About the Authors vii

Preface ix

Part 1 Basic Concepts and Tools in Economic Analysis

1 Accounting Income and Cash Flow 3

1.1 What Is Investment? 3

1.2 The Corporate Investment Framework 4

1.2.1 The Objective of the Firm 4

1.2.2 The Functions of the Firm 4

1.2.3 The Analysis Framework 6

1.2.4 Accounting Information 6

1.3 The Balance Sheet 7

1.3.1 Reporting Format 7

1.3.2 Cash versus Other Assets 10

1.3.3 Liabilities versus Stockholders’ Equity 10

1.3.4 Inventory Valuation 11

1.3.5 Depreciation 12

1.3.6 Working Capital 12

1.4 The Income Statement 13

1.4.1 Methods of Reporting Income 13

1.4.2 Reporting Format 13

1.4.3 Measurement of Revenue 15

1.4.4 Measurement of Expenses 16

1.4.5 Retained Earnings, Cash Dividends, and Earnings per Share 16

1.4.6 Return on Common Equity (ROE) 17

1.5 The Funds Flow Statement 18

1.5.1 The Cash Flow Cycle 19

1.5.2 Basic Relationship 20

1.5.3 Funds Statement on a Cash Basis 21

1.5.4 Funds Statement as Working Capital 23

1.6 Net Income Versus Cash Flows 24

1.6.1 Deferred Income Taxes 24

1.6.2 Computing Deferred Income Taxes 24

1.6.3 Estimating Cash Flows from Income Statement 26

1.6.4 Use of Cash Flows in Evaluating Investments 26

1.7 Investment Project and Its Cash Flows 27

1.7.1 The Project Cash Flow Statement 28

1.7.2 Cash Flows over the Project Life 29

Summary 31

Problems 32

2 Interest Rates and Valuing Cash Flows 36

2.1 Cash Flow Diagram 36

2.2 Time Preference and Interest 36

2.2.1 Time Preference 37

2.2.2 Types of Interest 37

2.2.3 Nominal and Effective Interest Rates 39

2.3 Discrete Compounding 42

2.3.1 Comparable Payment and Compounding Periods 42

2.3.2 Noncomparable Payment and Compounding Periods 53

2.4 Continuous Compounding 55

2.4.1 Discrete Payments 56

2.4.2 Continuous Cash Flows 58

2.5 Equivalence of Cash Flows 60

2.5.1 Concepts of Equivalence 61

2.5.2 Equivalence Calculations with Several Interest Factors 62

2.6 Effect of Inflation on Cash Flow Equivalence 65

2.6.1 Measure of Inflation 65

2.6.2 Explicit and Implicit Treatments of Inflation in Discounting 66

2.6.3 Case Study—Home Ownership Analysis during Inflation 71

Summary 74

Problems 75

3 Advanced Cash Flow Modeling Techniques 80

3.1 Z-Transforms and Discrete Cash Flows 80

3.1.1 The Z-Transform and Present Value 80

3.1.2 Properties of the Z-Transform 82

3.2 Development of Discrete Present Value Models 87

3.2.1 Extensive Present Value Models 87

3.2.2 Simplified Present Value Model 90

3.2.3 Applications of Z-Transforms 90

3.3 Laplace Transforms and Continuous Cash Flows 96

3.3.1 Laplace Transform and Present Value 96

3.3.2 Properties of Laplace Transforms 97

3.4 Development of Continuous Present Value Models 102

3.4.1 Extensive Present Value Models 102

3.4.2 Present Values of Impulse Cash Flows 105

3.4.3 Extension to Future and Annual Equivalent Models 106

3.5 Application of the Laplace Transform 107

Summary 109

Problems 110

4 Developing Project Cash Flows 113

4.1 Corporate Tax Rates 113

4.1.1 Tax Structure for Corporations 113

4.1.2 Depreciation and Its Relation to Income Taxes 113

4.1.3 Use of Effective and Marginal Income Tax Rates in Project Evaluations 115

4.2 Depreciation Methods 116

4.2.1 Depreciation Regulations and Notation 116

4.2.2 Book Depreciation Methods 117

4.2.3 Tax Depreciation Method 121

4.2.4 Multiple-Asset Depreciation 126

4.3 Capital Gains and Adjustments to Income Taxes 126

4.4 After-Tax Cash Flow Analysis 128

4.4.1 Income Statement Approach 128

4.4.2 Generalized Cash Flows 129

4.4.3 Effects of Depreciation Methods 131

4.4.4 Effects of Financing Costs 134

4.4.5 Effects of Inflation 137

4.4.6 Cash Flow Analysis for Tax-Exempt Corporations 139

Summary 140

Problems 140

5 Selecting a Discount Rate for Project Evaluation 144

5.1 Investment and Borrowing Opportunities 144

5.1.1 Future Investment Opportunities 144

5.1.2 Financing Sources 146

5.1.3 Capital Rationing 147

5.2 Costs of Capital from Individual Sources 147

5.2.1 Debt Capital 147

5.2.2 Equity Capital 154

5.3 Use of a Weighted-Average Cost of Capital 157

5.3.1 Net Equity Flows 158

5.3.2 After-Tax Composite Flows 160

5.4 Specifying the Weighted-Average Cost of Capital 161

5.4.1 Basic Valuation Forms 161

5.4.2 Valuation with Debt and Taxes 163

5.4.3 The Firm’s Capitalization Rate 163

5.4.4 Obtaining a Cutoff Rate 166

5.4.5 Other Issues 167

5.4.6 Effect of Inflation 168

Summary 168

Problems 169

Part 2 Deterministic Analysis

6 Measures of Investment Worth—Single Project 175

6.1 Initial Assumptions 175

6.2 The Net Present Value Criterion 176

6.2.1 Mathematical Definition 176

6.2.2 Economic Interpretation Through Project Balance 180

6.3 Internal Rate-of-Return Criterion 182

6.3.1 Computational Methods 182

6.3.2 Classification of Investment Projects 185

6.3.3 IRR and Pure Investments 188

6.3.4 IRR and Mixed Investments 190

6.3.5 Modified Internal Rate of Return 194

6.4 Benefit–Cost Ratios 197

6.4.1 Benefit–Cost Ratios Defined 198

6.4.2 Equivalence of B/C Ratios and PV 199

6.5 Payback Period 200

6.5.1 Payback Period Defined 200

6.5.2 Popularity of the Payback Period 201

6.6 Time-Dependent Measure of Investment Worth 202

6.6.1 Areas of Negative and Positive Balances 202

6.6.2 Investment Flexibility 203

Summary 205

Problems 207

7 Decision Rules for Selecting among Multiple Alternatives 213

7.1 Formulating Mutually Exclusive Alternatives 213

7.2 Project Ranking Based on Total Investment Approach 216

7.2.1 Total Investment Approach 216

7.2.2 Consistency Within Groups 217

7.2.3 Modification of Criteria to Include Unspent Budget Amounts 219

7.3 Incremental Analysis 220

7.3.1 Irrelevance of Ordering for PV, FV, AE, and PBN 220

7.3.2 Agreement on Increments Between PV and Other Relative Measures 221

7.3.3 Alternative Derivations 221

7.3.4 Decision Rules for IRR 222

7.3.5 A Comprehensive Example for Incremental Analysis 224

7.4 Reinvestment Issues 228

7.4.1 Net Present Value 228

7.4.2 Internal Rate of Return 230

7.4.3 Benefit–Cost Ratio 231

7.5 Comparison of Projects with Unequal Lives 232

7.5.1 Common Service Period Approach 232

7.5.2 Estimating Salvage Value of Longer-Lived Projects 235

7.5.3 Reinvestment Issues When Revenues Are Known 239

7.5.4 Summary Treatment of Unequal Lives 239

7.6 Decisions on the Timing of Investments 239

Summary 240

Problems 242

8 Deterministic Capital Budgeting Models 247

8.1 The Use of Linear Programming Models 247

8.1.1 Description of a Basic Capital Budgeting Problem 248

8.1.2 Criterion Function to Be Optimized 248

8.1.3 Multiple Budget Periods 249

8.1.4 Project Limits and Interdependencies 249

8.1.5 LP Formulation of Lorie–Savage Problem 250

8.1.6 Duality Analysis 250

8.2 Pure Capital Rationing Models 253

8.2.1 Criticisms of the PV Model 254

8.2.2 Consistent Discount Factors 255

8.3 Net Present Value Maximization with Lending and Borrowing 258

8.3.1 Inclusion of Lending Opportunities 258

8.3.2 Inclusion of Borrowing Opportunities 259

8.4 Weingartner’s Horizon Model 259

8.4.1 Equal Lending and Borrowing Rates 259

8.4.2 Lending Rates Less than Borrowing Rates 265

8.4.3 Inclusion of Borrowing Limits Supply Schedule of Funds 267

8.4.4 Dual Analysis with Project Interdependencies 271

8.5 Bernhard’s General Model 272

8.5.1 Model Formulation 272

8.5.2 Major Results 273

8.6 Discrete Capital Budgeting 276

8.6.1 Number of Fractional Projects in LP Solution 276

8.6.2 Branch-and-Bound Solution Procedure 277

8.6.3 Duality Analysis for Integer Solutions 279

8.7 Capital Budgeting with Multiple Objectives 281

8.7.1 Goal Programming 281

8.7.2 Interactive Multiple-Criteria Optimization 283

Summary 284

Problems 285

Part 3 Stochastic Analysis

9 Utility Theory 295

9.1 The Concept of Risk 295

9.1.1 Role of Utility Theory 297

9.1.2 Alternative Approaches to Decision Making 298

9.2 Preference and Ordering Rules 298

9.2.1 Bernoulli Hypothesis 298

9.3 Properties of Utility Functions 301

9.3.1 Risk Attitudes 301

9.3.2 Relationship between Certainty Equivalent and Risk Premium 304

9.3.3 Types of Utility Functions 304

9.4 Empirical Determination of Utility Functions 307

9.4.1 General Procedure 307

9.4.2 Sample Results 309

9.5 Mean–Variance Analysis 310

9.5.1 Indifference Curves 310

9.5.2 Coefficient of Risk Aversion 312

9.5.3 Justification of the Mean and Variance Criterion 312

9.5.4 Justification of Certainty Equivalent Method 314

Summary 317

Problems 318

10 Probabilistic Cash Flow Analysis—Single Project 322

10.1 Measures of Project Risk 322

10.1.1 Downside Risk 322

10.1.2 How Businesspeople Perceive Risk in Project Evaluation 323

10.2 Estimating Values in Probabilistic Terms 324

10.2.1 Statistical Moments of a Single Random Variable 325

10.2.2 Statistical Moments of Linear Combinations of Random Variables 328

10.2.3 Products of Random Variables 332

10.2.4 Quotients of Random Variables 334

10.2.5 Powers of Independent Random Variables 335

10.2.6 General Approximation Formulas 338

10.3 Statistical Moments of Discounted Cash Flows 339

10.3.1 Expected Net Present Value 339

10.3.2 Variance of Net Present Value 340

10.3.3 Mixed Net Cash Flows 343

10.3.4 Net Cash Flows Consisting of Several Components 344

10.3.5 Cash Flows with Uncertain Timing: Continuous Case 345

10.3.6 Cash Flows with Uncertain Timing: Discrete Case 352

10.4 Probability Distributions of Net Present Value 355

10.4.1 Discrete Cash Flows Described by a Probability Tree 355

10.4.2 Use of the First Two Statistical Moments 357

10.4.3 Use of the First Four Statistical Moments 358

10.5 Estimating Risky Cash Flows 359

10.5.1 Beta-Function Estimators for Single Cash Flows 359

10.5.2 Hiller’s Method for Correlated Cash Flows 365

10.6 Measure of Operational Risk 367

10.6.1 Value at Risk—Downside Risk Measurements 367

10.6.2 How to Calculate the Value at Risk? 367

10.6.3 Conditional Value at Risk (CVaR) 371

Summary 373

Problems 375

11 Comparing Risky Projects and Portfolio Optimization Theory 386

11.1 Comparative Measures of Investment Worth 386

11.1.1 Mean–Variance, E–V 386

11.1.2 Mean–Semivariance, E–S_h 388

11.1.3 Safety First 391

11.2 Stochastic Dominance 392

11.2.1 First-Degree Stochastic Dominance 392

11.2.2 Second-Degree Stochastic Dominance 395

11.2.3 Third-Degree Stochastic Dominance 399

11.2.4 Relationship Between Dominance and Mean–Variance Criterion 402

11.3 Portfolio Theory 403

11.3.1 Efficiency Frontier 404

11.3.2 Diversification of Risk 406

11.3.3 Full Covariance Model 407

11.3.4 Index Model 408

11.3.5 Capital Market Theory 409

11.4 Discrete Capital-Rationing Models Under Risk 412

11.4.1 Hillier’s Method for Correlated Projects 413

11.4.2 Stochastic Programming 414

11.5 Multiperiod Index Model for Project Portfolio 415

11.5.1 Model Structure and Assumptions 415

11.5.2 Procedure 417

11.6 Uncertainty Resolution 419

Summary 421

Problems 423

12 Risk Simulation 430

12.1 An Overview of the Logic of Simulation 430

12.1.1 Monte Carlo Sampling 431

12.1.2 Using the Simulation Output 431

12.2 Selecting Input Probability Distributions 432

12.2.1 Selecting a Distribution Based on Observed Data 432

12.2.2 Selecting a Distribution in the Absence of Data 439

12.3 Sampling Procedures for Independent Random Variables 441

12.3.1 Inverse Transformation Techniques 441

12.3.2 Other Frequently Used Random Deviates 444

12.4 Sampling Procedures for Dependent Random Variables 446

12.4.1 Assessment of Conditional Probabilities 446

12.4.2 Sampling a Pair of Dependent Random Samples 447

12.4.3 Sampling Based on Regression Equation 450

12.4.4 Conditional Sampling in the Absence of Data 455

12.4.5 Normal Transformation Method 457

12.5 Output Data Analysis 460

12.5.1 Replication and Precision of Results 460

12.5.2 Comparison of Two Projects 462

12.6 A Simple Risk Simulation Example 465

12.6.1 Decision Problem 465

12.6.2 Replication Results 468

Summary 469

Problems 470

13 Decision Analysis and Value of Information 474

13.1 Sequential Decision Process 474

13.1.1 Structuring the Decision Tree 474

13.1.2 Expected Value as a Decision Criterion 478

13.2 Obtaining Additional Information 478

13.2.1 The Value of Perfect Information 479

13.2.2 Determining Revised Probabilities 481

13.2.3 Expected Monetary Value after Receiving Sample Information 486

13.2.4 Value of the Market Survey 486

13.3 Decision Tree and Risk 487

13.3.1 Sensitivity Analysis 487

13.3.2 Decision Based on Certainty Equivalents 488

13.4 Investment Decisions with Replication Opportunities 490

13.4.1 The Opportunity to Replicate 490

13.4.2 Experiment Leading to Perfect Information 490

13.4.3 A Case Example—Flexible Cellular Manufacturing Operation 491

13.4.4 Sampling Leading to Imperfect Information 494

13.5 Bayesian Inference and Value of Sampling 495

13.5.1 Bayesian Inference 495

13.5.2 Bayesian Update with a Discrete Prior Distribution 497

13.5.3 Bayesian Update with a Continuous Prior Probability Distribution 500

13.6 Conjugate Prior Distributions 503

13.6.1 Types of Sampling 503

13.6.2 Conjugate Distribution for Bernoulli Process 505

13.6.3 Conjugate Distribution for Poisson Process 507

13.6.4 Conjugate Distribution for Normal Process 509

13.6.5 Lognormal Process 512

13.7 Terminal Analysis: Opportunity Loss and Value of Perfect Information 513

13.7.1 Opportunity Loss Function 513

13.7.2 The Expected Value of Sample Information 515

13.7.3 Optimal Sample Size 517

Summary 518

Problems 519

14 Basic Options Theory 527

14.1 Financial Options Concepts 527

14.1.1 Call Options 528

14.1.2 Put Options 529

14.2 Stochastic Process of Asset Dynamics 530

14.2.1 Underlying Asset Price Movement—Geometric Brownian Motion 531

14.2.2 Simulated Stock Prices Based on Brownian Motion 534

14.2.3 Discrete-Time Price Movement 535

14.2.4 How to Determine the Binomial Parameters 537

14.3 Upper and Lower Bounds for Option Prices 539

14.3.1 Upper and Lower Bounds 539

14.3.2 Put–Call Parity 540

14.4 Binomial Option Pricing Model 541

14.4.1 Option Pricing for a Single-Period Model 541

14.4.2 Risk-Neutral Probabilities 543

14.4.3 Properties of Option Attributes 544

14.4.4 Effects of Dividends 545

14.5 Option Pricing for the Multi-Period Binomial Model 546

14.6 Pricing an American Option 548

14.6.1 Early Exercise for an American Call Option 550

14.7 Black–Scholes Model 550

14.7.1 Call and Put Options Formulas 551

14.7.2 Components of the Black–Scholes Model 552

14.7.3 Formal Derivation of the Black–Scholes Formula 553

14.7.4 Relationship Between the Binomial Lattice Model and the Black–Scholes Model 555

14.8 Dividends and Black–Sholes Model 556

14.8.1 Known Dividend Yield 556

14.8.2 Known Dollar Dividend 556

14.9 Pricing Exotic Options 557

14.9.1 Exchange Options—Margrabe Model 557

14.9.2 The Geske Model—Compound Option 558

14.10 Estimating Volatility for Traded Financial Assets 560

Summary 563

Problems 564

15 Real Options Analysis 567

15.1 A New Way of Thinking of Investment Strategy under Uncertainty 567

15.1.1 Identify the Level of Uncertainty 567

15.1.2 Analytic Tools and Strategies to Resolve Uncertainty 568

15.2 What Is the Investment Flexibility? 572

15.3 Real Options Valuation with Financial Option Framework 575

15.3.1 Basic Modeling Concept 575

15.3.2 SNPV Calculation with Black–Scholes Formula 576

15.4 Real Call Options Models 577

15.4.1 Option to Wait—Delay Options 577

15.4.2 Option to Expand—Growth Options 579

15.4.3 Research and Development 580

15.4.4 Scale-Up Options by Binomial Lattice 582

15.4.5 Exchange Option—Delay Options with Stochastic Investment Cost 584

15.5 Real Put Options Models 586

15.5.1 Option to Abandon 586

15.5.2 Option to Switch 589

15.5.3 Option to Scale Down 590

15.6 Option to Choose 591

15.7 Compound Real Options 594

15.7.1 Geske Model 594

15.7.2 Compound Options with Changing Volatility 598

15.7.3 A Four-Phased Compound Option with Varying Volatility—A Case Example 599

15.8 Estimating the Implied Project Volatility 605

15.9 An Alternative Real Options Valuation Based on the Loss Function Approach 606

15.9.1 The Concept of Opportunity Loss Function 607

15.9.2 Valuing Real Call Option with the Standardized Loss Function Approach 607

15.9.3 Valuing Real Put Option with the Standardized Loss Function Approach 612

15.9.4 Determining the Correct Amount of Premium to Pay for Real Options 614

Summary 618

Problems 619

15A Bayesian Real Options Analysis 625

15A.1 Real Options Premium and Value of Information 625

15A.1.1 Real Options Valuation Based on Linear Payoff Analysis 625

15A.1.2 Expected Value of Perfect Information and Its Relation to Option Premium 626

15A.2 Option Valuation with Opportunity to Replicate 628

15A.2.1 Option Value with Imperfect Information 629

15A.2.2 Revised Option Values 631

15A.3 Bayesian Compound Option—Delay Real Options with Learning 632

15A.3.1 A Conceptual Modeling Framework 632

15A.3.2 Effects of Learning 634

15A.3.3 Decision to Invest in Phase 1 with Upstream Learning 634

15A.3.4 Development of a Learning Real Options Framework 635

15A.3.5 Incorporating Bayesian Learning 636

15A.3.6 Posterior Properties 638

15A.4 A Case Study—Learning Options in Aerospace Industry 638

15A.4.1 Background 638

15A.4.2 Applying the Decision Model 639

15A.4.3 Option Value Based on Posterior Information 640

15A.4.4 Economic Interpretation 641

Summary 642

Part 4 Special Topics in Engineering Economic Analysis

16 Evaluation of Public Investments 647

16.1 The Nature of Public Activities 647

16.2 The Procedure of Benefit–Cost Analysis 648

16.2.1 Valuation of Benefits and Costs 649

16.2.2 Decision Criteria 651

16.3 The Benefit–Cost Concept Applied to a Mass Transit System 654

16.3.1 The Problem Statement 655

16.3.2 Users’ Benefits and Disbenefits 656

16.3.3 Sponsor’s Costs 662

16.3.4 Benefit–Cost Ratio for Project 665

16.4 Cost–Benefit/Cost-Effectiveness Analyses 666

16.4.1 Cost–Benefit Analysis 666

16.4.2 Cost-Effectiveness Analysis 667

16.5 Risk and Uncertainty in Benefit–Cost Analysis 667

16.5.1 Exact Distribution of Benefit–Cost Ratio 668

16.5.2 Exact Distribution of Incremental Benefit–Cost Ratio 669

16.5.3 Computer Simulation Approach 673

Summary 676

Problems 677

17 Economic Analysis in Public Utilities 681

17.1 Utility Firms and Fair Returns 681

17.2 Capital Costs for Public Utilities 682

17.2.1 Debt and Equity Financing for Public Utilities 682

17.2.2 Weighted After-Tax Cost of Capital 682

17.2.3 Capital Recovery Cost Based on Book Depreciation Schedule 683

17.3 The Revenue Requirement Method 685

17.3.1 Assumptions of the Revenue Requirement Method 685

17.3.2 Determination of Annual Revenue Requirements 686

17.3.3 Effect of Inflation in Revenue Requirements 689

17.4 Equivalence of the Present Value and Revenue Requirement Methods 692

17.4.1 The A/T Equity Cash Flows and Revenue Requirement Series 692

17.4.2 Important Results Regarding the Equivalence of the PV and RR Methods 694

17.5 Flow-Through and Normalization Accounting 696

17.5.1 Flow-Through Method 696

17.5.2 Normalizing Method 698

Summary 704

Problems 704

18 Procedures for Replacement Analysis 708

18.1 Quantifying Obsolescence and Deterioration 708

18.2 Forecasting Future Data 713

18.3 Basic Concepts in Replacement Analysis 715

18.3.1 Sunk Costs 715

18.3.2 Outsider Point of View 716

18.4 Economic Life of an Asset 721

18.5 Infinite Planning Period Methods 724

18.5.1 No Technology or Cost Changes, AE Method 724

18.5.2 Geometric Changes in Purchase Costs and O&M Costs, PV Method 727

18.6 Finite Planning Period Methods 730

18.6.1 Sensitivity Analysis of PV with Respect to Inflation 730

18.6.2 Dynamic Programming Method 732

18.7 Building a Data Base 738

18.8 Recent Advances in Fleet Replacement Studies 740

Summary 741

Problems 742

Appendix A Discrete Interest Compounding Tables A-1

Appendix B Statistical Tables A-29

Table B.1 Cumulative Standard Normal Distribution A-29

Table B.2 Percentage Points of the χ² Distribution A-30

Table B.3 Standard Normal Distribution Loss Function A-31

Index I-1

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