List of Symbols(AIF,i,N) (AIF,r,T) (AIG,i,N)

sinking fund factor continuous sinking fund factor arithmetic gradient to annuity conversion factor capital recovery factor continuous capital recovery factor uniform series compound amount factor continuous uniform series compound amount factor compound amount factor geometric gradient to present worth conversion factor series present worth factor

A'

base annuity for arithmetic gradient to annuity conversion factor analytic hierarchy process annual worth present worth of benefits benefit-cost ratio modified benefit-cost ratio book value at end of period n using declining-balance method book value at end of period n using straight-line method present worth of costs capital cost ~llowance consistency index depreciation rate for . declining-balance method depreciation amount for period n using decliningbalance method depreciation amount for period n using straight-line method a column vector [lll ... lll]T equivalent annual cost external rate of return expected value of the random variable, X

AHP

AW B BCR BCRMBVdb(n)

(AIP,i,N) (AIP,r,T) (FIA,i,N) (FIA,r,T)

B~ln)

(FIP,i,N) (PIA,g,i,N)

cCCACI

(PIA,i,N) (PIA,r,T) (PIF,i,N)

d

continuous uniform series present worth factor

Ddb(n)present worth factor a PCM (pairwise comparision matrix) continuous cash flow over a period annuity amount, equivalent annual cost actual dollars in yearN total annuity for arithmetic gradient to annuity conversion factor

AA A AN A tot

Ds1(n)

e

EAC ERR E(X)

F

future value, future worth inflation rate per year future worth growth rate for geometric gradient actual interest rate

MARRRMAUT MCDMNp

real dollar MARR multi-attribute utility theory . multi-criterion decision making number of periods, useful life of an asset present value, present worth, purchase price, principal amount pairwise comparison matrix present worth probability distribution alternative expression of probability distribution nominal interest rate, rating for a decision matrix real dollar equivale~t to AN relative to year 0, the base year random index salvage value tax benefit factor tax rate undepreciated capital cost random variable an eigenvector the maximun eigenvalue an eigenvalue Laspeyres price index

fFWg

iI

interest amount real interest rate compound interest amount effective interest rate interest rate per subperiod simple interest amount growth adjusted interest rate internal rate of return actual dollar IRR real dollar IRR internal rate of return external rate of return approximate external rate of return the value of a global price index at yearN, relative to year 0 number of subperiods in a period minimum.acceptable rate of return actual dollar MARR

i'I,

PCM PWp(x)

ie isIs

Pr{X =xi}r

;oIRR IRRA IRRR i*

Ro,N

R1

'* tetea

sTBFt

'*

Io,N

uccXw

m

MARR MARRA

A max'A1tot

Gl I BAI ENGINEERING ECONOMICSFOURTH EDITION

Financial Decision Making for Engineers

Library and Archives Canada Cataloguing in Publication Global engineering economics: financial decision making for engineers I Niall M. Fraser ... [et al.].4th ed. Includes index. Previous editions published under title: Engineering economics in Canada. ISBN 978-0-13-207161-11. Engineering economy.

I. Fraser, Niall M. (Niall Morris), 1952-

TA177.4.F725 2008

658.15

C2008-903776-6

Copyright 2009,2006,2000, 1997 Pearson Education Canada, a division ofPearson Canada Inc., Toronto, Ontario. Pearson Prentice Hall. All rights reserved. This publication is protected by copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission, write to the Permissions Department. ISBN-13: 978-0-13-207161-1 ISBN-10: 0-13-207161-4 Vice-President, Editorial Director: Gary Bennett Acquisitions Editor: Cathleen Sullivan Marketing Manager: Michelle Bish Developmental Editor: Maurice Esses Production Editor: Imee Salumbides Copy Editor: Laurel Sparrow Proofreader: Susan Bindernagel Production Coordinator: Sarah Lukaweski Compositor: Integra Permissions Researcher: Sandy Cooke Art Director: Julia Hall Cover and Interior Designer: Anthony Leung Cover Images: Veer Inc. (architects looking at drafts in office) and Getty Images (electronic currency exchange sign in building) For permission to reproduce copyrighted material, the publisher gratefully acknowledges the copyright holders listed in the Mini-Cases and tables, which are considered an extension of this copyright page.12 34 5

12 11 10 09 08

Printed and bound in the United States of America.

------PEARSON

Prentice Hall

Brief ContentsPreface xiii

CHAPTER 1 Engineering Decision Making CHAPTER 2 Time Value of Money 18 CHAPTER 3 Cash Flow Analysis 44 Appendix 3A Continuous Compounding and Continuous Cash Flows 79 Appendix 38 Derivation of Discrete Compound Interest Factors 83 CHAPTER 4 Comparison Methods Part 1 86 Appendix 4A The MARR and the Cost of Capital 123 CHAPTER 5 Comparison Methods Part 2 126 Appendix 5A Tests for Multiple IRRs 161 CHAPTER 6 Depreciation and Financial Accounting 171 CHAPTER 7 Replacement Decisions 220 CHAPTER 8 Taxes 266 Appendix 8A Deriving the Tax Benefit Factor 304 CHAPTER 9 Inflation 306 Appendix 9A Computing a Price Index 339 CHAPTER 10 Public Sector Decision Making 343 CHAPTER 11 Dealing with Uncertainty: Sensitivity Analysis 386 CHAPTER 12 Dealing with Risk: Probability Analysis 420 CHAPTER 13 Qualitative Considerations and Multiple Criteria 472 Appendix 13A Calculating the Consistency Ratio for AHP 500 APPENDIX A APPENDIX B APPENDIX C APPENDIX DGlossary Index Compound Interest Factors for Discrete Compounding, Discrete Cash Flows 505 Compound Interest Factors for Continuous Compounding, Discrete Cash Flows 529 Compound Interest Factors for Continuous Compounding, Continuous Compounding Periods 547 Answers to Selected Problems 565 570

577

ContentsPreface xiii

CHAPTER 11.1 1.2 1.3 1.4 1.5

Engineering Decision Making2

1

Engineering Economics in Action, Part 1A: Naomi Arrives

Engineering Decision Making 2 What Is Engineering Economics? 3 Making Decisions 45

Engineering Economics in Action, Part 1B: Naomi Settles In

Dealing With Abstractions 6 The Moral Question: Three True Stories

8

NET VALUE 1.1: PROFESSIONAL ENGINEERING ASSOCIATIONS AND ETHICAL DECISIONS 10

1.6 1. 7

Uncertainty, Sensitivity Analysis, and Currencies How This Book Is Organized 12

1113

Engineering Economics in Actions, Part 1C: ATaste of What Is to Come

Problems 14 Mini-Case 1.1: Imperial Oil v. Quebec

16

CHAPTER22.1 2.2

TimeValueofMoney

1819

Engineering Economics in Action, Part 2A: ASteal For Steel

Introduction 19 Interest and Interest Rates20

19

NET VALUE 2.1: INTEREST RATES

2.3 Compound and Simple Interest 22 2.4 Effective and Nominal Interest Rates 2.5 Continuous Compounding 27 2.6 Cash Flow Diagrams 28 2. 7 Equivalence 312. 7.1 2. 7.2 2. 7. 3

24

Mathematical Equivalence 31 Decisional Equivalence 31 Market Equivalence 32

Review Problems Summary 37

3337

Engineering Economics in Action, Part 28: You Just Have to Know When

Problems 38 Mini-Case 2.1: Student Credit Cards

43

viii

C0 NTE NTS

CHAPTER 3

Cash Flow Analysis

4445

Engineering Economics in Action, Part 3A: Apples and Oranges

3.1 Introduction 45 3.2 Timing of Cash Flows and Modelling 46 3.3 Compound Interest Factors for Discrete Compounding 46 3.4 Compound Interest Factors for Single Disbursements or Receipts 3.5 Compound Interest Factors for Annuities 49 3.6 Conversion Factor for Arithmetic Gradient Series 56 3. 7 Conversion Factor for Geometric Gradient Series 59NET VALUE 3.1: ESTIMATING GROWTH RATES 60

47

3.8 Non-Standard Annuities and Gradients 63 3.9 Present Worth Computations When N-FXJ 65 Review Problems 66 Summary 69Engineering Economics in Action, Part 3B: No Free Lunch 70

Problems 70 Mini-Case 3.1: The Gorgon LNG Project in Western Australia 77 Appendix 3A Continuous Compounding and Continuous Cash Flows 79 Appendix 3B Derivation of Discrete Compound Interest Factors 83

CHAPTER 44.1 4.2 4.3 4.4

Comparison Methods Part 187

86

Engineering Economics in Action, Part 4A: What's Best?

Introduction 87 Relations Among Projects 89 Minimum Acceptable Rate of Return (MARR) 91 Present Worth (PW) and Annual Worth (AW) Comparisons4.4.1 4.4.2 4.4.3 4.4.4

9292

Present Worth Comparisons for Independent Projects Present Worth Comparisons for Mutually Exclusive Projects 95 Annual Worth Comparisons 9596

NET VALUE 4.1: CAR PAYMENT CALCULATORS

Comparison of Alternatives Wtth Unequal Lives 4.5 Payback Period 102 Review Problems 105 Summary 109Engineering Economics in Action, Part 4B: Doing It Right 109

98

Problems 110 Mini-Case 4.1: Rockwell International 122 Appendix 4A The MARR and the Cost of Capital

123

CHAPTER 5

Comparison Methods Part 2

126127

Engineering Economics in Action, Part 5A: What's Best? Revisited

5.1 Introduction 127 5.2 The Internal Rate of Return 127 5.3 Internal Rate of Return Comparisons

130

CONTENTS

ix

5.3 .1 5 .3.2 5.3.3

IRR for Independent Projects 130 IRR for Mutually Exclusive Projects Multiple IRRs 137

132139

NET VALUE 5.1: CAPITAL BUDGETING AND FINANCIAL MANAGEMENT RESOURCES

5. 3 .4 External Rate of Return Methods 140 5.3.5 When to Use the ERR 142 5.4 Rate of Return and Present/Annual Worth Methods Compared 143 5.4.1 Equivalence ofRate ofReturn and Present/Annual Worth Methods 5.4.2 Why Choose One Method Over the Other? 147 Review Problems 149 Summary 152Engineering Economics in Action, Part 58: The Invisible Hand 153

143

Problems 154 Mini-Case 5.1: The Galore Creek Project 160 Appendix SA Tests for Multiple IRRs 161

CHAPTERS6.1 6.2

Depreciation and Financial Accounting172

171

Engineering Economics in Action, Part SA: The Pit Bull

6.3

Introduction 172 Depreciation and Depreciation Accounting 173 6.2.1 Reasons for Depreciation 173 6.2.2 Value of an Asset 173 6.2.3 Straight-Line Depreciation 174 6.2.4 Declining-Balance Depreciation 176 Elements of Financial Accounting 17Q 6.3 .1 Measuring the Performance of a Firm 180 6.3.2 The Balance Sheet 180 6.3.3 The Income Statement 185 6. 3 .4 Estimated Values in Financial Statements 187 6.3.5 Financial Ratio Analysis 187 6.3.6 Financial Ratios 188188

NET VALUE 6.1: SECURITIES REGULATORS

Review Problems Summary 199 Problems 200

195

Engineering Economics in Action, Part 68: Usually the Truth

200

Mini-Case 6.1 Business Expense or Capital Expenditure? 213 Extended Case: Part 1 Welcome to the Real World 215

CHAPTER 77.1 7.2 7.3 7.4

Replacement Decisions

220221

Engineering Economics in Action, Part 7A: You Need the Facts

Introduction 221 A Replacement Example 222 Reasons for Replacement or Retirement Capital Costs and Other Costs 226

225

X

CONTENTS

7.5 7.6

Defender and Challenger Are Identical

227227

NET VALUE 7.1: ESTIMATING SALVAGE VALUES AND SCRAP VALUES

Challenger Is Different From Defender; Challenger Repeats Indefinitely7.6.1 7 .6.2 7 .6.3

231 Converting From Subcontracted to In-House Production 233 The Irrelevance of Sunk Costs 234 When Capital or Operating Costs Are Non-Monotonic 23S

7. 7 Challenger Is Different From Defender; Challenger Does Not Repeat 238 Review Problems 240 Summary 244Engineering Economics in Action, Part 78: Decision Time 245

Problems 246 Mini-Case 7.1: Paying for Replacement

264

CHAPTER 88.1 8.2 8.3 8.4 8.5

Taxes

266267

Engineering Economics in Action, Part 8A: It's in the Details

Introduction 267 Personal Income Taxes and Corporate Income Taxes Compared268

268

NET VALUE 8.1: GOVERNMENT TAX WE8SITES

Corporate Tax Rates 269 Before- and After-Tax MARR 270 The Effect of Taxation on Cash Flows8.5.1 8.5 .2 8.5.3

8.6 8. 7

271 The Effect ofTaxes on First Cost 272 The Effect of Taxes on Savings 273 The Effect ofTaxes on Salvage or Scrap Valu~ Present Worth and Annual Worth Tax Calculations 275

274

IRR Tax Calculations8. 7.1 8. 7.2

277277

Accurate IRR Tax Calculations 277 Approximate Mter-Tax Rate-of-Return Calculations 8.8 Specific Tax Rules in Various Countries 279 8.8.1 Australia Tax Calculations 279 8.8.2 UK Tax Calculations 281 8.8.3 US Tax Calculations 284 8.8.4 Canadian Tax Calculations 288 Review Problems 290 Summary 294Engineering Economics in Action, Part 88: The Work Report 294

Problems 295 Mini-Case 8.1: Flat Taxes 303 Appendix 8A Deriving the Tax Benefit Factor

304

CHAPTER 99.1 9.2

Inflation

306307

Engineering Economics in Action, Part 9A: The Inflated Expert

Introduction 307 Measuring the Inflation Rate

308308

NET VALUE 9.1: GOVERNMENT COLLECTION OF STATISTICS

CONTENTS

xi

Economic Evaluation With Inflation 310 9. 3 .1 Converting Between Real and Actual Dollars 31 0 9.4 The Effect of Correctly Anticipated Inflation 313 9.4.1 The Effect ofinflation on the MARR 313 9.4.2 The Effect oflnflation on the IRR 315 9.5 Project Evaluation Methods With Inflation 317 Review Problems 323 Summary 326 Problems 327Engineering Economics in Action, Part 9B: Exploiting Volatility 327

9.3

Mini-Case 9.1: Economic Comparison of High Pressure and Conventional Pipelines: Associated Engineering 338 Appendix 9A Computing a Price Index 339

Chapter 10 Public Sector Decision Making

343344

Engineering Economics in Action, Part 1OA: New Challenges Down Under

10.1 Introduction 344 10.2 Market Failure 346 10.2.1 Market Failure Defined 347 10.2.2 Remedies for Market Failure 348 10.3 Decision Making in the Public Sector 350 10.3.1 The Point ofView Used for Project Evaluation 351NET VALUE 10.1: INTERNATIONAL BENEFIT-COST ANALYSIS GUIDES 352

10.3.2 Identifying and Measuring the Costs of Public Projects 353 10.3. 3 Identifying and Measuring tJle Benefits of Public Projects 3 53 10.3.4 Benefit-Cost Ratios 357 1 0. 3. 5 The MARR in the Public Sector 3 62 Review Problems 364 Summary 369Engineering Economics in Action, Part 1OB: Look at It Broadly 369

Problems 370 Mini-Case 10.1: Emissions Trading

384

CHAPTER 11 Dealing With Uncertainty: Sensitivity AnalysisEngineering Economics in Action, Part 11 A: Filling a Vacuum 387

386

11.1 Introduction 387 11.2 Sensitivity Graphs 388 11.3 Break-Even Analysis 391 11.3 .1 Break-Even Analysis for a Single Project 392 11.3.2 Break-Even Analysis for Multiple Projects 394 11.4 Scenario Analysis 398 Review Problems 400 Summary 403 Problems 404Engineering Economics in Action, Part 11 B: Where the Risks Lie 404

xii

C0 NTE NTS

Mini-Case 11.1: China Steel Australia Limited 414 Extended Case: Part 2 Back to the Real World 417

CHAPTER 12 Dealing With Risk: Probability AnalysisEngineering Economics in Action, Part 12A: Trees From Another Planet 421

420

Introduction 421 Basic Concepts of Probability 422 Random Variables and Probability Distributions 423 Structuring Decisions With Decision Trees 430 Decision Criteria 433 12.5.1 Expected Value 433 12.5.2 Dominance 435 12.6 Monte Carlo Simulation 440 12.6.1 Dealing With Complexity 440 12.6.2 Probability Distribution Estimation 440 12.6.3 The Monte Carlo Simulation Approach 441NET VALUE 12.1: MONTE CARLO SIMULATION ANALYSIS SOFTWARE 442

12.1 12.2 12.3 12.4 12.5

12.7 Application IssuesReview Problems Summary 457448

447

Engineering Economics in Action, Part 128: Chances Are Good

45 7

Problems 458 Mini-Case 12.1: Predicting Water Demand in High-Rise Buildings in Hong Kong

470

CHAPTER 13 Qualitative Considerations and Multiple CriteriaEngineering Economics in Action, Part 13A: Don't Box Them In 473

472

13.1 13.2 13.3 13.4

Introduction 473 Efficiency 475 Decision Matrixes 477 The Analytic Hierarchy Process481

481 486

NET VALUE 13.1: AHP SOFTWARE

13.5 The Consistency Ratio for AHP Review Problems 486 Summary 489

Engineering Economics in Action, Part 138: Moving On

490

Problems 490 Mini-Case 13.1: Northwind Stoneware 498 Appendix 13A Calculating the Consistency Ratio for AHP Appendix A Appendix B Appendix C Appendix D Glossary 570 Index 577

500

Compound Interest Factors for Discrete Compounding, Discrete Cash Flows 505 Compound Interest Factors for Continuous Compounding, Discrete Cash Flows 529 Compound Interest Factors for Continuous Compounding, Continuous Compounding Periods 547 Answers to Selected Problems 565

PrefaceCourses on engineering economics are found in engineering curricula throughout the world. The courses generally deal with deciding among alternative engineering projects with respect to expected costs and benefits. For example, in Canada, the Canadian Engineering Accreditation Board requires that all accredited professional engineering programs provide studies in engineering economics. Many engineers have found that a course in engineering economics can be as useful in their practice as any of their more technical courses. There are several stages to making a good decision. One stage is being able to determine whether a solution to a problem is technically feasible. This is one of the roles of the engineer, who has specialized training to make such technical judgments. Another stage is deciding which of several technically feasible alternatives is best. Deciding among alternatives often does not require the technical competence needed to determine which alternatives are feasible, but it is equally important in making the final choice. Some engineers have found that choosing among alternatives can be more difficult than deciding what alternatives exist. The role of engineers in society is changing. In the past, engineers tended to have a fairly narrow focus, concentrating on the technical aspects of a problem and on strictly computational aspects of engineering; economics. As a result, many engineering economics texts focused on the mathematics of the subject. Today, engineers are more likely to be the decision makers, and they need to be able to take into account strategic and policy issues. Society has changed in other ways in recent years. In particular, the world has become more interlinked. An engineer may be trained in one part of the world and end up practising somewhere completely different. The mathematics of engineering economics, like all of an engineer's technical skills, is the same everywhere. This book is designed for teaching a course on engineering economics to match engineering practice today. It recognizes the role of the engineer as a decision maker who has to make and defend sensible decisions. Such decisions must not only take into account a correct assessment of costs and benefits; they must also reflect an understanding of the environment in which the decisions are made. This book is a direct descendant of a book entitled Engineering Economics in Canada, and in some senses is the fourth edition of that book. But given the increasing globalization of many engineering activities, the title and the contents have been updated. This is appropriate because the contents are applicable to engineers everywhere. For Canaqian users of the previous editions, this text retains all of the valued features that made it your text of choice. For new users, it is a proven text that can support a course taught anywhere in the world. This book also relates to students' everyday lives. In addition to examples and problems with an engineering focus, there are a number that involve decisions that many students might face, such as renting an apartment, getting a job, or buying a car.

xiv

PREFACE

Content and OrganizationBecause the mathematics of finance has not changed dramatically over the past number -of years, there is a natural order to the course material. Nevertheless, a modern view of the role of the engineer flavours this entire book and provides a new, balanced exposure to the subject. Chapter 1 frames the problem of engineering decision making as one involving many issues. Manipulating the cash flows associated with an engineering project is an important process for which useful mathematical tools exist. These tools form the bulk of the remaining chapters. However, throughout the text, students are kept aware of the fact that the eventual decision depends not only on the cash flows, but also on less easily quantifiable considerations of business policy, social responsibility, and ethics. Chapters 2 and 3 present tools for manipulating monetary values over time. Chapters 4 and 5 show how the students can use their knowledge of manipulating cash flows to make comparisons among alternative engineering projects. Chapter 6 provides an understanding of the environment in which the decisions are made by examining depreciation and the role it plays in the financial functioning of a company and in financial accounting. Chapter 7 deals with the analysis of replacement decisions. Chapters 8 and 9 are concerned with taxes and inflation, which affect decisions based on cash flows. Chapter 10 provides an introduction to public-sector decision making. Most engineering projects involve estimating future cash flows as well as other project characteristics. Since estimates can be in error and the future unknown, it is important for engineers to take uncertainty and risk into account as completely as possible. Chapter 11 deals with uncertainty, with a focus on sensitivity analysis. Chapter 12 deals with risk, using some of the tools of probability analysis. Chapter 13 picks up an important thread running throughout the book: a good engineering decision cannot be based only on selecting the least-cost alternative. The increasing influence on decision making of health and safety issues, environmental responsibility, and human relations, among others, maks it necessary for the engineer to understand some of the basic principles of multi-criterion decision making.

New to This EditionIn addition to clarifying explanations, improving readability, updating material, and correcting errors, we have made the following important changes for this new global edition: Throughout the text, the context of the examples and problems has been changed from a Canadian orientation to a global environment. Similarly, the currencies used vary-about 60% of the examples use dollars (Australian, Canadian, or American) and other currencies such as euros or pounds make up the remainder of the examples. Chapter 8 has been completely rewritten to demonstrate the impact of taxes on engineering decisions independent of the tax regime involved. Detailed examples are given for Australia, Canada, the United Kingdom, and the United States. About half of the Mini-Cases, which supplement the chapter material with a realworld example, have been replaced to address issues from around the world. The Net Value boxes, which provide chapter-specific examples of how the internet can be used as a source of information and guidance for decision making, have been updated to highlight the global perspective of the book. In many cases, web addresses specific to countries around the world are provided.

PREFACE

XV

A new More Challenging Problem has been added to each chapter. These are thought-provoking questions that encourage students to stretch their understanding of the subject matter. Additional Problems for Chapters 2-13, with selected solutions, are presented in the Student CD-ROM that accompanies this book. Students can use those problems for more practice. And instructors can use those problems whose solutions are provided only in the Instructor's Solutions Manual for assignments.

Special FeaturesWe have created special features for this book in order to facilitate the learning of the material and an understanding of its applications.

Engineering EconomiCs in Action boxes near the beginning and end of each chapter recount the fictional experiences of a young engineer. These vignettes reflect and support the chapter material. The first box in each chapter usually portrays one of the characters trying to deal with a practical problem. The second box demonstrates how the character has solved the problem by applying material discussed in the chapter. All of these vignettes are linked to form a narrative that runs throughout the book. The main character is Naomi, a recent engineering graduate. In the first chapter, she starts her job in the engineering department at Global Widget Industries and is given a decision problem by her supervisor. Over the course of the book, Naomi learns about engineering economics on the job as the students learn from the book. There are several characters, who relate to one another in various ways, exposing the students to practical, ethical, and social issues as well as mathematical problems.

~

Engineering Economics in Action, Part SA: The Pit BullNaomi liked to think of Terry as a pit bull. Terry had this endearing ~ab it of finding some detail that irked him, and not letting go of it until he was satisfied that things were done properly. Naomi had seen this several times in the months they had worked together Terry would sink his teeth into some quirk of Global Widgets' operating proeedures and, just like a fighting dog, not let go until the fight was over. This time, it was about t-he disposal of some computing equipment. Papers in hand, he quietly approached Naomi and earnestly started to explain his concern . "Naomi, I don't know what Bill Fisher is doing, but something's definitely not right here. Look at this." Terry displayed two documents to Naomi. One was an accounting statement showing the book value of various equipment, including some CAD/CAM computers that had been sold for scrap the previous week. The other was a copy of a sales receipt from a local salvage firm for that same equipment. "I don't like criticizing my fel.ow workers, but I really am afraid' that Bill might be doing something wrong." l Bill Fisher was the buyer responsible for capital equipment at Global Widgets, and he also disposed of surplus assets. "You know the CAD/CAM workstations they had in engineering design? Well, they were replaced recently and sold. Here is the problem. They were only three years old, and our own accounting department estimated their value as about $5000 each." Terry's finger pointed to the evidence on the accounting statement. "But here," his finger moving to the guilty figure on the sales receipt, "they were actually sold for $300 each! " Terry sat back in his chair. "How about that! " Naomi smiled. Unfortunately, she would have to pry his teeth out of this one. "Interesting observation, Terry. But you know, I think its probably OK. Let me explain."

xvi

PREFACE

Close-Up boxes in the chapters present additional material about concepts that are important but not essential to the chapter.

MethodStraight-line Declining-balanceSurn-of-the-ye~s' -digits

Description.The book value of an asset diminishes by an equal amount each year. The book value of an asset diminishes by an equal proportion each year. An .accelerated method, like declining-balance, in which the depreciation rate is calclliatecl as thtf rati