Fundamentals of Engineering Economics

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Summary of Discrete Compounding Formulas with Discrete Payments

Factor

Notation

Compound

amount

(F/e i, N)

Present

worth

(PIE i, N

Compound

amount

i, N)

Sinking

fund

(ME i. N)

Present

worth

(P/A, i, N)

Capital

recovery

(Me i, N)

Linear

gradient

Present

worth

(P/G, i, N)

Conversion fact01

(AIG, i, Rr)

Geometric

gradient

Present

worth

(PIA ,, g, i, N)

Formula

= .[(I

+ illv - 1

i(1 + i)" I

A = P[ (1 + ilN - 1

+ i)" - iN - 1

Excel

Command

= FV(i, N. P., 0)

= PV(i, N, F, -0)

= PV(i, N, A,. 0)

Cash Flow -

Diagram i

AAA AA /

5 i. I

Summary of Formulas

Effective Interest Rate per Payment Period

Discrete compounding i = [(I + ~/(cK)]' - 1

Continuous compounding i - erlK - 1 Recovery Period (Year

where i - effective interest rate per payment period

r = nominal interest rate or APR

C = number of interest periods per payment

period

K = number of payment periods per year

r/K = nominal interest rate per payment period

Market Interest Rate

i - i' + f + i'f

where i = market interest rate

if = inflation-free interest rate -

,f = general inflation rate

Present Value of Perpetuities

p = market related risk index

r, = market rate of return

Capital Recovery with Return Cost of Debt

CR(i) = (I - S)(A/P, i, N) + iS

Book Value

11

= I - x D, where id = cost of debt

1'1 c, - the amount of term loan

Straight-Line Depreciation c,, = the amount of bond financing

(I - S) c,, = total debt = c, t c,,

D,? - -

N k, = the before-tax interest rate on the term loan

Declining Balance Depreciation kh = the before-tax interest rate on the bond

t,,, = the firm's marginal tax rate

D,, - aI(1 - a)"-' -

Weighted-Average Cost of Capital 1

where a = declining balance rate. and 0 < a 5

N

Cost of Equity

where i, = cost of equity

rf = risk-free interest rate

where k = cost of capital

c,, = total equity capital

V = Cd + C,

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Table of Contents

nderstanding Money and Its Management

1.1 The Rational Decision-Making Process

1.1.1 How Do We Make Typical Personal Decisions?

1.1.2 How Do We Approach an Engineering Design Problem?

1.1.3 What Makes Economic Decisions Differ from Other

Design Decisions?

1.2 The Engineer's Role in Business

1.2.1 Making Capital-Expenditure Decisions

1.2.2 Large-Scale Engineering Economic Decisions

1.2.3 Impact of Engineering Projects on Financial Statements

1.3 Types of Strategic Engineering Economic Decisions

1.4 Fundamental Principles in Engineering Economics

Summary

2.1 Interest: The Cost of Money

2.1.1 The Time Value of Money

2.1.2 Elements of Transactions Involving Interest

2.1.3 Methods of Calculating Interest

2.2 Economic Equivalence

2.2.1 Definition and Simple Calculations

2.2.2 Equivalence Calculations Require a Common Time

Basis for Comparison

2.3 lnterest Formulas for Single Cash Flows

2.3.1 Compound-Amount Factor

2.3.2 Present-Worth Factor

2.3.3 Solving for Time and Interest Rates

viii TABLE OF CONTENTS

2.4 Uneven-Payment Series

2.5 Equal-Payment Series

2.5.1 Compound-Amount Factor: Find F, Given A, i, and N

2.5.2 Sinking-Fund Factor: Find A, Given 5 i, and N

2.5.3 Capital-Recovery Factor (Annuity Factor): Find A,

Given P. i, and N

2.5.4 Present-Worth Factor: Find P, Given A, i, and N

2.5.5 Present Value of Perpetuities

2.6 Dealing with Gradient Series

2.6.1 Handling Linear Gradient Series

2.6.2 Handling Geometric Gradient Series

2.7 Composite Cash Flows

Summary

Problems

3.1 Market Interest Rates

3.1 .I Nominal Interest Rates

3.1.2 Annual Effective Yields

3.2 Calculating Effective Interest Rates Based on Payment Periods

3.2.1 Discrete Compounding

3.2.2 Continuous Compounding

3.3 Equivalence Calculations with Effective Interest Rates

3.3.1 Compounding Period Equal to Payment Period

3.3.2 Compounding Occurs at a Different Rate than

that at which Payments Are Made

3.4 Debt Management

3.4.1 Borrowing with Credit Cards

3.4.2 Commercial Loans-Calculating Principal

and lnterest Payments

3.4.3 Comparing Different Financing Options

Summary

Problems

a'i ," : " & 'p.

4.1 Measure of Inflation

4.1.1 Consumer Price Index

4.1.2 Producer Price Index

TABLE OF CONTENTS

4.1.3 Average Inflation Rate Cf)

4.1.4 General lnflation Rate (7) versus Specific

Inflation Rate (f,)

4.2 Actual versus Constant Dollars

4.2.1 Conversion from Constant to Actual Dollars

4.2.2 Conversion from Actual to Constant Dollars

4.3 Equivalence Calculations under Inflation

4.3.1 Market and Inflation-Free Interest Rates

4.3.2 Constant-Dollar Analysis

4.3.3 Actual-Dollar Analysis

4.3.4 Mixed-Dollar Analysis

Summary

Problems

valuating Business and Engineering Assets

PM ".,

Sb e*

5.1 Loan versus Project Cash Flows

5.2 Initial Project Screening Methods

5.2.1 Benefits and Flaws of Payback Screening

5.2.2 Discounted-Payback Period

5.3 Present-Worth Analysis

5.3.1 Net-Present-Worth Criterion

5.3.2 Guidelines for Selecting a MARR

5.3.3 Meaning of Net Present Worth

5.3.4 Capitalized-Equivalent Method

5.4 Methods to Compare Mutually Exclusive Alternatives

5.4.1 Doing Nothing Is a Decision Option

5.4.2 Service Projects versus Revenue Projects

5.4.3 Analysis Period Equals Project Lives

5.4.4 Analysis Period Differs from Project Lives

Summary

Problems

x TABLE OF CONTENTS

6.1 Annual Equivalent Worth Criterion

6.1.1 Benefits of AE Analysis

6.1.2 Capital Costs versus Operating Costs

6.2 Applying Annual-Worth Analysis

6.2.1 Unit-Profit or Unit-Cost Calculation

6.2.2 Make-or-Buy Decision

6.3 Comparing Mutually Exclusive Projects

6.3.1 Analysis Period Equals Project Lives

6.3.2 Analysis Period Differs from Projects' Lives

Summary

Problems

7.1 Rate of Return

7.1.1 Return on Investment

7.1.2 Return on Invested Capital

7.2 Methods for Finding Rate of Return

7.2.1 Simple versus Nonsimple Investments

7.2.2 Computational Methods

7.3 Internal-Rate-of-Return Criterion

7.3.1 Relationship to the PW Analysis

7.3.2 Decision Rule for Simple Investments

7.3.3 Decision Rule for Nonsimple Investments

7.4 Incremental Analysis for Comparing Mutually

Exclusive Alternatives

7.4.1 Flaws in Project Ranking by IRR

7.4.2 Incremental-Investment Analysis

7.4.3 Handling Unequal Service Lives

Summary

Problems

7A.1 Net-Investment Test 258

7A.2 The Need for an External Interest Rate 260

7A.3 Calculation of Return on Invested Capital for Mixed Investments 261

TABLE OF CONTENTS xi

evelopment of Project Cash Flows 267

8.1 Accounting Depreciation

8.1.1 Depreciable Property

8.1.2 Cost Basis

8.1.3 Useful Life and Salvage Value

8.1.4 Depreciation Methods: Book and Tax Depreciation

8.2 Book Depreciation Methods

8.2.1 Straight-Line Method

8.2.2 Declining-Balance Method

8.2.3 Units-of-Production Method

8.3 Tax Depreciation Methods

8.3.1 MACRS Recovery Periods

8.3.2 MACRS Depreciation: Personal Property

8.3.3 MACRS Depreciation: Real Property

8.4 How to Determine "Accounting Profit"

8.4.1 Treatment of Depreciation Expenses

8.4.2 Calculation of Net Income

8.4.3 Operating Cash Flow versus Net Incomc

8.5 Corporate Taxes

8.5.1 Income Taxes on Operating Income

8.5.2 Gain Taxes on Asset Disposals

Summary

Problems

9.1 Understanding Project Cost Elements 308

9.1.1 Classifying Costs for Manufacturing Environmcnts 308

9.1.2 Classifying Costs for Financial Statement$ 310

9.1.3 Classifying Costs for Predicting Cost Behavior 312

9.2 Why Do We Need to Use Cash Flow in Economic Analysis? 314

9.3 Income-Tax Rate to Be Used in Economic Analysis 315

xiv TABLE OF CONTENTS

13.3 Using Ratios to Make Business Decisions

13.3.1 Debt Management Analysis

13.3.2 Liquidity Analysis

13.3.3 Asset Management Analysis

13.3.4 Profitability Analysis

13.3.5 Market-Value Analysis

13.3.6 Limitations of Financial Ratios in Business Decisions

Summary

Problems

Preface

Engineering economics is one of the most practical subject matters in the engineer￾ing curriculum. but it is always challenging and an ever-changing discipline.

Contemporary Engineering Economics (CEE) was first published in 1993, and since

then we have tried to reflect changes in the business world in each new edition,

along with the latest innovations in education and publishing. These changes have

resulted in a better, more complete textbook, but one that is much longer than it was

originally intended. This may present a problem: today, covering the textbook in a

single term is increasingly difficult. Therefore, we decided to create Fundamentals of

Engineering Economics (FEE) for those who like Fundanzentals but think a smaller,

more concise textbook would better serve their needs.

This text aims not only to provide sound and comprehensive coverage of the con￾cepts of engineering economics, but also to address the practical concerns of engi￾neering economics. More specifically, this text has the following goals:

1. To build a thorough understanding of the theoretical and conceptual basis

upon which the practice of financial project analysis is built.

2. To satisfy the very practical needs of the engineer toward making informed

financial decisions when acting as a team member or project manager for

an engineering project.

3. To incorporate all critical decision-making tools-including the most con￾temporary, computer-oriented ones that engineers bring to the task of mak￾ing informed financial decisions.

4. To appeal to the full range of engineering disciplines for which this course

is often required: industrial, civil, mechanical, electrical, computer, aero￾space, chemical, and manufacturing engineering, as well as engineering

technology.

This text is intended for use in the introductory engineering economics course. Un￾like the larger textbook (CEE), it is possible to cover FEE in a single term, and per￾haps even to supplement it with a few outside readings or cases. Although the

chapters in FEE are arranged logically, they are written in a flexible, modular for￾mat. allowing instructors to cover the material in a different sequence.

xvi PREFACE

We decided to streamline the textbook by retaining the depth and level of rigor

in CEE, while eliminating some less critical topics in each chapter. This resulted

in reducing the total number of chapters by four chapters in two steps. Such core

topics as the time value of money, measures of investment worth, development of

project cash flows. and the relationship between risk and return are still discussed

in great detail.

First, we eliminated the three chapters on cost accounting, principles of in￾vesting, and capital budgeting. We address these issues in other parts of the

textbook, but in less depth than was contained in the deleted chapters.

Second, we consolidated the two chapters on depreciation and income taxes

into one chapter, thus eliminating one more chapter. This consolidation pro￾duced some unexpected benefits-students understand depreciation and

income taxes in the context of project cash flow analysis, rather than a sep￾arate accounting chapter.

Third. moving the inflation material from late in the textbook to the end of

the equivalence chapters enables students to understand better the nature

of inflation in the context of time value of money.

Fourth, the project cash flow analysis chapter (Chapter 9) is significantly

streamlined-it begins with the definitions and classifications of various

cost elements that will be a part of a project cash flow statement. Then. it

presents the income tax rate to use in developing a project cash flow state￾ment. It also presents the appropriate interest rate to use in after-tax eco￾nomic analysis. Finally, it illustrates how to develop a project cash flow

statement considering (1) operating activities, (2) investing activities, and

(3) financing activities.

Fifth, the handling project uncertainty chapter (Chapter 10) has been consol￾idated by introducing the risk-adjusted discount rate approach and investment

strategies under uncertainty, but eliminating the decision-tree analysis.

Finally, the chapter on understanding financial statements has been moved

to the end of the book as a capstone chapter, illustrating that a corporation

does not make a large-scale investment decision on an engineering project

based on just profitability alone. It considers both the financial impact on

the bottom-line of business as well as the market value of the corporation.

FEE is significantly different from CEE, but most of the chapters will be familiar to

users of CEE. Although we pruned some material and clarified, updated, and other￾wise improved all of the chapters, FEE should still be regarded as an alternative ver￾sion of CEE.

Although FEE is a streamlined version of CEE, we did retain all of the pedagogical

elements and supporting materials that helped make CEE so successful. Some of

the features are:

PREFACE xvii

Each chapter opens with a real economic decision describing how an indi￾vidual decision maker or actual corporation has wrestled with the issues

discussed in the chapter. These opening cases heighten students' interest by

pointing out the real-world relevance and applicability of what might other￾wise seem to be dry technical material.

There are a large number of end-of-chapter problems and exam-type ques￾tions varying in level of difficulty; these problems thoroughly cover the

book's various topics.

Most chapters contain a section titled "Short Case Studies with Excel,"

enabling students to use Excel to answer a set of questions. These prob￾lems reinforce the concepts covered in the chapter and provide students

with an opportunity to become more proficient with the use of an elec￾tronic spreadsheet.

The integration of computer use is another important feature of F~lndametztuls of

Engineering Econortlics. Students have greater access to and familiarity with the

various spreadsheet tools, and instructors have greater inclination either to treat

these topics explicitly in the course or to encourage students to experiment inde￾pendently. A remaining concern is that the use of computers will undermine true un￾derstanding of course concepts. This text does not promote the trivial or mindless

use of computers as a replacement for genuine understanding of and skill in apply￾ing traditional solution methods. Rather, it focuses on the computer's productivity￾enhancing benefits for complex project cash flow development and analysis.

Specifically, Fundatnentuls of Engineering Economics includes:

A robust introduction to computer automation in the form of the Cash

Flow Analyzer problem, which can be accessed from the book's website

An introduction to spreadsheets using Microsoft Excel examples. For spread￾sheet coverage, the emphasis is on demonstrating complex concepts that can

be resolved much more efficiently on a computer than by traditional long￾hand solutions.

The companion website ( ) has been created and main￾tained by the author.This text takes advantage of the Internet as a tool that has become

an increasingly important resource medium used to access a variety of information on

the Web. This website contains a variety of resources for both instructors and students,

including sample test questions, supplemental problems, and various on-line financial

calculators. As you type the address and click the open button, you will see the Fz~nd￾amentals of Engineering Economics Home Page (Figure PI). As you will note from the

figure, several menus are available. Each menu item is explained as follows:

Study Guides. Click this menu to find out what resource materials are

available on the website. This site includes (1) sample text questions, (2)

solutions to chapter problems, (3) interest tables, and (4) computer notes

with Excel files of selected example problems in the text.

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PREFACE xix

Money and Investing. This section provides a gateway to a variety of infor￾mation useful to co~lducting engineering economic analysis. For example, a

direct link is provided to the most up-to-date stock prices. options, and mu￾tual funds performances.

FEE includes several ancillary materials designed to enhance the student's learning

experience, while making it easier for the instructor to prepare for and conduct

classes. The ancillaries are described below.

For Students

Excel for Engineering Economics (supplement), containing information

on how to use Excel for engineering economic studies and various Excel

applications.

Study Guides for F~~ndarnentals of Engineering Ecorlomics (supplement),

which contains more than 200 completely worked out solutions and guides on

how to take the FE exam on engineering economics and sample test questions.

For Instructors

A comprehensive Instructor's Manlrnl that includes answers to end-of-chapter

problems and Excel solutions to all complex problems and short case studies.

A CD-ROM containing Powerpoint slides for lecture notes. the entire con￾tents of the Instructor Manual in Word format, test questions, and Excel

spreadsheet files.

This book reflects the efforts of a great many individuals over a number of years. In particular, I would like to rec￾ognize the following individuals. whose reviews and comments have contributed to this edition. Once again, I

would like to thank each of them:

Richard V. Petitt, lJnited States Military Academy; James R. Smith, Tennessee Technological University;

Bruce Hartsough, University of California at Davis; Iris V. Rivero, Texas Tech University; Donald R. Smith,

Texas A&M University; Bruce McCann, University of Texas at Austin: Dolores Gooding, University of

South Florida; and Stan Uryasev. University of Florida.

Personally, I wish to thank the following individuals for their additional input to the new edition: Michael D.

Park, McKinsey & Company, who read the entire manuscript and offered numerous and critical comments to im￾prove the content of the book; Luke Miller, Yeji Jung and Edward Park, who helped me in preparing the Instruc￾tor's Manual: Junmo Yang, who helped me in developing the book website: Dorothy Marrero, my editor at Prentice

Hall. who assumed responsibility for the overall project; and Scott Disanno, the production editor. who oversaw

the entire book production.

CHAN S. PARK

Auburn, Alabama