Licensed to: iChapters User Licensed to: iChapters User 12e Managerial Economics Mark Hirschey University of Kansas Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States 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 Managerial Economics, 12th Edition © 2009, 2006 South-Western, a part of Cengage Learning Mark Hirschey ALL RIGHTS RESERVED. 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Library of Congress Control Number: 2007941977 Student Edition ISBN 13: 978-0-324-58886-6 ISBN 10: 0-324-58886-0 Student Edition with PAC ISBN 13: 978-0-324-58484-4 ISBN 10: 0-324-58484-9 South-Western Cengage Learning 5191 Natorp Boulevard Mason, OH 45040 USA Cengage Learning products are represented in Canada by Nelson Education, Ltd. For your course and learning solutions, visit academic.cengage.com Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Printed in the United States of America 1 2 3 4 5 6 7 12 11 10 09 08 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 Dedication For Christine—I still do. 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 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 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 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 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 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 Copyright 2009 Cengage Learning. 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Licensed to: iChapters User 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 Copyright 2009 Cengage Learning. 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May not be copied, scanned, or duplicated, in whole or in part. 124 Licensed to: iChapters User Contents 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 Copyright 2009 Cengage Learning. 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Licensed to: iChapters User 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 Copyright 2009 Cengage Learning. 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May not be copied, scanned, or duplicated, in whole or in part. 268 Licensed to: iChapters User Contents 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 Copyright 2009 Cengage Learning. 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Licensed to: iChapters User 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 Copyright 2009 Cengage Learning. 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May not be copied, scanned, or duplicated, in whole or in part. 434 Licensed to: iChapters User Contents 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 Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 513 Licensed to: iChapters User 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 Licensed to: iChapters User 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 Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 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 Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 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 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 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 Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 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. Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 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 Copyright 2009 Cengage Learning. All Rights Reserved. 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. Copyright 2009 Cengage Learning. All Rights Reserved. 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 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 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 Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 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 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 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? Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 790 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 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 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 Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 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. 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 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). Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 794 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. 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 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 Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 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. 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 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. Copyright 2009 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Licensed to: iChapters User 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. May not be copied, scanned, or duplicated, in whole or in part.

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