.626
18.291
20.023
21.824
23.697
25.645
27.671
29.778
31.969
34.248
36.617
39.082
41.645
44.311
47.084
49.967
52.966
56.084
95.025
152.66
237.99
1.0000
2.0500
3.1525
4.3101
5.5256
6.8019
8.1420
9.5491
11.026
12.577
14.206
15.917
17.713
19.598
21.578
23.657
25.840
28.132
30.539
33.066
35.719
38.505
41.430
44.502
47.727
51.113
54.669
58.402
62.322
66.438
120.79
209.34
353.58
1.0000
2.0600
3.1836
4.3746
5.6371
6.9753
8.3938
9.8975
11.491
13.180
14.971
16.869
18.882
21.015
23.276
25.672
28.212
30.905
33.760
36.785
39.992
43.392
46.995
50.815
54.864
59.156
63.705
68.528
73.639
79.058
154.76
290.33
533.12
1.0000
2.0700
3.2149
4.4399
5.7507
7.1533
8.6540
10.259
11.978
13.816
15.783
17.888
20.140
22.550
25.129
27.888
30.840
33.999
37.379
40.995
44.865
49.005
53.436
58.176
63.249
68.676
74.483
80.697
87.346
94.460
199.63
406.52
813.52
1.0000
2.0800
3.2465
4.5061
5.8666
7.3359
8.9228
10.636
12.487
14.486
16.645
18.977
21.495
24.214
27.152
30.324
33.750
37.450
41.446
45.762
50.422
55.456
60.893
66.764
73.105
79.954
87.350
95.338
103.96
113.28
259.05
573.76
1253.2
1.0000
2.0900
3.2781
4.5731
5.9847
7.5233
9.2004
11.028
13.021
15.192
17.560
20.140
22.953
26.019
29.360
33.003
36.973
41.301
46.018
51.160
56.764
62.873
69.531
76.789
84.700
93.323
102.72
112.96
124.13
136.30
337.88
815.08
1944.7
1.0000
2.1000
3.3100
4.6410
6.1051
7.7156
9.4872
11.435
13.579
15.937
18.531
21.384
24.522
27.975
31.772
35.949
40.544
45.599
51.159
57.275
64.002
71.402
79.543
88.497
98.347
109.18
121.09
134.20
148.63
164.49
442.59
1163.9
3034.8
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
808
Appendix B: Interest Factor Tables
Table B.3 Future Value of an Annuity of $1 for n Periods (continued)
n
FVIFAi,n ∑
(1 i)t 1
t1
(1 i) n 1
__________
i
Number
of
Periods
12%
14%
15%
16%
18%
20%
24%
28%
32%
36%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
1.0000
2.1200
3.3744
4.7793
6.3528
8.1152
10.089
12.299
14.775
17.548
20.654
24.133
28.029
32.392
37.279
42.753
48.883
55.749
63.439
72.052
81.698
92.502
104.60
118.15
133.33
150.33
169.37
190.69
214.58
241.33
767.09
2400.0
7471.6
1.0000
2.1400
3.4396
4.9211
6.6101
8.5355
10.730
13.232
16.085
19.337
23.044
27.270
32.088
37.581
43.842
50.980
59.117
68.394
78.969
91.024
104.76
120.43
138.29
158.65
181.87
208.33
238.49
272.88
312.09
356.78
1342.0
4994.5
18535.
1.0000
2.1500
3.4725
4.9934
6.7424
8.7537
11.066
13.726
16.785
20.303
24.349
29.001
34.351
40.504
47.580
55.717
65.075
75.836
88.211
102.44
118.81
137.63
159.27
184.16
212.79
245.71
283.56
327.10
377.16
434.74
1779.0
7217.7
29219.
1.0000
2.1600
3.5056
5.0665
6.8771
8.9775
11.413
14.240
17.518
21.321
25.732
30.850
36.786
43.672
51.659
60.925
71.673
84.140
98.603
115.37
134.84
157.41
183.60
213.97
249.21
290.08
337.50
392.50
456.30
530.31
2360.7
10435.
46057.
1.0000
2.1800
3.5724
5.2154
7.1542
9.4420
12.141
15.327
19.085
23.521
28.755
34.931
42.218
50.818
60.965
72.939
87.068
103.74
123.41
146.62
174.02
206.34
244.48
289.49
342.60
405.27
479.22
566.48
669.44
790.94
4163.2
21813.
*
1.0000
2.2000
3.6400
5.3680
7.4416
9.9299
12.915
16.499
20.798
25.958
32.150
39.580
48.496
59.195
72.035
87.442
105.93
128.11
154.74
186.68
225.02
271.03
326.23
392.48
471.98
567.37
681.85
819.22
984.06
1181.8
7343.8
45497.
*
1.0000
2.2400
3.7776
5.6842
8.0484
10.980
14.615
19.122
24.712
31.643
40.237
50.894
64.109
80.496
100.81
126.01
157.25
195.99
244.03
303.60
377.46
469.05
582.62
723.46
898.09
1114.6
1383.1
1716.0
2128.9
2640.9
22728.
*
*
1.0000
2.2800
3.9184
6.0156
8.6999
12.135
16.533
22.163
29.369
38.592
50.398
65.510
84.852
109.61
141.30
181.86
233.79
300.25
385.32
494.21
633.59
811.99
1040.3
1332.6
1706.8
2185.7
2798.7
3583.3
4587.6
5873.2
69377.
*
*
1.0000
2.3200
4.0624
6.3624
9.3983
13.405
18.695
25.678
34.895
47.061
63.121
84.320
112.30
149.23
197.99
262.35
347.30
459.44
607.47
802.86
1060.7
1401.2
1850.6
2443.8
3226.8
4260.4
5624.7
7425.6
9802.9
12940.
*
*
*
1.0000
2.3600
4.2096
6.7251
10.146
14.798
21.126
29.731
41.435
57.351
78.998
108.43
148.47
202.92
276.97
377.69
514.66
700.93
954.27
1298.8
1767.3
2404.6
3271.3
4449.9
6052.9
8233.0
11197.9
15230.2
20714.1
28172.2
*
*
*
*FVIVA 99,999.
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Appendix B: Interest Factor Tables
809
Table B.4 Present Value of an Annuity of $1 for n Periods
1
1 ______n
(1 i)
__________
PVIFAi,n t
i
t1 (1 i)
n
∑
1
______
Number
of
Payments
1%
2%
3%
4%
5%
6%
7%
8%
9%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
35
40
45
50
55
0.9901
1.09704
2.9410
3.9020
4.8534
5.7955
6.7282
7.6517
8.5660
9.4713
10.3676
11.2551
12.1337
13.0037
13.8651
14.7179
15.5623
16.3983
17.2260
18.0456
18.8570
19.6604
20.4558
21.2434
22.0232
22.7952
23.5596
24.3164
25.0658
25.8077
29.4086
32.8347
36.0945
39.1961
42.1472
0.9804
1.9416
2.8839
3.8077
4.7135
5.6014
6.4720
7.3255
8.1622
8.9826
9.7868
10.5753
11.3484
12.1062
12.8493
13.5777
14.2919
14.9920
15.6785
16.3514
17.0112
17.6580
18.2922
18.9139
19.5235
20.1210
20.7069
21.2813
21.8444
22.3965
24.9986
27.3555
29.4902
31.4236
33.1748
0.9709
1.9135
2.8286
3.7171
4.5797
5.4172
6.2303
7.0197
7.7861
8.5302
9.2526
9.9540
10.6350
11.2961
11.9379
12.5611
13.1661
13.7535
14.3238
14.8775
15.4150
15.9369
16.4436
16.9355
17.4131
17.8768
18.3270
18.7641
19.1885
19.6004
21.4872
23.1148
24.5187
25.7298
26.7744
0.9615
1.8861
2.7751
3.6299
4.4518
5.2421
6.0021
6.7327
7.4353
8.1109
8.7605
9.3851
9.9856
10.5631
11.1184
11.6523
12.1657
12.6593
13.1339
13.5903
14.0292
14.4511
14.8568
15.2470
15.6221
15.9828
16.3296
16.6631
16.9837
17.2920
18.6646
19.7928
20.7200
21.4822
22.1086
0.9524
1.8594
2.7232
3.5460
4.3295
5.0757
5.7864
6.4632
7.1078
7.7217
8.3064
8.8633
9.3936
9.8986
10.3797
10.8378
11.2741
11.6896
12.0853
12.4622
12.8212
13.1630
13.4886
13.7986
14.0939
14.3752
14.6430
14.8981
15.1411
15.3725
16.3742
17.1591
17.7741
18.2559
18.6335
0.9434
1.8334
2.6730
3.4651
4.2124
4.9173
5.5824
6.2098
6.8017
7.3601
7.8869
8.3838
8.8527
9.2950
9.7122
10.1059
10.4773
10.8276
11.1581
11.4699
11.7641
12.0416
12.3034
12.5504
12.7834
13.0032
13.2105
13.4062
13.5907
13.7648
14.4982
15.0463
15.4558
15.7619
15.9905
0.9346
1.8080
2.6243
3.3872
4.1002
4.7665
5.3893
5.9713
6.5152
7.0236
7.4987
7.9427
8.3577
8.7455
9.1079
9.4466
9.7632
10.0591
10.3356
10.5940
10.8355
11.0612
11.2722
11.4693
11.6536
11.8258
11.9867
12.1371
12.2777
12.4090
12.9477
13.3317
13.6055
13.8007
13.9399
0.9259
1.7833
2.5771
3.3121
3.9927
4.6229
5.2064
5.7466
6.2469
6.7101
7.1390
7.5361
7.9038
8.2442
8.5595
8.8514
9.1216
9.3719
9.6036
9.8181
10.0168
10.2007
10.3711
10.5288
10.6748
10.8100
10.9352
11.0511
11.1584
11.2578
11.6546
11.9246
12.1084
12.2335
12.3186
0.9174
1.7591
2.5313
3.2397
3.8897
4.4859
5.0330
5.5348
5.9952
6.4177
6.8052
7.1607
7.4869
7.7862
8.0607
8.3126
8.5436
8.7556
8.9501
9.1285
9.2922
9.4424
9.5802
9.7066
9.8226
9.9290
10.0266
10.1161
10.1983
10.2737
10.5668
10.7574
10.8812
10.9617
11.0140
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
810
Appendix B: Interest Factor Tables
Table B.4 Present Value of an Annuity of $1 for n Periods (continued)
1
1 ______n
(1
i)
1
______
__________
PVIFAi,n t
i
t1 (1 i)
n
∑
Number
of
Payments
10%
12%
14%
15%
16%
18%
20%
24%
28%
32%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
35
40
45
50
55
0.9091
1.7355
2.4869
3.1699
3.7908
4.3553
4.8684
5.3349
5.7590
6.1446
6.4951
6.8137
7.1034
7.3667
7.6061
7.8237
8.0216
8.2014
8.3649
8.5136
8.6487
8.7715
8.8832
8.9847
9.0770
9.1609
9.2372
9.3066
9.3696
9.4269
9.6442
9.7791
9.8628
9.9148
9.9471
0.8929
1.6901
2.4018
3.0373
3.6048
4.1114
4.5638
4.9676
5.3282
5.6502
5.9377
6.1944
6.4235
6.6282
6.8109
6.9740
7.1196
7.2497
7.3658
7.4694
7.5620
7.6446
7.7184
7.7843
7.8431
7.8957
7.9426
7.9844
8.0218
8.0552
8.1755
8.2438
8.2825
8.3045
8.3170
0.8772
1.6467
2.3216
2.9137
3.4331
3.8887
4.2883
4.6389
4.9464
5.2161
5.4527
5.6603
5.8424
6.0021
6.1422
6.2651
6.3729
6.4674
6.5504
6.6231
6.6870
6.7429
6.7921
6.8351
6.8729
6.9061
6.9352
6.9607
6.9830
7.0027
7.0700
7.1050
7.1232
7.1327
7.1376
0.8696
1.6257
2.2832
2.8550
3.3522
3.7845
4.1604
4.4873
4.7716
5.0188
5.2337
5.4206
5.5831
5.7245
5.8474
5.9542
6.0472
6.1280
6.1982
6.2593
6.3125
6.3587
6.3988
6.4338
6.4642
6.4906
6.5135
6.5335
6.5509
6.5660
6.6166
6.6418
6.6543
6.6605
6.6636
0.8621
1.6052
2.2459
2.7982
3.2743
3.6847
4.0386
4.3436
4.6065
4.8332
5.0286
5.1971
5.3423
5.4675
5.5755
5.6685
5.7487
5.8178
5.8775
5.9288
5.9731
6.0113
6.0442
6.0726
6.0971
6.1182
6.1364
6.1520
6.1656
6.1772
6.2153
6.2335
6.2421
6.2463
6.2482
0.8475
1.5656
2.1743
2.6901
3.1272
3.4976
3.8115
4.0776
4.3030
4.4941
4.6560
4.7932
4.9095
5.0081
5.0916
5.1624
5.2223
5.2732
5.3162
5.3527
5.3837
5.4099
5.4321
5.4510
5.4669
5.4804
5.4919
6.5016
5.5098
5.5168
5.5386
5.5482
5.5523
5.5541
5.5549
0.8333
1.5278
2.1065
2.5887
2.9906
3.3255
3.6046
3.8372
4.0310
4.1925
4.3271
4.4392
4.5327
4.6106
4.6755
4.7296
4.7746
4.8122
4.8435
4.8696
4.8913
4.9094
4.9245
4.9371
4.9476
4.9563
4.9636
4.9697
4.9747
4.9789
4.9915
4.9966
4.9986
4.9995
4.9998
0.8065
1.4568
1.9813
2.4043
2.7454
3.0205
3.2423
3.4212
3.5655
3.6819
3.7757
3.8514
3.9124
3.9616
4.0013
4.0333
4.0591
4.0799
4.0967
4.1103
4.1212
4.1300
4.1371
4.1428
4.1474
4.1511
4.1542
4.1566
4.1585
4.1601
4.1644
4.1659
4.1664
4.1666
4.1666
0.7813
1.3916
1.8684
2.2410
2.5320
2.7594
2.9370
3.0758
3.1842
3.2689
3.3351
3.3868
3.4272
3.4587
3.4834
3.5026
3.5177
3.5294
3.5386
3.5458
3.5514
3.5558
3.5592
3.5619
3.5640
3.5656
3.5669
3.5679
3.5687
3.5693
3.5708
3.5712
3.5714
3.5714
3.5714
0.7576
1.3315
1.7663
2.0957
2.3452
2.5342
2.6775
2.7860
2.8681
2.9304
2.9776
3.0133
3.0404
3.0609
3.0764
3.0882
3.0971
3.1039
3.1090
3.1129
3.1158
3.1180
3.1197
3.1210
3.1220
3.1227
3.1233
3.1237
3.1240
3.1242
3.1248
3.1250
3.1250
3.1250
3.1250
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Appendix C
Statistical Tables
Table C.1 Distribution of a Variable z (Percent of Total Area Under the Normal Curve Between x and μ)
z1
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
.0000
.0398
.0793
.1179
.1554
.1915
.2257
.2580
.2881
.3159
.3413
.3643
.3849
.4032
.4192
.4332
.4452
.4554
.4641
.4713
.4773
.4821
.4861
.4893
.4918
.4938
.4953
.4965
.4974
.4981
.4987
.0040
.0438
.0832
.1217
.1591
.1950
.2291
.2611
.2910
.3186
.3438
.3665
.3869
.4049
.4207
.4345
.4463
.4564
.4649
.4719
.4778
.4826
.4864
.4896
.4920
.4940
.4955
.4966
.4975
.4982
.4987
.0080
.0478
.0871
.1255
.1628
.1985
.2324
.2642
.2939
.3212
.3461
.3686
.3888
.4066
.4222
.4357
.4474
.4573
.4656
.4726
.4783
.4830
.4868
.4898
.4922
.4941
.4956
.4967
.4976
.4982
.4987
.0120
.0517
.0910
.1293
.1664
.2019
.2357
.2673
.2967
.3238
.3485
.3708
.3907
.4082
.4236
.4370
.4484
.4582
.4664
.4732
.4788
.4834
.4871
.4901
.4925
.4943
.4957
.4968
.4977
.4982
.4988
.0160
.0557
.0948
.1331
.1700
.2054
.2389
.2704
.2995
.3264
.3508
.3729
.3925
.4099
.4251
.4382
.4495
.4591
.4671
.4738
.4793
.4838
.4875
.4904
.4927
.4945
.4959
.4969
.4977
.4894
.4988
.0199
.0596
.0987
.1368
.1736
.2088
.2422
.2734
.3023
.3289
.3531
.3749
.3944
.4115
.4265
.4394
.4505
.4599
.4678
.4744
.4798
.4842
.4878
.4906
.4929
.4946
.4960
.4970
.4978
.4984
.4989
.0239
.0636
.1026
.1406
.1772
.2123
.2454
.2764
.3051
.3315
.3554
.3770
.3962
.4131
.4279
.4406
.4515
.4608
.4686
.4750
.4803
.4846
.4881
.4909
.4931
.4948
.4961
.4971
.4979
.4985
.4989
.0279
.0675
.1064
.1443
.1808
.2157
.2486
.2794
.3078
.3340
.3577
.3790
.3980
.4147
.4292
.4418
.4525
.4616
.4693
.4756
.4808
.4850
.4884
.4911
.4932
.4949
.4962
.4972
.4979
.4985
.4989
.0319
.0714
.1103
.1480
.1844
.2190
.2517
.2823
.3106
.3365
.3599
.3810
.3997
.4162
.4306
.4429
.4535
.4625
.4699
.4761
.4812
.4854
.4887
.4913
.4934
.4951
.4963
.4973
.4980
.4986
.4990
.0359
.0753
.1141
.1517
.1879
.2224
.2549
.2852
.3133
.3389
.3621
.3830
.4015
.4177
.4319
.4441
.4545
.4633
.4706
.4767
.4817
.4857
.4890
.4916
.4936
.4952
.4964
.4974
.4981
.4986
.4990
1 z is the standardized variable, where z x μ/σ and x is the point of interest, μ is the mean, and s is the standard deviation of a distribution. Thus, z measures
the number of standard deviations between a point of interest x and the mean of a given distribution. The table above indicates the percentage of the total area
under the normal curve between x and μ. Thus, .3413 or 34.13% of the area under the normal curve lies between a point of interest and the mean when z 1.0.
811
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Degrees of Freedom in the Numerator (df k 1)
1
2
3
4
5
6
7
53.59 55.83 57.24 58.20 58.91
1 39.86 49.50
9.35
9.33
9.29
9.24
9.16
9.00
8.53
2
5.27
5.28
5.31
5.34
5.39
5.46
8.54
3
3.98
4.01
4.05
4.11
4.19
4.32
4.54
4
3.37
3.40
3.45
3.52
3.62
3.78
4.06
5
3.01
3.05
3.11
3.18
3.29
3.46
3.78
6
2.78
2.83
2.88
2.96
3.07
3.26
3.59
7
2.62
2.67
2.73
2.81
2.92
3.11
3.46
8
2.51
2.55
2.61
2.69
2.81
3.01
3.36
9
2.41
2.46
2.52
2.61
2.73
2.92
3.29
10
2.34
2.39
2.45
2.54
2.66
2.86
3.23
11
2.28
2.33
2.39
2.48
2.61
2.81
3.18
12
2.23
2.28
2.35
2.43
2.56
2.76
3.14
13
2.19
2.24
2.31
2.39
2.52
2.73
3.10
14
2.16
2.21
2.27
2.36
2.49
2.70
3.07
15
2.13
2.18
2.24
2.33
2.46
2.67
3.05
16
2.10
2.15
2.22
2.31
2.44
2.64
3.03
17
2.08
2.13
2.20
2.29
2.42
2.62
3.01
18
2.06
2.11
2.18
2.27
2.40
2.61
2.99
19
2.04
2.09
2.16
2.25
2.38
2.59
2.97
20
2.02
2.08
2.14
2.23
2.36
2.57
2.96
21
2.01
2.06
2.13
2.22
2.35
2.56
2.95
22
1.99
2.05
2.11
2.21
2.34
2.55
2.94
23
1.98
2.04
2.10
2.19
2.33
2.54
2.93
24
1.97
2.02
2.09
2.18
2.32
2.53
2.92
25
1.96
2.01
2.08
2.17
2.31
2.52
2.91
26
1.95
2.00
2.07
2.17
2.30
2.51
2.90
27
1.94
2.00
2.06
2.16
2.29
2.50
2.89
28
1.93
1.99
2.06
2.15
2.28
2.50
2.89
29
1.93
1.98
2.05
2.14
2.28
2.49
2.88
30
1.87
1.93
2.00
2.09
2.23
2.44
2.84
40
1.82
1.87
1.95
2.04
2.18
2.39
2.79
60
1.77
1.82
1.90
1.99
2.13
2.35
120 2.75
1.72
1.77
1.85
1.94
2.08
2.30
2.71
∞
8
59.44
9.37
5.25
3.95
3.34
2.98
2.75
2.59
2.47
2.38
2.30
2.24
2.20
2.15
2.12
2.09
2.06
2.04
2.02
2.00
1.98
1.97
1.95
1.94
1.93
1.92
1.91
1.90
1.89
1.88
1.83
1.77
1.72
1.67
9
59.86
9.38
5.24
3.94
3.32
2.96
2.72
2.56
2.44
2.35
2.27
2.21
2.16
2.12
2.09
2.06
2.03
2.00
1.98
1.96
1.95
1.93
1.92
1.91
1.89
1.88
1.87
1.87
1.86
1.85
1.79
1.74
1.68
1.63
10
60.19
9.39
5.23
3.92
3.30
2.94
2.70
2.54
2.42
2.32
2.25
2.19
2.14
2.10
2.06
2.03
2.00
1.98
1.96
1.94
1.92
1.90
1.89
1.88
1.87
1.86
1.85
1.84
1.83
1.82
1.76
1.71
1.65
1.60
12
60.71
9.41
5.22
3.90
3.27
2.90
2.67
2.50
2.38
2.28
2.21
2.15
2.10
2.05
2.02
1.99
1.96
1.93
1.91
1.89
1.87
1.86
1.84
1.83
1.82
1.81
1.80
1.79
1.78
1.77
1.71
1.66
1.60
1.55
15
61.22
9.42
5.20
3.87
3.24
2.87
2.63
2.46
2.34
2.24
2.17
2.10
2.05
2.01
1.97
1.94
1.91
1.89
1.86
1.84
1.83
1.81
1.80
1.78
1.77
1.76
1.75
1.74
1.73
1.72
1.66
1.60
1.55
1.49
20
61.74
9.44
5.18
3.84
3.21
2.84
2.59
2.42
2.30
2.20
2.12
2.06
2.01
1.96
1.92
1.89
1.86
1.84
1.81
1.79
1.78
1.76
1.74
1.73
1.72
1.71
1.70
1.69
1.68
1.67
1.61
1.54
1.48
1.42
24
62.00
9.45
5.18
3.83
3.19
2.82
2.58
2.40
2.28
2.18
2.10
2.04
1.98
1.94
1.90
1.87
1.84
1.81
1.79
1.77
1.75
1.73
1.72
1.70
1.69
1.68
1.67
1.66
1.65
1.64
1.57
1.51
1.45
1.38
30
62.26
9.46
5.17
3.82
3.17
2.80
2.56
2.38
2.25
2.16
2.08
2.01
1.96
1.91
1.87
1.84
1.81
1.78
1.76
1.74
1.72
1.70
1.69
1.67
1.66
1.65
1.64
1.63
1.62
1.61
1.54
1.48
1.41
1.34
40
62.53
9.47
5.16
3.80
3.16
2.78
2.54
2.36
2.23
2.13
2.05
1.99
1.93
1.89
1.85
1.81
1.78
1.75
1.73
1.71
1.69
1.67
1.66
1.64
1.63
1.61
1.60
1.59
1.58
1.57
1.51
1.44
1.37
1.30
60
62.79
9.47
5.15
3.79
3.14
2.76
2.51
2.34
2.21
2.11
2.03
1.96
1.90
1.86
1.82
1.78
1.75
1.72
1.70
1.68
1.66
1.64
1.62
1.61
1.59
1.58
1.57
1.56
1.55
1.54
1.47
1.40
1.32
1.24
120
63.06
9.48
5.14
3.78
3.12
2.74
2.49
2.32
2.18
2.08
2.00
1.93
1.88
1.83
1.79
1.75
1.72
1.69
1.67
1.64
1.62
1.60
1.59
1.57
1.56
1.54
1.53
1.52
1.51
1.50
1.42
1.35
1.26
1.17
∞
63.33
9.49
5.13
3.76
3.10
2.72
2.47
2.29
2.16
2.06
1.97
1.90
1.85
1.80
1.76
1.72
1.69
1.66
1.63
1.61
1.59
1.57
1.55
1.53
1.52
1.50
1.49
1.48
1.47
1.46
1.38
1.29
1.19
1.00
812
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
1 The F statistic provides evidence on whether or not a statistically significant proportion of the total variation in the dependent variable Y has been explained. The F statistic can be calculated in terms of the coefficient of
determination as: Fk – 1,n – k R2/(k – 1) ÷ (1 – R2)/(n – k), where R2 is the coefficient of determination, k is the number of estimated coefficients in the regression model (including the intercept), and n is the number of data
observations. When the critical F value is exceeded, we can conclude with a given level of confidence (e.g., α 0.01 or 90 percent confidence) that the regression equation, taken as a whole, significantly explains the variation in Y.
Degrees of Freedom in the Denominator (df n k)
Table C.2 Critical F Values at the 90 Percent Confidence Level (α ⴝ .10)1
Licensed to: iChapters User
Appendix C: Statistical Tables
Degrees of Freedom in the Denominator (df n k)
8
9
10
12
15
20
24
30
40
60
120
∞
1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.9 245.9 248.0 249.1 250.1 251.1 252.2 253.3 254.3
2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.41 19.43 19.45 19.45 19.46 19.47 19.48 19.49 19.50
8.53
8.55
8.59 8.57
8.62
8.66 8.64
8.70
8.79 8.74
8.89 8.85 8.81
9.01 8.94
9.12
9.28
9.55
3 10.13
5.63
5.66
5.72 5.69
5.75
5.80 5.77
5.86
5.96 5.91
6.09 6.04 6.00
6.26 6.16
6.39
6.59
6.94
7.71
4
4.36
4.40
4.46 4.43
4.50
4.56 4.53
4.62
4.74 4.68
4.88 4.82 4.77
5.05 4.95
5.19
5.41
5.79
6.61
5
3.67
3.70
3.77 3.74
3.81
3.87 3.84
3.94
4.06 4.00
4.21 4.15 4.10
4.39 4.28
4.53
4.76
5.14
5.99
6
3.23
3.27
3.34 3.30
3.38
3.44 3.41
3.51
3.64 3.57
3.79 3.73 3.68
3.97 3.87
4.12
4.35
4.74
5.59
7
2.93
.301 2.97
3.04
3.08
3.15 3.12
3.22
3.35 3.28
3.50 3.44 3.39
3.69 3.58
3.84
4.07
4.46
5.32
8
2.71
2.75
2.83 2.79
2.86
2.94 2.90
3.01
3.14 3.07
3.29 3.23 3.18
3.48 3.37
3.63
3.86
4.26
5.12
9
2.54
2.58
2.66 2.62
2.70
2.77 2.74
2.85
2.98 2.91
3.14 3.07 3.02
3.33 3.22
3.48
3.71
4.10
4.96
10
2.40
2.45
2.53 2.49
2.57
2.65 2.61
2.72
2.85 2.79
3.01 2.95 2.90
3.20 3.09
3.36
3.59
3.98
4.84
11
2.30
2.34
2.43 2.38
2.47
2.54 2.51
2.62
2.75 2.69
2.91 2.85 2.80
3.11 3.00
3.26
3.49
3.89
4.75
12
2.21
2.25
2.34 2.30
2.38
2.46 2.42
2.53
2.67 2.60
2.83 2.77 2.71
3.03 2.92
3.18
3.41
3.81
4.67
13
2.13
2.18
2.27 2.22
2.31
2.39 2.35
2.46
2.60 2.53
2.76 2.70 2.65
2.96 2.85
3.11
3.34
3.74
4.60
14
2.07
2.11
2.20 2.16
2.25
2.33 2.29
2.40
2.54 2.48
2.71 2.64 2.59
2.90 2.79
3.06
3.29
3.68
4.54
15
2.01
2.06
2.15 2.11
2.19
2.28 2.24
2.35
2.49 2.42
2.66 2.59 2.54
2.85 2.74
3.01
3.24
3.63
4.49
16
1.96
2.01
2.10 2.06
2.15
2.23 2.19
2.31
2.45 2.38
2.61 2.55 2.49
2.81 2.70
2.96
3.20
3.59
4.45
17
1.92
1.97
2.06 2.02
2.11
2.19 2.15
2.27
2.41 2.34
2.58 2.51 2.46
2.77 2.66
2.93
3.16
3.55
4.41
18
1.88
1.93
2.03 1.98
2.07
2.16 2.11
2.23
2.38 2.31
2.54 2.48 2.42
2.74 2.63
2.90
3.13
3.52
4.38
19
1.84
1.90
1.99 1.95
2.04
2.12 2.08
2.20
2.35 2.28
2.51 2.45 2.39
2.71 2.60
2.87
3.10
3.49
4.35
20
1.81
1.87
1.96 1.92
2.01
2.10 2.05
2.18
2.32 2.25
2.49 2.42 2.37
2.68 2.57
2.84
3.07
3.47
4.32
21
1.78
1.84
1.94 1.89
1.98
2.07 2.03
2.15
2.30 2.23
2.46 2.40 2.34
2.66 2.55
2.82
3.05
3.44
4.30
22
1.76
1.81
1.91 1.86
1.96
2.05 2.01
2.13
2.27 2.20
2.44 2.37 2.32
2.64 2.53
2.80
3.03
3.42
4.28
23
1.73
1.79
1.89 1.84
1.94
2.03 1.98
2.11
2.25 2.18
2.42 2.36 2.30
2.62 2.51
2.78
3.01
3.40
4.26
24
1.71
1.77
1.87 1.82
1.92
2.01 1.96
2.09
2.24 2.16
2.40 2.34 2.28
2.60 2.49
2.76
2.99
3.39
4.24
25
1.69
1.75
1.85 1.80
1.90
1.99 1.95
2.07
2.22 2.15
2.39 2.32 2.27
2.59 2.47
2.74
2.98
3.37
4.23
26
1.67
1.73
1.84 1.79
1.88
1.97 1.93
2.06
2.20 2.13
2.37 2.31 2.25
2.57 2.46
2.73
2.96
3.35
4.21
27
1.65
1.71
1.82 1.77
1.87
1.96 1.91
2.04
2.19 2.12
2.36 2.29 2.24
2.56 2.45
2.71
2.95
3.34
4.20
28
1.64
1.70
1.81 1.75
1.85
1.94 1.90
2.03
2.18 2.10
2.35 2.28 2.22
2.55 2.43
2.70
2.93
3.33
4.18
29
1.62
1.68
1.79 1.74
1.84
1.93 1.89
2.01
2.16 2.09
2.33 2.27 2.21
2.53 2.42
2.69
2.92
3.32
4.17
30
1.51
1.58
1.69 1.64
1.74
1.84 1.79
1.92
2.08 2.00
2.25 2.18 2.12
2.45 2.34
2.61
2.84
3.23
4.08
40
1.39
1.47
1.59 1.53
1.65
1.75 1.70
1.84
1.99 1.92
2.17 2.10 2.04
2.37 2.25
2.53
2.76
3.15
4.00
60
1.25
1.35
1.50 1.43
1.55
1.66 1.61
1.75
1.91 1.83
2.09 2.02 1.96
2.29 2.17
2.45
2.68
3.07
3.92
120
1.00
1.22
1.39 1.32
1.46
1.57 1.52
1.67
1.83 1.75
2.01 1.94 1.88
2.21 2.10
2.37
2.60
3.00
3.84
∞
Degrees of Freedom in the Numerator (df k 1)
1
2
3
4
5
6
7
Table C.2 Critical F Values at the 95 Percent Confidence Level (α .05) (continued)
Licensed to: iChapters User
Appendix C: Statistical Tables
813
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Degrees of Freedom in the Denominator (df n k)
2
3
4
5
6
7
8
9
10
12
15
20
24
30
40
60
120
∞
6339 6336
6313
6287
6261
6235
6209
6157
6056 6106
1 4052
5982 6022
5764 5859 5928
5625
4999.5 -5403
99.43 99.45 99.46 99.47 99.47 99.48 99.49 99.50
2
99.17 99.25 99.30 99.33 99.36 99.37 99.39 99.40 99.42
98.50 99.00
26.87 26.69 26.60 26.50 26.41 26.32 26.22 26.13
3
29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 27.05
34.12 30.82
14.20 14.02 13.93 13.84 13.75 13.65 13.56 13.46
4
16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.37
21.20 18.00
9.02
9.11
9.20
9.29
9.38
9.47
9.55
9.72
9.89
5
12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05
16.26 13.27
6.88
6.97
7.06
7.14
7.23
7.31
7.40
7.56
7.72
7.87
7.98
6
8.10
8.26
8.47
8.75
9.15
9.78
13.75 10.92
5.65
5.74
5.82
5.91
5.99
6.07
6.16
6.31
6.47
6.62
6.72
7
6.84
6.99
7.19
7.46
7.85
8.45
9.55
12.25
4.86
4.95
5.03
5.12
5.20
5.28
5.36
5.52
5.67
5.81
5.91
8
6.03
6.18
6.37
6.63
7.01
7.59
8.65
11.26
4.31
4.40
4.48
4.57
4.65
4.73
4.81
4.96
5.11
5.26
5.35
5.47
9
5.61
5.80
6.06
6.42
6.99
8.02
10.56
3.91
4.00
4.08
4.17
4.25
4.33
4.41
4.56
4.71
4.85
4.94
5.06
10
5.20
5.39
5.64
5.99
6.55
7.56
10.04
3.60
3.69
3.78
3.86
3.94
4.02
4.10
4.25
4.40
4.54
4.63
4.74
11
4.89
5.07
5.32
5.67
6.22
7.21
9.65
3.36
3.45
3.54
3.62
3.70
3.78
3.86
4.01
4.16
4.30
4.39
4.50
4.64
12
4.82
5.06
5.41
5.95
6.93
9.33
3.17
3.25
3.34
3.43
3.51
3.59
3.66
3.82
3.96
4.10
4.19
4.30
4.44
13
4.62
4.86
5.21
5.74
6.70
9.07
3.00
3.09
3.18
3.27
3.35
3.43
3.51
3.66
3.80
3.94
4.03
4.14
4.28
14
4.46
4.69
5.04
5.56
6.51
8.86
2.87
2.96
3.05
3.13
3.21
3.29
3.37
3.52
3.67
3.80
3.89
4.00
4.14
4.32
15
4.56
4.89
5.42
6.36
8.68
2.75
2.84
2.93
3.02
3.10
3.18
3.26
3.41
3.55
3.69
3.78
3.89
4.03
4.20
16
4.44
4.77
5.29
6.23
8.53
2.65
2.75
2.83
2.92
3.00
3.08
3.16
3.31
3.46
3.59
3.68
3.79
3.93
4.10
17
4.34
4.67
5.18
6.11
8.40
2.57
2.66
2.75
2.84
2.92
3.00
3.08
3.23
3.37
3.51
3.60
3.71
3.84
4.01
18
4.25
4.58
5.09
6.01
8.29
2.49
2.58
2.67
2.76
2.84
2.92
3.00
3.15
3.30
3.43
3.52
3.63
3.77
3.94
4.17
19
4.50
5.01
5.93
8.18
2.42
2.52
2.61
2.69
2.78
2.86
2.94
3.09
3.23
3.37
3.46
3.56
3.70
3.87
4.10
20
4.43
4.94
5.85
8.10
2.36
2.46
2.55
2.64
2.72
2.80
2.88
3.03
3.17
3.31
3.40
3.51
3.64
3.81
4.04
21
4.37
4.87
5.78
8.02
2.31
2.40
2.50
2.58
2.67
2.75
2.83
2.98
3.12
3.26
3.35
3.45
3.59
3.76
3.99
4.31
22
4.82
5.72
7.95
2.26
2.35
2.45
2.54
2.62
2.70
2.78
2.93
3.07
3.21
3.30
3.41
3.54
3.71
3.94
4.26
23
4.76
5.66
7.88
2.21
2.31
2.40
2.49
2.58
2.66
2.74
2.89
3.03
3.17
3.26
3.36
3.50
3.67
3.90
4.22
24
4.72
5.61
7.82
2.17
2.27
2.36
2.45
2.54
2.62
2.70
2.85
2.99
3.13
3.22
3.32
3.46
3.63
3.85
4.18
25
4.68
5.57
7.77
2.13
2.23
2.33
2.42
2.50
2.58
2.66
2.81
2.96
3.09
3.18
3.29
3.42
3.59
3.82
4.14
26
4.64
5.53
7.72
2.10
2.20
2.29
2.38
2.47
2.55
2.63
2.78
2.93
3.06
3.15
3.26
3.39
3.56
3.78
4.11
4.60
27
5.49
7.68
2.06
2.17
2.26
2.35
2.44
2.52
2.60
2.75
2.90
3.03
3.12
3.23
3.36
3.53
3.75
4.07
4.57
28
5.45
7.64
2.03
2.14
2.23
2.33
2.41
2.49
2.57
2.73
2.87
3.00
3.09
3.20
3.33
3.50
3.73
4.04
4.54
29
5.42
7.60
2.01
2.11
2.21
2.30
2.39
2.47
2.55
2.70
2.84
2.98
3.07
3.17
3.30
3.47
3.70
4.02
4.51
5.39
30
7.56
1.80
1.92
2.02
2.11
2.20
2.29
2.37
2.52
2.66
2.80
2.89
2.99
3.12
3.29
3.51
3.83
4.31
5.18
40
7.31
1.60
1.73
1.84
1.94
2.03
2.12
2.20
2.35
2.50
2.63
2.72
2.82
2.95
3.12
3.34
3.65
4.13
4.98
60
7.08
1.38
1.53
1.66
1.76
1.86
1.95
2.03
2.19
2.34
2.47
2.56
2.66
2.79
2.96
3.17
3.48
3.95
4.79
6.85
120
1.00
1.32
1.47
1.59
1.70
1.79
1.88
2.04
2.18
2.32
2.41
2.51
2.64
2.80
3.02
3.32
3.78
4.61
6.63
∞
1
Degrees of Freedom in the Numerator (df k 1)
Table C.2 Critical F Values at the 99 Percent Confidence Level (α ⴝ .01) (continued)
Licensed to: iChapters User
814
Appendix C: Statistical Tables
Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Appendix C: Statistical Tables
815
Table C.3 Students’ T Distribution1
Degrees
of
Freedom
Area in the Rejection Region (Two-Tail Test)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.05
0.02
0.01
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
60
120
∞
0.158
0.142
0.137
0.134
0.132
0.131
0.130
0.130
0.129
0.129
0.129
0.128
0.128
0.128
0.128
0.128
0.128
0.127
0.127
0.127
0.127
0.127
0.127
0.127
0.127
0.127
0.127
0.127
0.127
0.127
0.126
0.126
0.126
0.126
0.325
0.289
0.277
0.271
0.267
0.265
0.263
0.262
0.261
0.260
0.260
0.259
0.259
0.258
0.258
0.258
0.257
0.257
0.257
0.257
0.257
0.256
0.256
0.256
0.256
0.256
0.256
0.256
0.256
0.256
0.255
0.254
0.254
0.253
0.510
0.445
0.424
0.414
0.408
0.404
0.402
0.399
0.398
0.397
0.396
0.395
0.394
0.393
0.393
0.392
0.392
0.392
0.391
0.391
0.391
0.390
0.390
0.390
0.390
0.390
0.389
0.389
0.389
0.389
0.388
0.387
0.386
0.385
0.727
0.617
0.584
0.569
0.559
0.553
0.549
0.546
0.543
0.542
0.540
0.539
0.538
0.537
0.536
0.535
0.534
0.534
0.533
0.533
0.532
0.532
0.532
0.531
0.531
0.531
0.531
0.530
0.530
0.530
0.529
0.527
0.526
0.524
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.697
0.695
0.694
0.692
0.691
0.690
0.689
0.688
0.688
0.687
0.686
0.686
0.685
0.685
0.684
0.684
0.684
0.683
0.683
0.683
0.681
0.679
0.677
0.674
1.376
1.061
0.978
0.941
0.920
0.906
0.896
0.889
0.883
0.879
0.876
0.873
0.870
0.868
0.866
0.865
0.863
0.862
0.861
0.860
0.859
0.858
0.858
0.857
0.856
0.856
0.855
0.855
0.854
0.854
0.851
0.848
0.845
0.842
1.963
1.386
1.250
1.190
1.156
1.134
1.119
1.108
1.100
1.093
1.088
1.083
1.079
1.076
1.074
1.071
1.069
1.067
1.066
1.064
1.063
1.061
1.060
1.059
1.058
1.058
1.057
1.056
1.055
1.055
1.050
1.046
1.041
1.036
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.303
1.296
1.289
1.282
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.684
1.671
1.658
1.645
12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052
2.048
2.045
2.042
2.021
2.000
1.980
1.960
31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.423
2.390
2.358
2.326
63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.704
2.660
2.617
2.576
0.001
636.619
31.598
12.924
8.610
6.869
5.959
5.408
5.041
4.781
4.587
4.437
4.318
4.221
4.140
4.073
4.015
3.965
3.922
3.883
3.850
3.819
3.792
3.767
3.745
3.725
3.707
3.690
3.674
3.659
3.646
3.551
3.460
3.373
3.291
1 Columns in bold-face type indicate critical t values for popular levels of significance for two-tail hypothesis testing. Thus, critical t values for α 0.1 (90 percent
confidence), α 0.05 (95 percent confidence), and α 0.01 (99 percent confidence) are highlighted. When the calculated t statistic b/σb exceeds the relevant critical
t value, we can reject the hypothesis that there is no relationship between the dependent variable Y and a given independent variable X. For simple t tests, the
relevant number of degrees of freedom (column row) is found as follows: df n k, where n is the number of data observations and k is the number of estimated
coefficients (including the intercept).
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Index
A
Absolute risk, 637–639
Accountability, of board of
directors, 726
Accounting
economic valuations
and, 382
Generally Accepted
Accounting Principles
(GAAP), 296
tricks of, 296
Accounting earnings
manipulation, 719
Ace Ltd., 482
Activism, corporate, 732
Advertising
brand names and, 148, 504
elasticity example, 137
optimal level of, 569–572
sampling technology
for, 163
Agency costs, 716–717, 736
Agency problems
defined, 716
information asymmetry
problems, 719–720
investment horizon
problems, 719
risk management problems,
717–719
Agency theory, 731
Agreements (franchise),
732–733
Agriculture price supports, 449
price floors and, 449–450
Airline industry
September 11, 2001,
effect on, 213–214
Alcoa Inc., 10
Alliances, strategic, 733–734
Altria Group, Inc., 11
Aluminum industry, 416–417
Amazon.com, 392
Amenity potential, 731
American Economic
Association (AEA), 216
American Express
Company, 11
American International
Group, Inc., 11, 482
America Online, Inc. (AOL),
demand and supply
troubles, 84
Anheuser-Busch Cos., 452
Annuities, interest factors
tables for, 792–796
Antitrust laws, 14. See also
Monopoly
AOL-Time Warner, vertical
integration of, 620
Apple, 12, 380
Arc elasticity, 135
Archer Daniels Midland, 745
Association health plans
(AHPs), 770
AT&T, monopoly
breakup of, 465
Auctions, 561–562
Auction strategy, 561–563
Australia, 214, 416
Authority
centralized versus
decentralized, 721–722
defined, 720
Automobile industry
competition in, 503
“give-backs,” 143
import supply battle, 88
September 11, 2001, effect
on, 213–214
Average cost, 32
minimization, 33–34
Average product, 250–251
Average relations,
marginal and total
relations and, 33
B
Bank of America, 216, 729
Barings Bank, 717–718
Barometric price
leadership, 519
Barrett, Craig R., 507
Barrier to entry, 382, 399
Barrier to exit, 382
Barrier to mobility, 382
Barron’s, 216–217, 592
Baumol, William, 519
Becker, Gary S., 755
Behavioral equations
(forecasting), 223–224
Bell System, 465
Benefit/cost (B/C) ratio
analysis, 762–763
Benefit/cost concepts. See
Government, in the
market economy
Benefit/cost ratio analysis, 680
Berkshire Hathaway, Inc., 3, 5,
19, 434, 671, 693, 722
Berle, Adolf, 717, 743
Bertrand, Joseph Louis
François, 519
Bertrand oligopoly, 519–523
differentiated products,
520–523
identical products, 519–520
Beta, 639–640, 665–666
Beta coefficient, 689–690
Bilateral monopoly, 476–477
Board of directors
attributes of (table), 726
problems with, 743–744
role of, in corporate
governance, 724–726
10 best and 10 worst
(table), 745
Boeing Company, 11
Brand-name advertising,
148, 504
Brazil, 416
Breakeven point, 35
Breakeven quantity, 315, 319
Budget constraints. See
Consumer demand
Budgeting. See Capital
budgeting
Budget line (isoquant curve),
261–262
Buffett, Warren E., 3, 5, 19,
434, 693, 722, 742
Bundle pricing, 599–600
Bureau of Labor Statistics
(BLS), productivity
measurements of, 270
Business, role of, in society,
14–16. See also Social
responsibility
Business cycle. See
Forecasting
Business ethics, 735
Business profit
economic profit versus,
9–10
variability of, 10–11
Business profit rates, market
structure and, 432–434.
See also Competitive
markets
Business risk, 632
Business Week, 216
Buyer power, 475–476
Byers, Walter, 460
By-product, 601, 610
C
Cabela’s, 130
Campbell Soup, 745
Canada, 416, 433
Capacity, 301
Capellas, Michael, 744
Capital budgeting, 671.
See also Cash flow
estimation
Berkshire Hathaway, Inc.,
example, 693
classification types, 672
cost of capital, 695
component cost of debt
financing, 687–688
component cost of equity
financing, 688–690
defined, 671
weighted-average,
691–693
823
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
824
decision rules
benefit/cost ratio
method, 680
internal rate of return
(IRR), 680–681
net present-value (NPV)
analysis, 677–679
payback period analysis,
681–682
profitability
index (PI), 680
defined, 671
government support for
R&D example, 688
market-based, 674
Ministry of Finance (MOF;
Japan) example, 683
net present-value (NPV)
analysis at Level 3
Communications, Inc.
(case study), 677–679
optimal, 693
investment opportunity
schedule, 693–695
marginal cost of capital,
695
postaudit, 695
project selection
decision making and, 687
decision rule conflict
problem, 682–683
ranking reversal
problem, 684–687
steps in
cash flow estimation, 673
incremental cash flow
evaluation, 673
project valuation,
sequence of, 672–673
Capital deepening, 270, 271
Capitalism
democracy and, 9
greed versus self-interest, 25
Cardinal utility, 114
Cartels, 512–513, 535
Cash flow estimation, 673.
See also Capital budgeting
analysis and, 675–677
incremental, 673
project description, 674–675
Caterpillar Inc., 11
Celler-Kefauver Act, 481
Census measures. See Market
concentration, census
measures of
Centralized decision
authority, 721
Cereal Partners
Worldwide, 733
Index
Certainty equivalent, 645–646
Certainty equivalent
adjustment factor, 647–648
Chance events (decision
tree), 650
Change in the quantity
demanded, 83
Change in the quantity
supplied, 90
Charles Schwab, 392
Chief executive officers
(CEOs)
compensation, 269
problems with, 743–746
typical, 719
Child labor provisions of the
Fair Labor Standards Act
(FLSA), 258
China, 9, 416
Christie, William G., 384
Cisco Systems, Inc., 733, 745
Citigroup Inc., 11, 384
Clayton Act of 1914
(antitrust), 480–481
Clean Air Act, 768
Clean Water Act, 768
Coase, Ronald, 715
Coase Theorem, 716, 752
Coca-Cola
distribution and economy
of scale, 148
executive compensation
package, 718
infinitely repeated games
and, 557
intangible investments, 10
as a perfect business (case
study), 19–22
return on stockholders’
equity (ROE) of, 10
as a wonderful business, 434
Coefficient of
determination, 179
Coincident economic
indicators, 212–213
Collusion, 512–513
Command-and-control
regulation, 751
Commodity Exchange Act
(1974), 398
Commodity Futures
Modernization Act
(2000), 398
Commodity Futures Trading
Commission (CFTC), 398
Common costs, 602
Common resources, 753
Company information, on the
Internet, 725
Comparative advantage, 563
Comparative statics analysis
defined, 95
demand and supply change
and, 98
demand change and, 95–97
spreadsheet analysis
example (case study),
107–109
supply change and, 97–98
Compensation policy. See
Production analysis and
compensation policy
Compensatory profit theories,
12–13
Competence, of board of
directors, 726
Competition. See also Perfect
competition
in capital markets, 8
of Dell Computer Corp.,
with itself, 504
nature of, 503
Competitive advantage,
563–564
Competitive environment.
See Competitive markets
Competitive firm long-run
supply curve, 392
Competitive firm short-run
supply curve, 389–391
Competitive market pricing
rule-of-thumb, 585
Competitive markets,
585–587, 396
business profit rates,
432–434
corporate examples
(table), 436
mean reversion in,
435, 437
return on stockholders’
equity (ROE),
432–433, 451–453
typical, 433
characteristics of, 383–385
e-business and, 392
economic profits and,
measurement of, 428
efficiency of
deadweight loss
problem, 415–416,
422–424
perfect competition and,
413–415
Enron example, 398
environment of
entry and exit conditions,
382–383
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
market structure, 379
potential entrants’ role,
380
product differentiation,
380–381
production methods, 382
equilibrium and
normal profit
equilibrium, 397–398
supply and demand,
balance of, 252,
396–397
examples of, 383–384
free trade and, 381
government and, 419–421
innovation and (ethanol
example), 421
long-run firm
performance, 438
marginal cost and firm
supply
long-run firm supply
curve, 391–392
short-run firm supply
curve, 389–391
market failure and
incentive problems, 419
structural problems,
418–419
price controls
price ceilings, 431–432
price floors, 429–431
profitability effects of firm
size (case study),
409–411
profit margins among the
most profitable S&P
500 companies (case
study), 451–454
profit maximization in
imperative, 385
marginal analysis role,
385–389
short-run firm
performance, 437–438
social considerations,
420–421
stock market and, 384
subsidy policy, 422
supply curve
market supply with a
fixed number of
competitors, 393
market supply with entry
and exit, 393–395
taxes, deadweight loss
from, 422–424
tax incidence and
burden, 424–429
Licensed to: iChapters User
Index
825
Wal-Mart Stores, Inc., 418
“wonderful businesses,”
434
Competitive strategy
competitive advantage/
comparative
advantage, 563–564
concepts, 563
defined, 438
in monopoly markets,
482–485
network switching costs
example, 568
nonprice competition
advantages, 568–569
advertising, optimal
level of, 569–572
defined, 568
pricing strategies and
limit pricing, 565–567
market penetration
pricing, 567–568
size as a disadvantage, 565
tobacco issue, 750
in value maximization
process, 15
Complements, 120–121, 146
Component cost of debt
financing, 687–688
Component cost of equity
financing, 688–690
Composite index, 212–213
Computer simulations, 651–654
Concentration ratios, 527–529
Conference Board
Coincident Index of
Business Cycle
Indicators, 213
Leading Economic
Indicators, 212–213
Conflict. See Agency problems
Constant returns to scale, 266
Constrained cost
minimization, 287
Constrained optimization,
70–76
defined, 71
Lagrangian multipliers
and, 72–76
Constrained production
maximization, 285–287
Constraints, theory of the
firm and, 7–8. See also
Constrained optimization
Consumer behavior, 78,
117. See also Consumer
demand
Consumer choice. See
Consumer demand
Consumer demand, 147
brand name advertising
and, 148
budget constraints
changing income/
changing prices and,
123–124
characteristics of, 120–123
defined, 120
income/substitution
effects, 124
consumer choice
marginal utility and,
130–131
revealed preference
and, 131
consumer surplus
bundle pricing and,
599–600
defined, 414
two-part pricing and,
597–600, 610
demand curves and,
graphing, 165–166
indifference curves
defined, 118
perfect substitutes/
perfect, 120
complements, 120–121
properties of, 118–119
individual demand
Engle curves, 127–130
income-consumption
curve, 127
price-consumption curve,
124–127
odd-numbered pricing
and, 118
optimal consumption
marginal rate of
substitution, 131–133
utility maximization, 133
relationship marketing, 130
utility theory and
consumer preferences
and, 119
law of diminishing
marginal utility,
116–118
marginal utility, 115–116
utility functions, 114–115
Consumer Expenditure
Survey Extracts, 215
Consumer interviews, in
demand estimation,
161–162
Consumer preferences,
assumptions about,
113–114
Consumer sovereignty, 420
Consumer surplus, perfect
competition and,
414–415. See also
Consumer demand
Consumption path, 133
Contestable markets theory,
519–520
Continuous production
function, 246
Cooperative games, 550
Corner point, 346
Corporate governance
agreements and alliances
among firms
franchising, 732–733
strategic alliances,
733–734
board of directors’ role,
724–726
(case study), 743–746
defined, 724
inside the firm, 726–727
institutional investors as
activists, 732
legal and ethical
environment, 734–735
ownership structure
dimensions of,
727–731, 732
endogenous possibility,
731–732
problems in, 743–746
Sarbanes–Oxley Act,
734–735, 737
Corporate stakeholders, 725
Corporations
as legal device, 7
profitability, 451
in competitive markets
(table), 436
in niche markets (table), 484
restructuring and, 451
top performing, 269
Corrected coefficient of
determination, 179
Correlation analysis
(forecasting), 225
Correlation coefficient, 179
Corruption, political, 755
Cost analysis, 24
Cost analysis and
estimation, 289
cost-volume-profit analysis
breakeven quantity and,
315, 319
charts, 314–315
degree of operating
leverage, 315–318
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
difficulty of
accounting and economic
valuations, 289–291
historical versus current
costs, 289–290
replacement cost, 290
economic and accounting
costs, 289
historical versus
current costs,
289–290
opportunity costs,
290–291
economies of scope
concept of, 313
defined, 313
exploiting, 313–314
Financial Accounting
Standards Board
(FASB) and, 301
firm size and plant size
flexibility and,
308–309
multiplant diseconomies
of scale, 303–304
multiplant economics of,
303–308
multiplant economies of
scale, 303–304
fixed costs, 293
Generally Accepted
Accounting Principles
(GAAP) and, 296
GE’s “20–70–10”
plan, 292
health care services
example (case study),
326–327
incremental cost, 291–292
learning curves
concept of, 309–310
defined, 309
example, 310–312
strategic implications of,
312–313
long run, 293
long-run cost curves
cost elasticities, 299
defined, 297
economies of scale and,
297–299
long-run-average costs,
299–301
minimum efficient
scale (MES)
competitive implications
of, 302
transportation costs and,
302–303
Licensed to: iChapters User
826
opportunity costs, 290–291
defined, 290
explicit and implicit,
290–291
role of time in, 291
incremental versus sunk
cost, 291–292
operating period,
292–293
short run, 292–293
short-run cost curves
categories, 293–294
defined, 293
relations, 294–296
sunk costs, 292
variable costs, 293
Cost containment, 771
Cost-effectiveness analysis,
764–765
Cost elasticity, 299
Cost function, 30, 292
Cost of capital, 687. See
Capital budgeting
Cost of uncertainty, 631–632
Cost reduction projects, 672
Cost relations, 30
average cost minimization
example, 33–34
marginal and average cost,
32–33
output, 31
relations between total,
marginal, average cost
and output, 32
total cost, 30–32
Costs. See also Opportunity
costs
current, 289–290
explicit, 290–291
fixed, 293
historical, 289–290
implicit, 290–291
incremental, 290–292
long-run average, 299–301
optimal markup on, 589
replacement, 290
sunk, 291–292
transaction, 715
transportation, and
minimum efficient
scale (MES), 302–303
variable, 293
Cost-volume-profit analysis.
See Cost analysis and
estimation
Council of Institutional
Investors, 732
Countercyclical, 147
Cournot equilibrium, 513–515
Index
Cournot, Augustin, 513
Cournot oligopoly, 513–516
Credit risk, 633
Crossover discount rate,
686–687
Cross-price elasticity of
demand. See Demand
analysis
Cross section of data, 172
Cultural risk, 633
Currency risk, 633
Current cost, 289–290.
See also Historical versus
current costs
Current Population Survey, 215
Customer lock-in effect, 567
Customer loyalty, 511
Cyclical fluctuation, 203
Cyclical normal goods, 147
D
DaimlerChrysler, 88
Deadweight loss
illustration, 416–417
from monopoly, 464–467
problem, 415–416
of taxation, 422–424
Decentralized decision
authority, 721–722
Decision authority, 720
Decision control, 723
Decision costs, 715
Decision making, managerial
economics and, 3–5.
See also Consumer
demand; Economic
optimization
Decision management, 722–724
Decision point (decision tree),
650–651
Decision rights, assigning,
722–723
Decision rule conflict
problem, 682–684
Decision trees, 650–651
Decreasing returns to
scale, 266
Degree of operating leverage
(DOL), 315–318
Degrees of freedom, 179
DeKalb Corporation, 469
Delaney Clause of the Food,
Drug, and Cosmetics
Act, 768
Dell Computer Corp.
as potential entrant, 380
price war with itself, 504
as virtual corporation, 713
Delphi method (forecasting),
202
Demand. See also Consumer
demand; Demand
analysis; Demand
estimation; Forecasting;
Market demand function;
Market equilibrium;
Supply
comparative statics and,
95–98
defined, 77
demand estimation
and, 161
derived, 78–79
determinants of, 79–80
direct, 77–78
economists and, 88
elastic, 137–139
individual. See Consumer
demand
industry versus firm, 81
inelastic, 137–139
Internet’s effect on, 79
ISP customers and, 84
spreadsheet analysis
example (case study),
107–109
unitary, 140
Demand analysis. See also
Consumer demand;
Demand estimation
cross-price elasticity of
demand
example, 145
substitutes and
complements, 146
demand for oranges
experiment, 177
elasticity (demand
sensitivity analysis)
arc elasticity, 135
concept of, 134
defined, 134
point elasticity, 134–135
income elasticity of
demand
defined, 146
inferior goods, 147–148
normal goods, 147–148
market demand
evaluating, 166–168
market demand curve,
graphing of, 165–166
multivariate optimization
(case study), 158–159
price elasticity of demand
defined, 135
determinants of, 146
formula for, 136
marginal revenue and,
139–143
optimal pricing policy
and, 143–145
price changes and,
140–142
total revenue and,
137–139, 141
varying elasticity at
different points on a
demand curve, 139
price haggling, 143
Demand curve. See also
Demand estimation
defined, 81
demand function relation
to, 79–80
determination of, 81–82
elasticity and, 139–140
graphing, 165
kinked, 442–443
Demand estimation, 161
brand-name consumer
products (case study),
195–197
consumer interview
method, 161
demand curve and, 162–168
government statistics
and, 177
identification problem
defined, 168
demand and supply and,
168–169
demand relations
and, changing nature
of, 168
simultaneous
relations, 171
variable significance, 181
one-tail t tests, 184
t statistic, 181
two-tail t tests, 181–184
market experiments
technique, 162
regression analysis
defined, 171
least squares method,
175–176
specifying, 173–175
statistical relations,
171–173
regression model
significance,
measures of
coefficient of
determination,
179–180
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Index
827
corrected coefficient of
determination, 179
correlation coefficient,
176–178
degrees of freedom, 179
F statistic, 180–181, 182
goodness of fit, 179–180
standard error of the
estimate, 177–179
sampling technology
(TV advertising), 163
spreadsheet and statistical
software, 182
Demand function. See
Demand; Demand curve
Demand interrelations, 600
Demand sensitivity analysis.
See Demand analysis,
elasticity (demand
sensitivity analysis)
Democracy, capitalism and, 9
Dempsey, Cedric W., 460
Department of Health and
Human Services, 766
Dependent variables, 26
Derivative risk, 633
Derivatives
concept of, 61–62
defined, 61
partial, concept, 68–69
Derived demand, 78–79
Design patents, 469
Deterministic relation, 171
Dillards Department
Stores, 745
Diminishing marginal utility
for money, 643–644
Direct demand, 77
Dire predictions, 209
Discounting, 6n
Discrete production function,
246–247
Discrimination, in pricing, 590
Diseconomies of scale
multiplant, 303–304
size as a disadvantage, 565
size, effect of, 295–296
Disequilibrium losses, 437–438
Disequilibrium profits, 437–438
Disequilibrium profit
theories, 12
Disney (Walt) Company,
11, 238–241, 745
Dominant strategy, 552–553
Dow Jones Industrial
Average, 10, 410–411
Drucker, Peter, 25
Dumping, 607–609
Duopoly, 513
DuPont (E.I.) de Nemours, 11
Dutch auction, 562
E
Early Indicators of Later
Work Levels, Disease and
Death, 215
Earnings before interest,
taxes, depreciation,
and amortization
(EBITDA), 428
East Asia, 416
Eastern Europe, 9
E-business, creation of, 392
Econometric forecasting.
See Forecasting
Economic analysis. See
Economic optimization
Economic census, 445–447
Economic concepts, 4
Economic efficiency, 260, 420
Economic expansion, 213
Economic expectations, 724
Economic indicators, 212–213
Economic losses, 385
Economic luck, 438
Economic markets, 435
Economic optimization
Berlin Wall example, 42
cost relations, 30
average cost
minimization
example, 33–34
marginal and average
cost, 32–33
total cost, 30–32
total, average, and marginal
relations, 28–29
greed versus self-interest, 25
incremental concept
example, 40–41
incremental profits, 38
marginal versus, 38
Lagrangian technique/
function/ multipliers,
72–76
marginal analysis in
decision making
maximums and
minimums,
distinguishing
between, 33
multivariate optimization,
68–72
process of, 23
maximizing the value of
the firm, 24
optimal decisions, 23
profit relations, 34
profit maximization
example, 35–38
total and marginal profit,
34–35
revenue relations, 25
marginal revenue, 28–29
price and total revenue,
25–28
revenue maximization
example, 29–30
spreadsheet analysis
example (case study), 53
Economic order quantity
(EOC), spreadsheet
analysis example (case
study), 53
Economic profit
defined, 10, 383
measuring, 362
Economic realizations, 724
Economic recessions,
213–215, 216
Economic regulation,
defined, 420
Economic relations. See
Economic optimization
Economic rents, 438
Economic risk, 632
Economies of scale, 297
of Coca-Cola, 120
cost elasticities and, 299
defined, 297
monopoly and, 468
multiplant, 303–304
organization structure and,
713–714
size as a disadvantage, 565
size, effect of, 303
Economies of scope. See
also Cost analysis and
estimation
concept of, 313–314
defined, 313
exploiting, 313
organization structure and,
713–714
PepsiCo, Inc. and,
313–314
Economy
profit role in, 12
Eddie Bauer, 558
Efficiency. See Competitive
markets
Efficiency gains, 270
Elastic demand, 137, 139
Elasticity, output, returns
to scale and, 266–267.
See also Demand analysis
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Electric power generation,
competition in, 767
El Paso Corp., 745
Employee productivity, in
S&P 500 firms (case
study), 281
Employee stock options, 645
Employment
optimal, 258–259
profit maximization and,
264–265
End-of-game problem
defined, 560
executive compensation
package, 718
Endogenous variables,
134, 223
Enforcement costs, 715–716
Engle curves, 127–129
Engle, Ernst, 127
English auction, 561–562
Enron Corp., 398
Entrepreneurs, economy
and, 34
Entry barrier, 322, 382
Environmental Protection
Agency (EPA), 751
Environmental regulation
reform, 768
Equation
defined, 25–26
Equilibrium. See also
Competitive markets;
Market equilibrium
defined, 93
long-run high-price/lowoutput, 508–509
long-run low-price/highoutput, 510
short-run monopoly,
507–508
Equilibrium outcome, 550
Ethics
in business, 5, 735
Europe, 381
European Union, 416
Excel software, 182
Excessive risk-taking
problem, 717
Exclusion concept, 753
Exit barrier, 383
Exogenous variables, 134, 223
Expansion path, 262
Expansion projects, 672
Expansions (business cycle),
210, 211
Expected value, 635
Expected value maximization,
6–7, 15
Licensed to: iChapters User
828
Index
Explicit costs, 290–291
Exponential smoothing. See
Forecasting
Expropriation risk, 633
Externalities. See also
Government, in the
market economy;
Negative externalities;
Positive externalities
defined, 419
network, 567
Extrapolation
techniques, 203
ExxonMobil Company,
10, 499
F
Failure by incentive, 419
Failure by market
structure, 418
Fair Labor Standards Act
(FLSA), 258
Farming. See Agriculture
price supports
Fast-food business, 714
Feasible space, 338, 344.
See also Corner point
Federal Communications
Commission (FCC),
420, 767
Federal Energy Regulatory
Commission, 413
Federal Reserve Economic
Data (FRED), 215
Federal Trade Commission
Act (1914), 480
Federal Trade Commission
(FTC), 480
FedEx, 130
Financial Accounting
Standards Board
(FASB), 301
Finitely repeated games.
See Game theory
Fiorina, Carly, 744
Firm demand, industry
demand versus, 80–81
Firms. See also Corporations;
Theory of the firm; Value
of the firm
large, profitability effects
of, 409–411
nature of, 715–716
optimization and, 30
Firm size. See Cost analysis
and estimation
Firm supply. See Competitive
markets
First-degree price
discrimination, 591–592
First-mover advantage
game theory and,
549–550
Stackelberg oligopoly
and, 516
Fixed costs, 293
Flat organization, 722
Food, Drug, and Cosmetics
Act, 768
Forbes, 217, 592
Ford Motor Company, 88
Forecast group, 225
Forecasting, 199
applications
macroeconomic, 199
microeconomic, 200–197
techniques, 200–201
art and science of, 198
business cycle
defined, 210–211
economic indicators,
212–213
economic recessions,
213–215
stock market and, 216
choosing the best
technique
data requirements, 228
judgment and, 228
time horizon
considerations, 226
dire predictions, 209
econometric
advantages, 220
defined, 220
multiple-equation
systems, 223–225
single-equation models,
222–223
exponential smoothing
concept of, 217
defined, 217
one-parameter
(simple), 217
three-parameter
(Winters), 219
two-parameter (Holt),
218, 220
use of, 219–220
forecast reliability
correlation analysis, 225
defined, 225
predictive capability,
tests of, 225
sample mean forecast
error analysis,
225–226
of global performance, for
Walt Disney Company
(case study), 238–240
information sources,
215–217
qualitative analysis
defined, 202
expert opinion, 202
survey techniques,
202–203
software programs, 223
techniques, comparison of
(table), 227
trend analysis
defined, 203
of economic data, 203
growth, 206–208
linear, 203–205, 206
linear and growth
comparison, 208–209
Forecast reliability, 225
Fortune, 216
Foster Associates, 216
France, 214
Franchise agreements,
732–733
Fraud, via Internet, 654
Free-rider problem, 754–655
Free trade, 381, 765
Frictional profit theory, 12
Friedman, Milton, 593
Fruit of the Loom, 3
F statistic, 180–181, 182, 812
Future value tables,
787–788, 789
G
Game theory, 549. See also
Risk analysis
defined, 549
at the FCC, 563
finitely repeated games
end-of-game problem,
560–561
first-mover advantage, 561
uncertain final period,
559–560
infinitely repeated games
defined, 557
product quality games, 558
Intel and, 551
interdependence and, 550
Nash equilibrium
defined, 556
Nash bargaining, 556–557
Prisoner’s Dilemma
business application,
553–554
described, 552
implications of, 554–555
strategic considerations, 551
Time Warner games with
stockholders (case
study), 582–484
types of games, 549
Wrigley’s gum example, 563
Game-theory strategy, 552
Gates, Bill, 469
Gateway, 380
General Agreement on
Tariffs and Trade
(GATT), 381
General Electric Company
(GE), 11, 717
20–70–10 plan, 292
capital budgeting and, 671
organization design at, 717
Generally Accepted
Accounting Principles
(GAAP), 296
General Mills, Inc., 733
General Motors Company
(GM), 11, 282
board of directors of, 745
market niche search, 88
size as a disadvantage, 565
Germany, 214
“Give-backs” (auto
industry), 143
Glassman-Oliver Economic
Consultants, Inc., 216
Global transfer pricing. See
Pricing practices
Goffe, Bill, 216
Goodness of fit, 179–180
Goods and services
derived demand and, 78
odd-numbered pricing and,
118
optimal market basket of,
130–131
rivalry and exclusion and,
752–753
supply and demand effect
on, 85
utility of, 78
Google, social responsibility
and, 13
Government
competitive markets
influenced by, 419–420
research and development
support by, 688
statistics of, 177
Government, in the market
economy, 747
benefit/cost concepts
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Index
829
benefit/cost
methodology, 680
Pareto improvement, 756
social rate of discount,
759–760
benefit/cost criteria
benefit/cost (B/C) ratio
analysis, 764–765
limitations of, 764
social internal rate
of return (SIRR),
763–764
social net present-value
(SNPV), 760–762
externalities
government solutions,
750
market solutions, 751–752
negative, 747, 748
positive, 748–650
free trade and, 765
Mercedes-Benz AG in
Alabama (case study),
784–785
political corruption, 755
price controls for
pharmaceutical drugs,
769
public goods
free riders and hidden
preferences, 753–755
rivalry and exclusion,
752–753
public management
improvement
cost-effectiveness
analysis, 764
privatization, 765–766
regulatory reform
in electric power
generation, 767
environmental, 768
health and safety,
768–769
health care, 769–772
in telecommunications,
706–707
Government policy risk, 633
Greed, self-interest versus, 25
Grocery retailing, 379
Gross domestic product
(GDP)
1950–present (figure), 210
defined, 199
forecasting, 199
Groupthink, 723
Grove, Andrew S., 507
Growth trend analysis,
206–208
H
Hartford Financial Services
Group Inc., 482
Health and safety regulation
reform, 768
Health care reform, 769–771
Health care services, 326–329
Herfindahl-Hirschmann
Index (HHI), 529
Hewlett-Packard Company,
11, 282, 499
Hidden preferences problem,
754–755
Hierarchical organization
structure, 714
High-price/low-output
equilibrium, 508–509
Historical cost, 289–290
Historical versus current costs,
289–290
Holt, C.C., 218
Home Depot, Inc., 11, 745
bilateral monopoly and,
476–479
Homogeneous production
functions, 267
Honda, 88
Honeywell International, 11
Horizontal mergers,
guidelines for, 534
Horizontal relation, 714
HP-Compaq, 380
Human capital, 718
Hyundai, 72
I
IBM, 13
board of directors of, 719
Clayton Act and, 480
licensing error, 726
as potential entrant, 380
size as a disadvantage, 565
IBM Global Services, 733
Identification problem. See
Demand estimation
Identities (forecasting), 223
Imperfectly competitive
market pricing rule-ofthumb, 586–587
Implicit costs, 290–291
Incentive problems, 419
Incentives, matching with
objectives, 718
Income, changing, budgets
and, 123–124
Income-consumption curve,
127, 128
Income effect, of a price
change, 124
Income elasticity of demand.
See Demand analysis
Income inflation, 720
Income smoothing, 720
Increasing returns to scale, 266
Incremental cash flow
evaluation, 673
Incremental change, 38
Incremental concept
example, 40–41
incremental profit, 37
marginal versus, 38
Incremental cost, 291
versus sunk cost, 291
Independence, of board of
directors, 726
Independent variables, 26
India, 9
Indifference, 114
Indifference curves. See
Consumer demand
Individual demand. See
Consumer demand
Individual variable
significance. See Demand
estimation
Industry demand, firm
demand versus, 80–81
Industry supply, firm supply
versus, 87–89
Inelastic demand, 137, 138
Inferior goods, 127, 147
Infinitely repeated games. See
Game theory
Inflation risk, 632
Inflection point, 251
Information asymmetry
problems, 719–720
Information barriers, to
competitive strategy,
483, 485
Information costs, 715–716
Initial public offering (IPO),
of Wal-Mart Stores,
Inc., 418
Innovation, 468–469
Innovation profit theory, 12–13
Input combination choice. See
Production analysis and
compensation policy
Input combination
relationships. See
Production analysis and
compensation policy
Input factor substitution,
255–256
Input prices, supply and, 86
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Input substitution, 255–256
Inside equity, 728
Insiders, 719–720
Institutional equity, 728
Institutional investors, 732
Insurance industry
health care reform, 769–771
price fixing by, 482
Intangible investments, 10
Integrated decision
analysis, 24
Integrity, of board of
directors, 726
Intel Corp., 11, 726
board of directors of, 719
strategic considerations,
551–552
Interdependence, game
theory and, 550
Interest factor tables, 803–810
Interest-rate risk, 632
Intermediate goods, 384
Internalize the externality, 750
Internal rate of return (IRR),
680–681, 664
International Longshore
and Warehouse Union
(ILWU), 459
Internet
company information
on, 725
demand and supply
affected by, 79
e-business and, 392
fraud via, 654
market experiments on, 172
revolution of, 16
travel industry use of, 585
Interviews, in demand
estimation, 161
Invention, 468–469
Investment decisions, 687
Investment horizon
problems, 619
Investment opportunity
schedule (IOS), 693–694
Invisible hand of the
marketplace, 747
Irregular or random
influences, 203
Isoquant curve (budget line),
262–263
Isoquants, 254
J
Japan, 214, 683
Jensen, Michael, 743
Jobs, 722
Licensed to: iChapters User
830
Index
Johnson & Johnson, 11, 745
Joint products. See Pricing
practices
J.P. MorganChase & Co., 499
Judgment, in forecasting, 228
Just-in-time production, 14
K
Kellogg Company, 453
Kinked demand curve,
523–524
Kroger Co., 605
Kumar, Sanjay, 744
L
Labor productivity growth,
269
Lagging economic indicators,
212–213
Lagrangian function, 72
Lagrangian technique
(multipliers), 72–76
Lands’ End, 130
Latin America, 9
Law of diminishing marginal
utility, 116–118
Law of diminishing returns to
factor, 251–253
Laws, constraints of, 8
Leading economic indicators,
212–213
Learning curves. See Cost
analysis and estimation
Least squares method,
175–176
Leeson, Nick, 718
Legal environment, in value
maximization process, 15
Lerner Index of Monopoly
Power, 590
Leverage, 433
Leveraged buyouts (LBOs),
743
Life cycle. See Product life
cycle
Limit concentration, 421
Limit pricing, 565–567
Linear demand curves,
simple, 162–165
Linear model, 174–175
Linear programming, 331
algebraic solution, 348–352
algebraic specification,
346–348
basic assumptions, 331
inequality constraints,
331–332
linearity assumption,
332–333
dual constraints, 353–354
slack variables, 354
dual, 352
duality concept, 352
shadow prices, 352–353
dual problem, solving,
355–356
solving primal, 356–358
dual specification, 353
dual objective function,
353
feasible space, 338, 344
determining zero-valued
variables, 349
graphing, 342–343
objective function
coinciding with
boundary of, 347
graphic solution, 345
graphic specification, 342
analytic expression, 342
graphing feasible space,
342–343
graphing objective
function, 344–346
input constraints, 343
for managment decision
problems. See Optimal
solution
and Military Airlift
Command (MAC), 332
and more than visual
approach, 340
on PC, 351
pension funding model
(case study), 372–374
production planning for
multiple products, 340
constraint equation, 341
nonnegativity, 341–342
objective function,
340–341
production planning for
single product, 333
least-cost input, 336–337
optimal input, 337–339
production isoquants,
334–336
production processes,
333–334
rules, 375–377
Linear trend analysis,
203–206
Liquidity risk, 633
L.L. Bean, 130
Lollapalooza effects, 20, 22
Long run, 296
Long-run average costs,
299–301
Long-run cost curves. See Cost
analysis and estimation
Long-run, 30, 293
cost functions, 293
Long-run firm performance,
438
Long-run firm supply curve,
391–392
Long-run high-price/
low-output equilibrium,
508–509
Long-run low-price/highoutput equilibrium, 510
Long-run value
maximization, 8
Look ahead and extrapolate
back, 550
Loss leader, 605
Lotteries, risk and, 642
Lotus 1–2–3, 182
Lotus Corporation, 469
Low-price/high-output
equilibrium, 510
Lucent Technologies, 713
M
Macroeconomic
forecasting, 199
Macros, 53
Major League Baseball,
monopoly, monopsony,
and, 457
Managed competition, in
health care, 769–770
Management decision
problems, 4
Managerial economics. See
also Theory of the firm
applications, 4
decision making and, 3, 4–5
defined, 3
ethical conduct and, 5
usefulness of, 3–5
Managerial labor market,
476, 479
Managerial myopia
problem, 719
Manufacturing, economy
influenced by, 265
Manufacturing Industry
Productivity
Database, 216
Marginal analysis. See also
Economic optimization
defined, 385
in monopoly, 462–463
profit maximization and,
385–389
Marginal and average cost,
32–33
Marginal cost, 32. See also
Competitive markets
Marginal cost of capital
(MCC), 695
Marginal external
benefits, 756
Marginal external costs, 756
Marginal private
benefits, 756
Marginal private costs, 756
Marginal product, 248
Marginal profit, 35
Marginal rate of substitution,
131–133
Marginal rate of technical
substitution, 256–257
Marginal relations
defined, 38
total and average relations
and, 32–34
Marginal revenue, 28–29
defined, 28
price elasticity and, 139–142
Marginal revenue product,
258
Marginal revenue product of
labor, 278–279
Marginals, as derivatives of
functions, 33
Marginal social benefits,
756–758
Marginal social costs, 756–758
Marginal utility, 115–116
consumer choice and,
130–131
law of diminishing, 116–118
Market, 379
Market-based capital
budgeting, 674
Market baskets, 115, 124
Market concentration, census
measures of
concentration ratios,
527–529
Herfindahl-Hirschmann
Index (HHI), 529, 531
limitations of, 531–534
Market demand
demand for oranges
experiment, 177
evaluating, 166–168
measuring, 134
Market demand curve
defined, 165
graphing, 165–166
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Index
831
Market demand function
defined, 79
determinants of demand,
79–80
industry demand versus
firm demand, 80–81
Market environment, in value
maximization process, 15
Market equilibrium
comparative statics
defined, 95
demand and supply
change, 98
demand change, 95–97
supply change, 97–98
defined, 93
surplus and shortage, 93–95
Market equilibrium price, 94
Market experiments, in
demand estimation
defined, 162
examples, 162
on the Web, 172
Market failure, 418. See also
Competitive markets
Market imbalance. See Market
equilibrium
Marketing, relationship, 130
Market niches
in the auto industry, 88
competitive strategy,
monopoly markets,
and, 438, 440
Market penetration pricing,
567
Market power, 418
Market risk, 632
Markets. See Competitive
markets
Market segment, 591
Market structure
analysis of (case study),
545–546
defined, 379–380
measurement of, 525
economic census, 525–526
economic markets, 525
profit rates and, 435–437
Market supply. See
Competitive markets
Markup on price, 588
Markup pricing
on cost, 587–588
on price, 588–589
technology, 587
Marsh & McLennan Cos., 482
Mars Incorporated, 148
Mass production, 9
MasterCard/VISA lawsuit, 568
Maximin decision rule, 553
Maximization
of multivariate functions,
69–70
utility, 133
Maximums and minimums
distinguishing between, 33
finding, 38
Mazda, 88
McDonald’s Corporation, 11,
282, 499
Mean reversion in profit
rates, 435, 437
Means, Gardiner, 717, 738
Meijer Inc., 605
Mercedes-Benz AG in
Alabama (case study), 784
Merck & Co., Inc., 11, 499
Mergers, horizontal, 534
Merrill Lynch & Co., 384
Microeconomic forecasting, 200
Microeconomics, purpose
of, 200
Microsoft Corporation, 11
above-normal returns, 12
bundling charges
against, 459
Excel, 182
growth trend analysis,
206–208
social benefits of, 499
Minimum efficient scale
(MES). See Cost analysis
and estimation
Military Airlift Command
(MAC)
linear programming and, 332
Ministry of Finance (MOF;
Japan), 683
MINITAB, 182
Mitsubishi, 88
Mobility barriers, 458
Money, utility of, 643–644
Monopolistic competition
characteristics of, 503–505
defined, 502
oligopoly contrasted with,
501–503
price/output decisions,
460–461
process of
long-run high-price/
low-output
equilibrium, 508–509
long-run low-price/
high-output
equilibrium, 510
short-run monopoly
equilibrium, 507–508
Monopoly, 457
antitrust laws
Celler–Kefauver Act, 481
Clayton Act of 1914,
480–481
competition blocking
ruling (VISA/
MasterCard), 568
defined, 480
enforcement of, 481–482,
502
Federal Trade
Commission Act of
1914, 480
Robinson–Patman Act of
1936, 480
Sherman Act of 1890,
480–481
characteristics of, 458
competitive strategy and
information barriers to,
483, 485
market niches, 482, 483
defined, 457
examples of, 458–459
Lerner Index of Monopoly
Power, 590
Major League Baseball
example, 479
monopsony
bilateral monopoly and,
476–479
buyer power and,
475–476
natural monopoly
defined, 468
economies of scale and,
468
regulation and, 469–470
NCAA cartel and, 460
price fixing (insurance
cartel), 482
as price makers, 457
profit maximization under
marginal analysis
and, 463
price/output decisions,
460–461
q ratio and (case study),
497–498
regulation and
natural monopoly
dilemma, 469–471
utility price and profit
regulation,
471–472
social benefits of
economies of scale,
297–298
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
invention and
innovation, 468–469
social costs of
deadweight loss from
monopoly problem,
464–465
monopoly
underproduction, 464
Ticketmaster and, 470
Monopoly profit theory, 12
Monopoly seller of labor, 476
Monopoly underproduction,
464
Monopsony. See Monopoly
Monopsony buyer of
labor, 476
Monopsony power, 475
Moral hazard, 771
Morgenstern, Oskar, 549
Most-favored-nation (MFN)
status, 381
Mrs. Smyth’s Inc., 195–196
Multiplant diseconomies of
scale, 303–304
Multiplant economies of
scale, 303–304
Multiple-equation systems
(forecasting), 223–225
Multiple inputs. See
Production analysis and
compensation policy
Multiple-product pricing.
See Pricing practices
Multiple regression model,
175
Multiplicative model, 174
Multistage games, 561–562
Multivariate optimization.
See also Constrained
optimization
defined, 68
in demand analysis,
158–159
maximizing functions,
69–70
partial derivative concept
and, 68–69
Munger, Charlie, 5, 19, 722
N
NAFTA (North American Free
Trade Agreement), 765
Nash bargaining, 556–557
Nash equilibrium, 555–557
National Association of
Securities Dealers
Automated Quotations
(Nasdaq), 384
Licensed to: iChapters User
832
Index
National Bureau of Economic
Research (NBER), 213–214
Business Cycle Dating
Committee, 215
National health insurance,
771–772
National Science Foundation
(NSF), 688
Natural monopoly
defined, 470–471
regulation and, 469–471
NCAA cartel, 460
Negative externalities, 419,
747–748
Negative-sum game, 550
Nestlè, 733
Net marginal revenue,
260–261
Net present-value (NPV)
analysis, 677
Net present-value profile, 686
Network externalities, 567
Network switching costs, 568
Neumann, John von, 549
New York Stock Exchange
(NYSE), 384
Niche markets, in the auto
industry, 484–485
Nielsen Media Research, 163
NIMBY (not in my back
yard), 751
Nissan, 88
Nixon Administration, wage/
price controls of, 431
Noncyclical normal goods, 147
Nonexclusion concept, 752
Nonprice competition. See
Competitive strategy
Nonrival consumption, 752
Nonsatiation principle, 113
Normal distribution, 640
Normal goods
defined, 127
inferior goods versus, 147
types of, 127
Normal profit, 385
Normal rate of return, 10
North America, 416
North American Industry
Classification System
(NAICS), 526–527
O
Objective function, 340–341
Odd-numbered pricing, 118
Off-peak periods, 589
Offshore frauds (Internet), 654
Oklahoma City bombing, 214
Oligopoly
cartels and collusion,
512–513
characteristics of, 511
defined, 502
enforcement problems, 513
examples of, 511–512
monopolistic competition
contrasted with,
501–503
output-setting models
Cournot model, 513–515
Stackelberg model, 516
overt and covert
agreements, 512–513
price-setting models
Bertrand model:
differentiated
products, 520–523
Bertrand model: identical
products, 519–520
model comparison, 524
Sweezy model, 523–524
Southwest Airlines and, 525
Oligopoly theory, 524
Oligopsony, 475
One-parameter (simple)
exponential smoothing,
217–218
One-price alternative (price
discrimination), 594–596
One-shot game, 552
One-tail t tests, 184
Operating curves, 293
Operating period, 292–293
Opportunity costs, 10, 290
defined, 290
explicit and implicit costs
and, 290–291
Optimal capital budget, 693
Optimal capital structure, 691
Optimal consumption. See
Consumer demand
Optimal decision, 23
Optimal market basket,
130–131
Optimal markup on cost, 587
Optimal markup on price, 588
Optimal price formula,
143–144
Optimal pricing policy, price
elasticity and, 143–145
Optimal solution, 332
location in feasible space.
See Corner point
Optimization. See Constrained
optimization; Economic
optimization; Global
optimization
Optimize, 8
Oracle Corp., 734
Ordinal utility, 114
Organization design
centralization versus
decentralization,
721–722
company information on
the Internet, 725
conflict within firms,
resolving, 720–721
decision management and
control, 722–724
decision rights
assignments, 722–723
defined, 720
General Electric example, 671
in value maximization
process, 17
Organization of Petroleum
Exporting Countries
(OPEC), 431
externalities and, 751
monopoly use of, 459
Organization structure. See
also Organization design
agency problems, 716–717
Coase Theorem, 716
defined, 713–714
information asymmetry
problems, 719–720
investment horizon
problems, 719
risk management problems,
717–719
transaction costs and nature
of firms, 715–716
“Other people’s money”
problem, 717, 718, 744
Output elasticity, returns to
scale and, 267
Output per hour
measurements, 260
Output prices, supply
and, 85
Output-reaction curve, 513
Output-setting models. See
Oligopoly
Ownership control potential,
731
Ownership structure. See
Corporate governance
P
Page, Larry, 13
Panel consensus (forecasting),
202
Panzar, John, 519
Pareto optimal, 756
Pareto satisfactory, 756
Pareto, Vilfredo, 756
Partial derivative concept,
68–69
Patents, 468–469
Payback period, 681–682
Pay for performance, 15, 564
Payment-in-kind (PIK)
programs, 422
Payoff matrix, 552, 635
Pay-or-play health care, 771
Peak periods, 589
PepsiCo, Inc., 714
economies of scope and,
313–314
infinitely repeated games
and, 557–559
Perfect competition, 413–415
defined, 383
stock market and, 384
Perfect complements, 120
Perfect substitutes, 120
Perot, Ross, 765
Personal insight
(forecasting), 202
Pfizer Inc., 11, 282
Pharmaceutical drugs
price controls and,
429–432
return on stockholders’
equity (ROE) of, 10
Philip Morris, 148
Pigou, Arthur, 751
Pigovian taxes, 751
Planning curves, 293
Plant patents, 469
Plant size. See Cost analysis
and estimation
Point elasticity, 134
Political corruption, 755
Political events, as influence
on economy, 214–215
Positive externalities, 419,
422, 748–750
Positive-sum game, 550
Postaudit, 695
Potential entrant, 380
Potential Pareto
improvement, 756
Power production
functions, 268
Predatory pricing, 566–567
Predictive capability, 225
Preferences, of consumers,
115, 119
Present value
of the firm, 6
tables, 791, 795
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Index
833
Price
and output, relationship, 27
and total revenue, 25–28
dependent and
independent
variable, 26
marginal revenue and
output, 28
Price ceilings, 431, 432
Price-consumption curve,
124–127
Price controls, 429–432, 769
Price discrimination, 590, 593.
See also Pricing practices
Price elasticity of demand. See
Demand analysis
Price-fixing
insurance cartel, 482
Nasdaq lawsuit, 384
Price floors, 429–431
Price gouging, 431
Price haggling, 143
Price leadership, 517
Price makers, 457
Price/output decisions,
460–461
monopolistic competition
and, 505–507
price discrimination and,
593–594
Price-reaction curve, 520
Prices
changing
budget constraints and,
123–124
income and substitution
effects of, 124
price elasticity and,
140–142
sticky, 523
utility, and profit
regulation, 471–472
Price-setting models. See
Oligopoly
Price signaling, 517
Price supports, 144
Price takers, 383
Price wars, 504, 609
Pricing. See also Optimal
pricing policy, price
elasticity and
bundle, 599–600
flexible, 587
limit, 566–567
market penetration, 567
nonprice competition,
568–572
odd-numbered, 118
optimal, 144–145
predatory, 566–567
two-part, 597, 599
Pricing practices, 585
competitive market pricing
rule-of thumb, 585–586
Denver, Colorado,
newspaper market and
(case study), 617–618
imperfectly competitive
market pricing rule-ofthumb, 586–587
joint products
with excess by-product
(dumping), 607–609
in fixed proportions,
602–604
in variable proportions,
602
without excess byproduct, 604–605
markup pricing
optimal markup on cost,
587–588
optimal markup on price,
588–589
technology, 587
multiple-product pricing
demand interrelations,
600–601
product interrelations, 601
price discrimination, 590
of colleges, 593
degrees of, 591–592
graphic illustration,
596–597
one-price alternative,
594–595
price/output
determination,
593–594
profit-making criteria,
590–591
price wars, 568, 609
transfer pricing
defined, 609
products with
competitive external
markets, 621–622
products with imperfectly
competitive external
markets, 622
products without
external markets,
620–621
transfer pricing, global
competitive external
market with excess
internal demand,
621–622
competitive external
market with excess
internal supply,
625–626
with no external market,
623–624
profit maximization for
an integrated firm,
622–623
Pricing strategies. See
Competitive strategy
Prisoner’s Dilemma. See
Game theory
Private good, 752
Privatization, 765–766
Probability concepts. See Risk
analysis
Probability, defined, 634
Probability distribution,
634–635
Procter & Gamble Co.,
452, 499
Producer price index, 177
Producer surplus, 414
Product differentiation
Bertrand oligopoly model
and, 520–523
defined, 380–381
effect of, 505
forms of, 504
Product homogeneity, 383
Production analysis and
compensation policy, 245
average product, 248–251
Bureau of Labor Statistics
(BLS) measurements,
270
compensation for CEOs,
269
diminishing returns to
factor concept, 251–252
employee productivity
among the largest S&P
500 firms (case study),
451–454
input combination choice
input factor substitution,
255–256
marginal rate of technical
substitution, 256–257
production isoquants,
254
relational limits of input
substitution, 257
labor productivity growth
example, 297
manufacturing’s impact on
the economy, 265
marginal product, 248
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
marginal revenue product,
258–259
multiple inputs, optimal
combination of
budget lines, 261–262
expansion path, 262–263
optimal input
proportions, 261
multiple inputs, optimal
levels of, 261
illustration of, 263–264
optimal employment and
profit maximization,
264–265
optimal employment,
258–261
optimal input combinations
relations, developing
constrained cost
minimization, 287
constrained production
maximization,
285–287
optimal level of single
input, 259–260
production function
estimation
cubic production
functions, 268
power production
functions, 268
production functions
defined, 245
properties of, 245–246
returns to scale and
returns to factor,
246–246
productivity and worker
compensation, 270
productivity
measurement, 268
causes of productivity
growth, 270–271
economic productivity,
269–270
returns to scale, 266
estimation and, 267–268
evaluating, 304
output elasticity and,
266–267
total product, 248
Production function
estimation. See
Production analysis and
compensation policy
Production functions. See
Production analysis and
compensation policy
Production interrelations, 601
Licensed to: iChapters User
834
Production isoquants, 254
Production planning for
multiple products, 340
constraint equation
specification, 341
nonnegativity requirement,
341–342
objective function
specification, 340–341
Production planning for
single product, 333
least-cost input
combinations, 336–337
determining, 337
optimal input combinations
with limited resources,
337–339
feasible space, 338
production isoquants,
334–336
production processes,
333–334
rays in linear
programming, 334
Productive inefficiency, 464
Productivity growth, 269
Productivity measurement.
See Production analysis
and compensation policy
Product life cycle, exponential
smoothing and, 219
Product quality games, 558
Profit
business versus economic, 9
compensatory theories, 9–10
disequilibrium theories, 12
economic, 10
economy and, 13–14
variability of, 10–11
Profitability effects. See
Competitive markets
Profitability index (PI), 680
Profit concept, 10
Profit contribution, 291
Profit margin, 10
defined, 433
on gasoline, 436
markup on cost and, 587
of S&P 500 companies (case
study), 451–452
Profit maximization, 35–38.
See also Competitive
markets
defined, 35
in global transfer pricing,
622
markup pricing and,
587–590
under monopoly, 460–464
Index
optimal employment and,
258–261
rule, 35
Profit-maximizing output, 34
Profit regulation, utility price
and, 471–472
Profit relations, 34
profit maximization
example, 35–38
quantity, revenue, cost,
and, 36
relations between total and
marginal profits and
output, 37
total and marginal profit,
34–35
Profit theories, 12
Projects. See Capital
budgeting
Public goods. See
Government, in the
market economy
Publicly traded corporations,
monopolies and, 459
Public utilities, as
monopolies, 592
Pump and dump Internet
scam, 654
Pyramid Internet scam, 654
Q
q ratio, 497–498
Qualitative analysis. See
Forecasting
Quality uncertainty and
market mechanism, 559
Quality control potential, 731
Quantitative methods, 3
R
Randomized strategies, 556
Random or irregular
influences, 203
Ranking reversal problem,
684–687
Ratios
benefit/cost, 680
q, 497–498
Recessions, 213–214, 216
Regression analysis. See
Demand estimation
Regression model
significance. See Demand
estimation
Regulations. See also
Government, in the
market economy
cost and efficiency
implications, 420
monopoly and, 469–475
social purpose of, 421
Regulatory lag, 475
Regulatory potential, 731
Regulatory reform. See
Government, in the
market economy
Relations. See Economic
optimization
Relationship marketing, 130
Relative distance method, 336
Relative risk, 639
Remote Interactive
Optimization Testbed
(RIOT), 358
Rent control, 431
Repeated game, 552
Replacement costs, 290
Replacement projects, 672
Reputation capital, 735
Research and development
government support of, 688
Tobin’s q ratio and, 497–498
Reserve Fund, 469
Resource Conservation and
Recovery Act, 768
Resources for Economists
(RFE), 216
Restaurant business, 384
Return on stockholders’
equity (ROE)
attractiveness of, 434
business profit rates and,
433–434
defined, 10, 432
of firms in the United
States and Canada, 433
profit measurement and, 9–11
for 30 profitable companies
(table), 453
Returns to factor, 247
Returns to scale, 266. See also
Production analysis and
compensation policy
defined, 246
estimation of, 267–267
evaluating, 267–268
output elasticity and,
266–267
Revealed preferences, 131
Revenue and price relations,
26
Revenue maximization, 29
Revenue relations, 25
marginal revenue, 28–29
price and total revenue,
25–28
revenue maximization
example, 29–30
Reversion to the mean, 435
Ridge lines, 257
Risk-adjusted discount rates,
648–649
Risk-adjusted valuation
model, 646
Risk analysis, 631
categories of, 568
computer simulations,
651–654
decision trees, 650–651
economic risk, 631–633
employee stock options
and, 645
game theory and
auction strategy and,
561–563
at the FCC, 562
global operations and, 633
Internet fraud, 654
lotteries, 642
probability concepts
absolute risk
measurement,
637–639
beta, 639–640
expected value, 635–637
probability distribution,
634–635
relative risk
measurement, 639
standard normal concept
example, 641–642
normal distribution, 640
standardized variables,
641
stock-price beta estimation
(case study), 665–668
uncertainty, 631–633
utility theory and, 642
money/utility
relationship, 643–644
risk attitudes, 643
valuation model
adjustment and
basic model, 644–645
certainty equivalent
adjustments, 645–646
risk-adjusted discount
rates, 648–649
Risk aversion, 643
Risk-free Internet fraud, 654
Risk-free rate of return, 648
Risk management problems,
717–719
Risk neutrality, 643
Risk premium, 648
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Licensed to: iChapters User
Index
Risk seeking, 643
Rival consumption, 752
Robinson-Patman Act of
1936, 481
Rubbermaid, 481
Russia, 416
S
Safety and environmental
projects, 672
Salomon Smith Barney, 384
Sample mean forecast error,
225–226
Sara Lee Corp., 453
Sarbanes-Oxley Act, 727
defined, 734
Satisfice, 8
Saturn, 130
SBC Communications Inc.,
499
Scatter diagram, 173
Schultz, Paul, 384
Sealed-bid auction, 562
Sears, 476
Seasonality, 203, 217
Second-degree price
discrimination, 592
Secular trend, 203, 204
Secure strategy, 553
Self-interest
ethics and, 5
greed versus, 25
invisible hand of the
marketplace and, 747
September 11, 2001, 213
airlines affected by, 168
auto industry affected by,
289
economic toll of, 213–214
Sequential auctions, 562
Sequential game, 550
Services. See Goods and
services
Sherman Act of 1890
(antitrust), 480, 481
Shift in demand, 83–84
Shift in supply, 91
Shortage
defined, 93–95
Short-run, 30, 293
cost functions, 292
Short-run cost curves. See
Cost analysis and
estimation
Short-run cost functions,
292–293
Short-run firm performance,
437–438
835
Short-run firm supply curve,
389–391
Short-run growth
maximization, 8
Short-run monopoly
equilibrium, 507–508
Simple linear demand curves,
162–164
Simple regression model, 175
Simplex solution method, 349
Simulations. See Computer
simulations
Simultaneous-move game,
550
Simultaneous relation, 171
Single-equation models
(forecasting), 222–223
Slack variables, 346
Slope
of budget constraints, 123
of indifference curves, 118
Smith, Adam, 549, 717, 744
Snack Food Ventures Europe,
733
Social benefits of monopoly,
468–469
Social costs, 14, 419
Social equity, 420
Social internal rate of return
(SIRR), 763–764
Social net present-value
(SNPV), 760–762
Social rate of discount,
759–760
Social responsibility
of business, 15–16
Google and, 13
Social welfare, 414–415, 748
Soft drink industry, 714
Software
for regression analysis,
171–173
spreadsheet and statistical,
182
“Solver” PC software, 331
South Korea, 214
Southwest Airlines Co., 525
Soviet Union (former), 9
Spillover effects, 718
Spitzer, Eliot, 482
Spreadsheets
defined, 25, 53
in demand and supply
analysis, 107–109
in economic analysis, 53
software for, 182
Sprint Corporation, 673
SPSS for Windows, 182
Stackelberg, Heinrich von, 516
Stackelberg oligopoly,
516–519
Standard error of the estimate
(SEE), 177–179
Standard Industrial
Classification (SIC), 216
Standardization factors, 212
Standardized variable, 641–642
Standard normal concept. See
Risk analysis
Statistical Abstract of the United
States, 221
Statistical relations, 171–174
Statistical tables, 811–815
Statistics, software for, 182
Stealth virtual
corporations, 713
Sticky prices, 523
Stock market
business cycle and, 210
employee stock options
and, 645
perfect competition and,
383
Strategic alliances, 733–734
Subaru, 88
Subsidy policy, 422
Substitute goods, price
elasticity and, 146
Substitutes
defined, 120
product differentiation and,
380–381
types of, 120
Substitution effect, of a price
change, 124–127
Substitution
input, 255–256
marginal rate of, 131–133
Sunk costs, 291–292
Supply. See also Market
equilibrium
auto industry import
battle, 88
comparative statics and, 95
defined, 85
demand estimation and,
168–169
Internet’s effect on, 79
ISP customers and, 84
other determinants of, 86
output prices’ effect on, 85
spreadsheet analysis
example (case study),
107–108
technology as determinant
of, 79
Supply and demand, balance
of, 396–397, 413–414
Copyright 2009 Cengage Learning. All Rights Reserved.
May not be copied, scanned, or duplicated, in whole or in part.
Supply curve. See also
Competitive markets
defined, 89
determination of, 89
supply function relation to,
86–87
Supply function. See also
Supply curve
defined, 86
determinants of, 86–87
industry supply versus
firm supply, 87–88
Surface Transportation
Board, 481
Surplus
defined, 93–95
Survey techniques
(forecasting), 202–203
Sweezy oligopoly, 523–524
Sweezy, Paul, 523–524
T
Tables, 25–26
Tangent, 61
Target stores, 476, 534
Tasks, 722–723
Tax burden, 424–425
Tax cost-sharing, 426–428
Tax credits, 422
Taxes
cost and efficiency
implications, 420
deadweight loss from,
422–424
per unit, 424
social purpose of, 421
Tax incidence
defined, 424
elasticity and, 424–425
Team, 723
Technical efficiency, 254
Technology. See also Internet
markup pricing and, 587
supply and, 79
in value maximization
process, 15
Telecommunications,
competition in, 767–768
Terrorism. See September 11,
2001
Test group, 225
Texas Instruments (TI), 312, 745
Theory of the firm
constraints and, 7
defined, 6
expected value
maximization, 6–8
limitations of, 7–9
836
Third-degree price
discrimination, 592
3M Company, 11
Three-parameter (Winters)
exponential smoothing,
219–220
Ticketmaster, 470
Time-series analysis, 203,
204, 226
Time series of data, 172
Time Warner, Inc., game
theory and, 582–583
Tobacco industry, 750
Tobin, James, 497–499
Tobin’s q ratio, 497–498
Total asset turnover, 433
Totalitarianism, 9
Total and marginal profit,
34–35
Total cost, 30–32
Total product, 248
Total profits, 34
defined, 463n
Total relations, marginal and
average relations and,
32–33
Total revenue, 25–28
defined, 25
price elasticity and,
137–138, 140–142
quantity sold and, 26
Toyota, 81
Tradable emission
permits, 422
Trade liberalization, 381
Trade-offs, 113
Trade unions, as monopolies,
386
Tragedy of the commons, 753
Transaction costs, 715–616,
727
Transferable health insurance
certificate, 770
Transfer pricing. See Pricing
practices
Transitive preferences, 114
Transparency, of board of
directors, 726
Index
Transportation costs,
minimum efficient scale
(MES) and, 302–303
Trend analysis. See
Forecasting
Trigger strategy, 559
TRW Inc., 734
t statistic, 181–184
Two-parameter (Holt)
exponential smoothing,
218–219, 220
Two-part pricing, , 597–600
Two-tail t tests, 181–182
U
Uncertainty
defined, 632
economic risk and, 631–632
Underproduction, in
monopoly, 464
Unitary elasticity, 137
United Kingdom, 214
United States
aluminum exporter and
importer, 416
privatization in, 765–766
ROE rates in, 410
United Technologies
Corporation, 11
U.S. Department of
Agriculture (USDA),
price floors and, 429–431
U.S. Justice Department,
Federal Trade
Commission and, 459
U.S. Postal Service
as a monopoly, 459
privatization and, 765–766
U.S. Supreme Court,
competition blocking
ruling (VISA/
MasterCard), 568
Utility. See also Marginal
utility
defined, 78, 113
money and, 643–644
Utility functions, 114–115, 131
Utility maximization, 133
Utility patents, 469
Utility price, profit regulation
and, 471–474
Utility theory. See Risk
analysis
Utils, 113
V
Valuation model. See Risk
analysis
Value-added, of Wal-Mart
Stores, Inc., 352
Value maximization. See
also Expected value
maximization
complex process of (figure),
564
economic profits and,
measurement of, 385
value of the firm and,
24–25
Value of the firm, 6
maximizing, 24–25
Variable costs, 293
Variables
dependent, 26
endogenous/exogenous,
134, 223
independent, 26
Verizon Communications, 11
Vertical integration, 620,
726–727
Vertical organization, 722
Vertical relation, 620, 713
Vickrey auction, 562
Virtual corporation, 713
VISA/MasterCard
lawsuit, 568
Volkswagen, 88
W
Wage/price controls, 429
Wal-Mart Stores, Inc., 11
infinitely repeated games
and, 557–558
monopsony power of,
475–476
operating performance, 418
return on stockholders’
equity (ROE) of,
432–433
vertical relation
example, 714
Walt Disney Company
board of directors of, 745
forecasting by, 238–241
Waste Management, 745
Wealth effect, 130
Wealth transfer problem, 467
Weather, as supply
determinant, 86
Weighted-average cost of
capital, 691–693
Weighted-average payoff, 635
Weights, 218
Welfare economics, 413–415
Welfare loss triangle, 416
Wells Fargo Economic
Reports, 216
“What if?” scenarios, 53
Willig, Robert, 519
Winner’s curse, 562
Winters, P.R., 219
Wonderful businesses, 434
World Trade Organization
(WTO), 381
World Wide Web. See
Internet
Wrigley’s gum, brand-name
advertising and, 563
Wrigley, William, Jr., 562
X
Xerox, 148
Y
Yahoo! Finance, 567
Z
Zero-sum games, 550
Copyright 2009 Cengage Learning. All Rights Reserved.
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