Engineering economy book mc graw hill higher education part 1

engineering economy book mc graw hill higher education part 1

Glossary of Common Terms

Term

Annual amount or wonh

Annual opemling cost

Estimated annuul costs to maintain and support an ultemrtivc (1.3)

Ratio of apmjecc's benefits to costs exprerscd in PW

Equivrlcnt annual cost of oivnillg an asset plus

the required rctum on the initial invesmn?enr(6.2)

present worth of an alternrtivc h a t will last forwcr

(or 31 long time) (5.5)

Acaal cash amounu which are icceipu (inflow) and disbursements (outflow) (1.10)

Cash flaw amount before relevant rlxcs or after taxes are npplicd (17.2)

Unique rate of return when a reinvesf~~~ent rate c in

applied to a multiple~rrre ciqh flow series (7.5)

Relrtions chat use design variables and changing costs over time to estimrte current and future costs (13.34)

Percentages of debt and equity invesment cupilal used by ucorporrfion (1.9, 10.3)

Reduction iil the value of asscts "sing specific modcls and rules: there are book and tux deprecisrion mehodn (16.1)

Antlurl r r r for reducing thc value of assets using dcpicciaion models (16.1)

Number of yeam at which rhe AW of uosrs is n rninilnurn (11.2)

Long-mn expected avemgc if a randam wrirblc is sampled m a y limes (18.3, 19.4)

All c o ~ w n i c c o r t s i n c u i r c d i n transacting business (17.11

TorN initial costGpurchnre, constmcrion setup, erc (1.3 16.1)

ENGINEERING

McGraw-Hill Series in Industrial Engineering

and Management Science

Consulting Editors

Kennellr E Cose, Depamnent of rndusrriai Engineel-ing oiid Mnsa~tnieer,

Oklahorrm State University

Philip M Wol/e, Dqannrenl of Indusrrinl nndMriniigement Sy.~re,ns Engineerink

Arizona Sfore UniversiQ

Blank and Tarquin: Engineering Economy

Chapra: Applied Numerical MeUlads with MATLAB for Engineers md Scientists

Grant and Leavenworth: Statistical Quality Control

Gryna: Quality Planning and Analysis: From Product Development trough Use

Harrell, Ghosh, and Bowden: Simulntion Using PROMODEL

Hiliicr and Lieberman: Introduction to Operations Research

Kelton, Sadowski, and Sturmck: Simulation with Arena

Law a n d Kclton: Simulation Modeling and AnuIyris

Navidi: Statistics for Engineers and Scientists

Nicbel and Freivalds: Methods, Standards, and Work Design

ENGINEERING ECONOMY

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Higher Education

ENGINEERING ECONOMY, SIXTH EDITION

hblished by ~ c C ~ r ~ ~ i i i , r business u n i t o l n l s M'GnvHlll Compmies Inc 1221 nvenlio o f t h e Amencar NEW Ywk, NY

10020 Copyn:hio ZOOS 2W2 1998, 1989, 1983, 1976byThe M ~ ~ n ~ w H i l l companies I n s ~ l l rights reserved No pan of Ulrs

publication may br repraluccd or distnbuiid in any form or by my mcans, or rtorcd in r daabr,oor rclrisvjll rysttlem withoutthe

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or tcm,~lussial or brordcrY for dirtmcc I c m b g

some mnilm,, including eicciionic printcompoena, notbprvuiirb,c to ~ u s t o n ~ r r ~ o u c r i d ~ thc united stst=

This book is p n l s d on acid-tree pripcr

I 2 3 4 5 6 7 X 9 0 Q P F / Q P F O Y 8 7 6 j 4

ISBN WO7-lIISS8-7

This book is dedicated to our mothers for their ever-present

Chapter 1 Foundations of Engineering Economy 4

, - 1.1 Why ~ ~ ~ i n e e r i " ~ ~ ~ o n o m y 1s lmpomnt to ~ n g i n e e n (and Olher Profcsrionrls) 6

1.2 Role of Engineering Economy in Decision Mallng 7

1

Extended Exercis-Efrects of Compound Interest 45

Case Study-Dcsctibing Alremrtives for Producing Refrigcralor Shells 46

Chapter 2 Factors: M o w T i m e : a n d - l n t e r e s t A f f e d M o n e y Y Y Y Y Y Y ~ ~

2.1 Single-Paymc"rFucto~(F/PandPln

2.2 Uniformseries Present Wonh Factor and Capital Recovely Factor (PIA and AIP)

2.3 Sinbng Fund Factor and Uniform-Series Compound Amount

Faclor (AlF and FIA)

2.4 Interpalalion in hfenslTables

Chapter 3 Combining Factors 92

3.1 Calculations for Uniform Series That Arc Shifted 94 3.2 Calculations Involving Unifoim-Series and Randomly Piaced Single Amounts 98 3.3 Calcc~lations for Shifted Gradients

103

3.5 Spreadsheet Application-Using Difierenr Functions 110

Extended ExercBcPrcseiving Land for h b l i c Use 123

Chapter 4 Nominal and Effective Interest Rates

4.1 Nominal m d Effective Inlercn Rate Staremcntr 4.2 Effcicctive Annual lntereit R l e s

4.3 Elfecliue Interest Rates for Any Time Period 4.4 Equivalence Relations: Cnmpvring Paymcnt Pcnod tmd Compounding

Period Lengths (PP versus CP) 4.5 Equivalence Rehnians: Single Amounts with PP 2 CP

4.6 Equivale~~cc Relations: Series with P P z CP 4.7 Equivrlencc Relulions: Single Amounts and Series with PP c CP 4.8 Effective Inteicst Ratc for Continuous Compounding 4.9 Interest Rates Thrt V a q over Time

ChaptcrSummary Problems

F E Rcvicw Pmblemr Case Study-Financing a House

Chapter 5 Present Worth Analysis

168

5.1 Farmulaling Mutually Erclurive Altcmvtiver

170 5.2 Present Wonh Analysis of EqurlbLifc Alremuti\,~~ 172 5.3 Present Wonh Analysis oIDiffem1-Life Alcernaiver 174 5.4 Future Wonh Analysis

177 5.5 Capiralized Cost Calculation andAnalysis

179 5.6 Payback Peiiod Analysis

185 5.7 Life-cycle Cost

190 5.8 Presenl Worth of Bonds

194 5.9 Sprrndshecl Applicrtions-PWAnvlyris undPayb;ok P c r i ~ d

197 ChapterSummary

202

F E Review Prohiems

210 Extended Exercise Evaluation of Social Security ~ e t i r e ~ n c s ~ Estimates 212 Case Study-Payback Evaluation of Ulsalow-Flush Toiler Program

213

CONTENTS

Chapter 6 Annual Worth Analysis

6.1 Advantages m d Uses of Annual Worth Anvlysis

6.2 Calculation of Capital Recovery and AW Values

6.3 Evaluilling Alfemstivcs by Anllual Worth Anvlysis 6.4 AW of a Pcrmrncnl Investment

Chapter Summary

problem^

F E Review Problems Csrc Study-The Changing Scene of an Annual Worth Allalysis

Chapter 7 Rate of Return Analysis: Single Alternative

7.1 Inteiprc~alion ofa Rate of Return Value

7.2 Role of Retum Calculation Using a PW or AW Equation 7.3 Cautions When Using t h t ROR Method

7.4 Multiple Ra~cofReturn Valucs

7 j Colnposilc Rate of Returh: Removing Multiplc i Values 7.6 Rvteof Return o f a ~ i l d lnvesmcnt

Chapter Summary Problems

FE Review Pmbloms '

~ x t e n d o d ~ x e r e i s e I- he c o s t of u ~ o n r Credit ~ n t i n g Extended Erercirc2-When Is It Bcrt t o s e l l >Business?

Case Study-Bob Levins Aboul Multiple Rates of Return

Chapter 8 Rate of Return Analysis: Multiple Alternatives

8.1 Why Incremental Analysis is Necersvv 8.2 Cvlculvlion of lncrerncntvl Cash Flows for RDRAnalysin 8.3 lntcrpietation of Rate of Rcmm on ihr Enrrv lnvertiiient

8.4 Rate of Return Evaluarion Using PW Increlnenrvl ;md Brekikcven

8.5 Rofc of Return E\,aluntion Using AW

8.6 Incremental RORAnalysis of Multiple Mutually Exclusive Alternatives 8.7 Spreadsheet Appliceinn-PW, r W and ROR Anslyrcs All in O n e

C h a p a r Summary Problems

FE Review Problems Extended Exercis+lncnmentul ROR Analysis When Estin~vtsd Alfernalivc Lives are Uncenain

Case Study 1-So Many Options C;m a New Engincerhg Gmduatc HelpHis Father?

Case Study L P W A n a l y s i s When Multiple Interest Rates Are Present

Chapter 9 BenefitICost Analysis and Public Sector Economics

9 Publlc Sccfur Prqeclr

9 2 BenefitiCosLAnvlyils of a Singlc Prolrct

9.3 Alrehativve Sclcctian Using Incremental BIC Andyris 324 9.4 lncremenral BIC h v l y s i s of Multiple, Muluvlly Exclusive Alremativor 327

extended Exercis&ona io Provide Ladder Truck Service

Chapter 1 0 Making Choices: The Method, MARR,

~ .~ ~

10.1 ComprringMuturlly E X ~ I ~ S ~ V ~ Allenlalives by Different EvuluvtiooMethodd 348

10.3 Debt-Equity Mix and Weighted A t t a g c Cod of Capital 354

10.5 Determination of the Cost of Equity Capilal and the MARR 359 10.6 Effcclaf Debt-Equity Mix (I" 11111tmttt Risk 362 10.7 Mul"1e Alltibute Analysis: Identification m d Importance of Each Atiribute 364

~ x t e n d e d E ~ ~ ~ i ~ ~ the - Right Things E ~ ~ h ~ ~ i ~ i ~ ~ 381

c a s e Study-Which Way lo Go Debt or Equity Financing? 382

M A K I N G DECISIONS O N REAL-WORLD PROJECTS

Problems

FE ~ e v i e w Pmblams

!3aended Erereis-Economic ServiceLifc llnder Varying Conditions

C u e Study-Replacement A ~ d y s i s for Q u q Equipmen,

Chapter 1 2 Selection from Independent Projects

I ' Under Budget Limitation

12.1 ~ n ~ v e r v i e w o f c ~ ~ i ~ a l ~ a r i o n i n g ~ m o n g P r ~ j ~ c ~ r

12.2 Capital Rationing Using PW Analysis of Equal-Life Pmjecrs

12.4 Capital Budgeting Problem Forlnulrtion Usillg Linear Programming 432

Case Sludy-Lifelong Engiaceting Educ8tiorl in it Web Enriran~~ient 440

13.3 Spreadshecl Applicalion-Using Encci's SOLVER for Breakeven

Case Study-Water Tream~oit Pisnt Process Costs 464

Chapter 14 Effects of Inflation

14 I Underitandme &e l~novct of Innruon

Chsptcrsummary I'mblcmn

F E Review Pmblcmr Extended E x e r c i r t F i r e d ~ l n c o m c Invci~mcas versus the Forces of

I n n a i o n n ~~~

Chapter 15 Cost Estimation and Indirect Cost Allocation

15.1 Understanding How Cost Esrimatian 1s Accomplished 15.2 Cost Indexes

15.3 Cost Eslinlsting Relaionships: Cost-Capacity Eqvsrions 15.4 Cost &timating Relationships: Factor Method

15.5 Trrdilionvl Indirect CoslRrtes m d Alloartion 15.6 Activity-Based Costing (ABC) for Indirect Cascs Chaptcrsummar)

Problems

FE Review Problems Care Study-Tufrl Cost Escimrrei for Olltimiling Coogulrn~ Dosage Cane Study-lndirccr Cost Comparison of Medics1 Equipmcnl s,cn1iZanio,, unit

Chapter 1 6 Depreciation Methods

16.1 DepreciationTerminology 16.2 Staighr Linc (SL) Depreciation 16.3 Declining Balance (DB) and Double Declining Balance (DDB) Depreciation 16.4 Modificd Accelerated Cost R R R O D D ' ~ System (MACRS)

16.5 Determining Lhe MACRS Recovery Period 16.6 DepletianMethods

Chapter Summary Problems

F E Review Problcms 16A.I Sum-of-Year D i g i s (SYD) Depreciation 16A.2 Switching Between DcpreciaLion Methods

16A.3 Determination of MACRS Rates

Appendix Pmblems

Chapter 1 7 After-Tax Economic Analysis

17.1 Illcome Tar Terminoiogy m d Rclrrions for Corporations (and Individuals) 17.2 Before-Tax and Afrer-Tax Cash Flow

17.3 Effect on Tvres of Different Deprecivtio~ Methods and Recovery Periods 17.4 Depreciation Recapture and Cnpirai Grins b o s s e s ) : for Corporario~>r

17.5 After-Tux PW, AW,md ROR Evaluation 17.6 Spread:heer Applicarions-After-Tax Incremental ROR Analysis 17.7 AffeiTrx Replrccment Study

17.8 After-Tux Value-Added Analysis 17.9 After-Tux Analysis far International Projects Chapter Summary

Problems Case Study-After-Tax Evaluation of Debt m d Equity Financing

Chapter 1 8 Formalized Sensitivity Analysis and Expected Value Decisions

18.1 Determining sensitivi,y to Panmeler Vrrirtion 18.2 Formalized Sensitivity Analysis Using Three brimarcs

18.3 Economic Variability and ihc Expccred Value 18.4 Expected Value Computations for Alamariver 18.5 Staged Evaluation ofAlfernrtives Using a Decision Trec ChapterSummsry

Problcms Extended Exercis-Looking ai Altemarivcs from Different Angles Care Study-Sensitivity Aclvlysis of Public Sccfor

Proj~~t~-Waler Supply Phlls

Chapter 19 More on Variation and Decision Making Under Risk

19.1 lnlerprer~tion oiCcnuinv, Risk, and Uncenainty 19.2 ElrmenL~ l m p a m l to Dccision Making Under Risk

19.3 Rmdom Samples 19.4 Expected Value and Standard Deviation 19.5 Monte Carlo Sampling and Simulation Analysis Additional Examples

Chapter Summary Probiamr Extended Exercis-Using Simulation and rile Excci RNG for Sensitivity Analysis

Appendix A Using Spreadsheets and Microsoft Excel"

A l lntrduction to Using Excel

A 2 Organization (Layout) of rhc Spreadsheet A.3 Excel Fahnctions Imponant to Engineering Economy (alphubeticd order)

A 4 SOLVER-An Excel Tool far Breakcven and "What IWAnalysis A.5 List of Excel Financial Funcrioos

A.6 ErrorMesrnges

Appendix B Basics of Accounting Reports and Business Ratios

8.1 Tho Bainncc Sheet

8.2 Income Starernelit and Cost of Goods Sold Statement

8 3 Busincas Ratios Problems

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PREFACE

the i o d u l a r design allowsfor great flexibility in the selection and sequencing of

tooics The chanter oramession a r a ~ h i c , (which follows the flowchart) shows

rc,mc JI chc ?pin n r idr illlro~lu;l#lg :lllptcr~ clrlirr th:lll I I I C I I ~llllllelii~l 18r.tr.l

I ~ ~ r ~ r ~ m p l ~ , t r ~ c ~ c c c ~ u r ~ ~ I., J?u<ncJ ~ ~ ~ ~ r ~ ~ p 1 t ~ ~ 1 , c x l t e r - t ~ a c ~ ~ l ~ ~ t ~ c ~ r l > t n tlw

, ~ m ? ~ w r j r ,~udrtx, CII pter I ~ ~ I I J ~ h c imlidl ~ ~ ' t ~ ~ ~ n ~ ~ r Clt:8pccr 17 nlL) h: I n -

troduced at i n y point after Chapter 6 without loss of foundation preparation

There are clear primary and alternate envy points for the major categories af in-

flation, estimation, taxes, and risk Alternative entries are indicated by a dashed

arrow on the graphic

The material in Level One emphasizes basic computational skills, so these

chaoters are orerequisites far all the others in the book The chapters in Level

Two are primarily devoted to the most common analytical techniques for com-

paring alternatives While it is advisable to cover all the chapters in this level

only the first two (Chapters 5 and 6) are widely used throughout the remain-

der of the text The three' chapters of Level Three show how any of the

techniques in Level Two can be used to evaluate presently owned assets or in-

dependent alternatives, while the chapters in Level Four emphasize the tax

consequences of decision making and some additional concepts in cost esti-

mation, activity-based costing, sensitivity analysis, and risk, as treated using

Monte Carlo simulation

01.eanizorion - - o f Chaofers and End-of-Clzaoler Exercises Each chuoter con- -

t ~ l n , a p ~ r p , , ~ !#.I 1 \r.r.r.* oi pr $rtw\c Ic rtllrl: J ~ > ~ L C I # \ C > i01101~.Y h) ~hl

,t~d! ~t~.tr.r#al S s i t ~ , ~ bc d~r.g\ conr.rpon<l to ea.h le.trntn2 uhj:ahc, lor

I c c u # n 5 1 :,1111.1111\ th: 111_1l~rl.d pcndnlny loth: lird i8hj"ctlvrul 1112

chap& Each section contains one or mare illustrative examples solved by hand,

or ~ hv bath hand and comouter methods Examoles are seoarated from the textual ~2~~

material and include comments about the solution and pertinent connections to

other topics in the book The crisp end-of-chapter summilries neatly tie together

the concepts and malor topics covered to reinforce the learner's understanding ~ -

prior to engaging in the end-of chapter exercises

The end-of-chuoter unsolved ~roblerns are erouoed and labeled in the same

ing when the chapter is completed

Appendices A and B contain supplementary information: abasic introduction

to the use of spreadsheets (Microsoft Excel) for readers unfamiliar with them

and the basics of accounting and business reports Interest factor tables are la-

cated at the end of the text for easy access Finally, the inside front covers offer

a quick reference to factor notation, formulas, and cash flaw diagrams, plus a

guide to the format for commonly used spreadsheet functions A glosswy of

common terms and symbols used in engineering economy appears inside the

back cover

LEVEL ONE

PREFACE

OPTIONS FOR PROGRESSION THROUGH CHAPTERS

Topics may k inlroducd a, Uis point indicnlcd or my point illci~rfler

(iiiarnriius cnw ace fndicrtcd by )

APPRECIATION T O CONTRIBUTORS

Throughout this and previous editions, many individuals at uni\,ersities, in

industry, and in private practice have helped in the development of this text We

thank all of them far their contributions and the privilege to work with them

Some of these individuals are

Roza Abubakcc, American University of Shajah

Robyn Adams 12' Man Foundalian, Texas A&M University

Jeffrey Adler, MindBox, Inc., and formerly of Rensselaer

Polvtechnic Institute

Richard H Bernhard, North Carolina State University

Stanley E Bullington, Mississippi State University

Peter ~ h a n , ~ ~ ~ ~ ~ n g i n e e r i n g ,

Ronald T Cutwright, FloridaA&M University

J o h ~ F Dacquisto, Gonraga University John Yancey Easley, Mississippi State University Nader D Ebmhimi University of New Mexico Charles Edmonsan, University of Dayton Ohio Sebastian Fixson, University of Michigan Louis Gennaro, Rochester Institute of Technology Joseph Hartman, Lehigh University

John Hunsucker, University of Houston Cengiz Kahraman, Istanbul Technical University, Turkey Walter E LeFevre, University of Arkansas

Robert LundquiSt, Ohio State University Gerald T Mackulak, Arizona State University Mike Momot, University of Wisconsin, Plaaeville James S Noble, University of Missouri-Columbia Richard Patterson, University of Florida Antonio Pertence Jr, Faculdade de Sabara, Minas Gerais, Brazil William R Peterson Old Dominion University

Stephen M Robinson, University of W~sconsin-Madison David Salluday, San Jose State University

Mathew Sanders, Kettiring University Tep Sastri, formerly of Texas A&M University Michael 1 Schwandt, Tennessee Technological University Frank Sheppard, 111, The Trust for Public Land

Sallie Sheppard, American University of Sharjah Don Smith, Texas A&M University

Alan Stewart Accenture LLP

Ciriaco Valdez-Flores, Sielken and Associates Consulting Richard Wcst, CPA, Sanders and West

We would also like to thank Jack Beltran for his accuracy cbeck of this and pre- vious editions His work will help make this text a success

Finally, we welcome any comments or suggestions you may have to help improve the textbook or the Online Learning Center You can reach us at lblank@ausharjah.edu or lbIank@tamu.edu and atarquin@utep.edu We look

forward to heating from you

D e BIarlk

Tony Torquin

CROSS-REFERENCING -

Blank and Tarquin reinforce the

engineering concepts presented

Uuoughaut the book by malang

them crrily accessible from other

sections of the book Cross-

reference icons in the margins

refcr thereader to additional

seciian numbers, speciflc

examples, or entire chvplcrs thar

contain either foundvti~ml

(backward) or more advanced :

(fo~.urdpinformalion that is,

relevant to that in the paragraph

next to the icon

sets as they eye assigned to students in the course This helps instructon to quiclily find solutions and keep a record of problems assigned, to avoid duplication of tests and

quizzes in subsequent semesters The ISBN for the Enginee~ing Ecorlomy C.O.S.M.O.S CD-ROM is 0-0739845&3 Contact your McGraw-Hill representative to get a copy

ENGINEERING ECONOMY

- - - " " ~ ' ~ " U , , L ' , ~ i , " equ

ferent interest rates The techniques master h - = - - .,

an enqineer in anv dircinlino n n +.LO -:

ters When you have completed level one, you will b e able t o understand and work problems that account for the time value of money cash flows

occurring at different times with rliffor-nt =m-ll-t A

rvalence at dif-

~ i l u r i r l c me basis of how

, - r - .- - C L Y I I Y I I I ~ ~ value into account in virtu-

ally any project environment

The eight factors commonly used in all engineering economy computa tions are introduced and applied in this level Combinations of these fat

t o n assist in moving monetary values forward and backward through tirne

and at different interest rates Also, after these four chapters, you be

comfortable with usina man" nf +hp F Y P P I .-=A.L A I - ~ ,

Foundations of

Engineering Economy

The need for engineering economy is pilmarily motivated by the work that

engineers d o in performing analysis, synthesizing, and coming t o a conclu-

sion as they work on projects o f all sires In other words, engineering econ-

omy is at the heart of making decisions These decidons involve the funda-

mental elements of cash flows of money time, and interest rates This

chapter introduces the basic concepts and terminology necessaty for an en-

aineer to combine thesO three essential elements i n orsanized rnathemati-

tally correct ways t o solve problems that will lead to better decisions Many

of the terms common t o economic decision making are introduced here and

used in later chapters of the text Icons in the margins serve as back and for-

ward cross-references t o more fundamental and additional material through-

out the ~ book ~

The case studies included after the end-of-chapter problems focus on the

development of engineering economy alternatives

This chapter will help you:

1 Understand the types of questtons engtneertng economy can answer

2 Determine the role of engineering economy in the decirion~ making process

3 Identify what is needed to successfuily peitoim an engineering economy study

4 Perform calculations about interest rates and rate of return

5 Understand what equ8baience means in economlc terms

6 Calculate s~rnple lnterest and compound merest for one or more interest perlodr

7 Identify and use engtneerlng economy terminology and symbols

8 ldentlfy the ExcelB spreadsheet funct8onr commonly used to

solve engineering economy problems

9 Understand the rneanzng and use of M8nlmurn Attractrve

Rate of Return (MARR)

10 Understand cash flows their estimation and how to graphically represent them

11 Use the rule of 72 to estimate a compound interest rate or number of years foia present worth amount t o double

12 Develop a spreadsheet that invaives simple and compound interest, incorporating sensitivity analysis

1.1 W H Y ENGINEERING E C O N O M Y IS IMPORTANT T O

ENGINEERS (and o t h e r p r o f e s s i o n a l s )

Decisions made by engineers, managers, corpomtionpresidents and individuals

are commonly the result of choosing one alternative over another Decisions

often reflect a person's edtlcated choicc of how to best invest funds, also called

capitol The amount of capital is usually restricted, just as the cash available to

an individual is usually limited The decision of how to invest capital will in-

variably change the futurc, hopefully fo, the better; that is, it will be value

adding Engineers play a maior role in caWtal investment decisions based on

Fundamentally, engineering economy involves formalating, estimating,

and evaluating the economic outcomes when alternatives to accom*lish a

defined purpose arc available Another way to define engineering econ-

omy is as a collection of mathematical techniques t h a t simplify economic

comparison

For many corpordtions, especially laiger ones, many of the projects and services

are international in scope They may be developed in one country for application

in another People and plants located in sites around the world routinely separate

product design and manufacturing from each other, and from the customers who

utilize the product The approaches presented here we easily implemented in

multinational settings or within a single country or location Correct use of the

techniques of engineering ccanomy is especially imponant, since virtually any

project-local, national, or intemational-will affect costs andlor revenues ~ ~

Some of the typical questions that can be addressed using the material in this

book are posed below

F~rEngineerin~Activitie ~ ~~ ~ - ~ ~ ~-

Should a new banding technique be incorporated into the manufacture of au-

tomobile brake oads? ~ ~~

If a computer-vision system replaces the human inspector in performing qual-

ity tests on an automobile welding line, will operating costs decrease ovcr a

time horizon of 5 years?

Is it an economically wise decision to upgrade the composite material pro-

duction center of an airplane factory in order to reducc casts by 20%?

Should a highway bypass be constructed around a city of 25,000 people, or

should the current roadway through the city be expanded?

Will we make the required rate of return if we install the newly offered tech-

nology onto our medical laser manufacturing line?

For Public Sector Projccts and Government Agencies

- How much new tax revenue does the city need to generate to pay for an up-

grade to the electric distribution system'?

- Do the benefits outweigh the cost; of a bridge o v a the inVacoastal waterway

Should I pay off my credit card balvuce with borrowed money?

What are graduate studies worth hnuncially over my professional career?

- Are federal income tax deductions for my home mortgage a good deal, or should I accelerate my mongage payments?

- Exactly what iate of retum did we make on nor stock investments? Should 1 buy or lease my next car, or keep the onc I have now and pay off the

~

~ ~ loan?

1.2 ROLE OF ENGINEERING E C O N O M Y

IN DECISION MAKING People make decisions; computers, mathematics, and other tools do not The tech niques and models of engineering economy assist people in moking decisions

Sincedecisions affect what will bedone, the time f m e a f engineering economy is primarily lhe funrre Therefore, numbers used in an eneineerineeconomic analvsis - "

ure best estimates of what is expecrrd to occur ?hex estimates often involve the

lllree essential elements mentioned earlier: cash flows, time of occurrence, and in- terest rates These estimates ure about the future, and will be somewhat different

than what actually occurs, primarily because of changing circumstances and unplanned-for events In other words, the stochoslicnorure of estimates will likely make the observed value in the future differ from the estimate made now

{$! 8 CHAmER I Foundations of ~ngineeting Economy

,

especially those that may vary widely For example, an engineer who cxpects i i - tial software development costs to vary as much as 220% from an estimated

$250,000 should perform the economic analysis for first-cost estimates of

$200.000 5250.000 and $300.000 Other uncertain estimates about the oroiect

analysis possible by simply changing the estimated values The power of spread-

& sheets is used to advantaee thrauehout this text and on the suooonine website.)

specified criterion, such as a mte of return requirement For example, suppose that 5 years ago, a United States-based engineering design company initiated a detailed-design servicein Asiafar automobilecharsis Now thecornoanv oresident

tion of alternatives Commonly referred to us the probimm-solvinx rrppr-onch or the decision-ntakirzgpro~e5S, the steps in the approach follow

1 Understand the problem and define the objective

2 Collect relevant information,

3 Define the feasible alternative solutions and make realistic estimates

4 Identify the criteria for decision making using one or more attribute

5 Evaluate each alternative, using sensitivity analysis to enhance the

evaluation

6 Select the b e t alternative

7 Implement the solution

8 Monitor the results

Engineering economy has a major role in all steps and is primary to steps 2 through 6 Steos 2 and 3 establish the alternatives and make the estimates for

economy models to complete the evaluation and perform any sensitiviti analysis upon which a decision is based (step 6)

The concept of the rime value ofmoney was mentioned above It is often said

that money makes money The statement is indeed true, for if we elect to invest maney today, we inherently expect to have more money in the future If a per- son or company borrows money today, by tomorrow more than thc original loan principal will be owed This fact is also explained by ihe time value of money

The change in the amount of money over a given time period i s called the

hme value of money; it is the most important concept in engineering

economy

1.3 PERFORMING AN ENGINEERING ECONOMY STUDY

Consider the terms engineering eco,loszy, eengineerirtg econonric nnnlysis, eco-

rzomic decisiorz mnking, cnpifnl allocoliotr snrdx eco,lontic nnnlysis and similar

terms to be synonymous throughout this book There is a eeneral anoroach

Alternative Description The result ofdecision-making process step 1 is a basic

understanding of what the problem requires for solution There may initially be

many alternatives, but only a fcw will be fcasible and actually evaluated IL

alternatives A, B, and c have been identified for analysis, when methad D, 1 Cash Flows The estimilted inflows (revenues) and outflows (costs) of money

though not recognized as an alternative, is thc must attractive, the wrong decision

I are called cash flows These estirnotes are made for each alternative (st$ ;)

~ l t ~are stand-alone options that involve a word description and best ~ ~ t i ~ ~ ~ i study can be conducted Expecred variation ir,, cash flows indicates a real need

estimates of oarameters, such asfirst cosr (including purchase price develop- ! for sensitivity analysis in step 5

merit, i n s t ~ ~ ~ a t i o n j , useful life, ~ssli~noted nrtni~ul incontes ond expenses, s a l w e

voler or trade-in value), an ir~ieresr rare (rate of return), and possibly i * l ~

&tion and incollle tax c f f e ~ s Estimates of annual expenses are usually lilmped

i

Analyris Usirrg Engineering Econo,ny Computations that consider the tirne

together and called annual operating casts (AOC) or maintenance and Operation

i value of money arc pcifomed measure of worth on the cash flows of each alternative to obtain the

expected 10% Der )fear retunl Some combination of economic criteria urino the ~~~~ - ~~~~

measure of worth, and the nancconon>ic and intangible factors, miry be applied

Lo help sclect onc alternative

If only one feasible altemative is defincd, a sccoild is often present in the form

of the do-nothing airemativc This is the as-is or strittrs yrro alternative Do noth- ~ l m o u l i n z ing can be selected if no alternative has a favorable measure of worth

Whether we are aware ofit or not, we use cnlcria every day to choose between alternatives For example, when you drive to campus you decide to takc the Chap

'best"roule But how did you define bert? Was the best route the safest, shortest, fastest, cheapest, most scenic, or what? Obviously, depending upon which crite- rion or combination of criteria is used to identify the bca, a different route might

be selected each time In economic analysis,finaricinl unin (dollars or other cur- rency) are generally used as the tangible basis far cvaluatian Thus, when there are seveml ways of accol~lplishing a stated ubjective the alternative with the

~ ~ lowest overall cost or highest overall net income issclected ~~ ~ ~ ~~

' An afrer-tau nrtalysis is perfamed during prcject evaluation, usually with

only sianificant effects far asset deoreciatioi~ m d income taxcs accounted f o i - Taxes imposed by local, stale, feder;il, and international governments usually lake the formof an income lax on revenues, value-added tax (VAT), impon taxes, sales taxes, real estate taxes, and othcrs Taxes affect alternative estimates for

cash flows; they lend to improve cash Bow estimates for expenses, cost savings, and asset depreciation, while they reduce cash Row estimates for revenue and after-tax net income This tent delays the details of aftertax analysis until the fundamental tools a d techniques of engineeriug economy are covercd Until then, it is assumed that all alternatives are taxed equally by picvailing tax laws

(If the cffects of taxes must be considered carlier, it is recornmended that Chap-

t e n 16 and 17 be covered after Chapter 6.8 or 11.) Now, we turn to same fundamentals of engineering economy that are applic-

able in the everyday life of engineering practice, us well as personal decision

making

12 CHAPTER I Fuundvtlons of Engtneerlng Economy

1.4 INTEREST RATE AND RATE OF RETURN

Interest is the manifestation of the time value of money Computationally, inter-

est is the difference between an ending amount of money and the beginning amount If thedifferenceis zeroor negative, there is no interest There arealways two perspectives to an amount of interest-interest paid and interest earned In- terest is paid when a person or organization borrowed money (obtained a loan) and repays a larger amount Intercst is eunred when a person or organization saved, invested, or lent money and obtains a return of a largcr amount It is shown below that the computations and numerical valuei are essentially the

same for both perspectives, but there are different interpretations

, L o

1, , mm,er~iatc I Interest paid on bormwed funds (a loan) is determined by using the relation

Interest = amount owed now - original amount l1.11 When interest paid over a s,~+clfic lime unit is expressed as a percentage of the

original amount (plincipal), the result is called the interest mre

interest accrued per time unit

The time unit of the rateis called the interestperiod By far the most commonin- terest period used to state an interest rate is 1 year Shorter time periods can be used, such as, I% per month Thus, the interest period of the interest rate should always be included If only the rate is stated, far example, 8.5% a I-year inter- est period is assumed

I L C ~ C In; plan I h lrrou S21,01,, from 3 b.nl cur I ) r u !l Y- IIIICIL ~ for n: $ r ; ~ r l rb ; 1 4 ~ 1 ~ ~ # r $ t t ., C Y I O ~ I ~ I : I I C inlcrc\c a8.J I I C toll1 .lnl.ldnl Jus ahcr

;e' I )cnr ( b C~,4,ar ;r ., ; ~ l ~ r n ~ l ,.rrplt lcba j18nu5 tl8c IIIIII arn.,l>ni ,nd 1~ 1.1

C a n ~ c t ~ n , ~ a : ~ c c r I tu>cd i n c o r n p ~ r ~ ihu b,.n in~ rr.~r rare oi i r b pel )

SECTION 1.4

From thc perspective of a saver, a lender, or an investor, interest earned is the

/ ~ n ~ ~ m e s r a L a i d r u m I

final amount minus the initial amount, or principal

Interest earned = total amount now - original amount Interest earned aver a specific period of time is expressed as a percentage of the original amount and is called rote ofrearm (ROR)

Sruii Rank

interert accrued per time unit Rate of return (90) = originalamount x 100% [lA]

i

The time unit for rvte of reern is called the inrer-esrperiod, just as for the bar- rawer's perspective Again, the most common pcriad is 1 year

The term ,-elurn on invesrr?rerir (ROlJ is used equivalently with RORindifferent

industries and settings, especially where large capital funds are committed m

engineering-oriented progruins

The numerical values in Equation [1.2] and Equation [1.4] are the same, but the term inrer-esi rnre paid is more apprapnate for the borrower's perspective, while the role of rerurn eonzed is better far the investor's perspective

.,~ ~, .~ In Eivmnles 1.3 to 1.5 the interesroeriodwas 1 vear;and~theinrcrest amount^

e:.11101111~ :< ~ n , J ~ r ~ l # u n f a n) ',ng~n;~.ring :;on.,nl) i t ~ J y I.;

C O I ~ J I ~ ~ ~ ! S~.>cr.,l L ) ~ I ~ ~ C I I I ~ .IIXIUI th: i u ~ J ~ m c n t ~ l i u t nrl.~t~.m ~re aurdntcd at

this early stage First, inflation represents a decrease in the value of a given cur- rency That is, $1 now will not purchase the same number of apples (or most other things) as $1 did 20 years ago The changing value of the currency affects

market interest rates In simple terms, bank interest mtes reflect two things: a so-called rcal rate ofreturnplur the expected inflation rate The real rate ofreturn allows the investor to purchase more than he or she could have purchased before the investment The safest investments (such as U.S government bonds) typi- cally have a 3% to 4% real rate of return built into their overall interest rates

Thus, an interest rate of, say, 9% pnryear on aU.S government hondmeans that

investors expect the inflation rate to be in the range of 5 % to 6% per year

Clearly, then, inflation causes interest rates to rise

SECTION 1 5 Equlvvlence

investment Inflation means that cost and revenue cash flaw estimates increase over time This increase is due to the chanoine value of money that is forced upon

A reduction in purchasing power of the currency

- An increase in the CPI (consumer price index)

An increase in the cost of equipment and its maintenance ~

An increase in the cost of salaried professionals and hourly employees

Areduction in ihi real rite of return on pefsonal'sai'ings and certain corporate investments

In other words, inflation can materially contribute to changes in corporate and personal economic analysis

Commonly, engineering economy studies assume that inflation affects all es- timated values equally Accordingly, an interest rate or rvte olreturn, such as 8%

per year, is applied throughout the analysis without accounting for an additional inflation rate However if inflation were exlllicitly taken into account, and it ~ was

reducing the value of money at, say, an average of 4% per year, it would be nec-

~ ; c a r u ro nerfnrm the economic analvsis usine an inflated interest rvte of 12.32%

rateaf 4% per year results in a real rate of return of only 3.85% per year!

1.5 EQUIVALENCE

- - Equiudent-terms are.used.very ofteni~themnsfe~ir~~n~one~~_~~~!efo~a~narher~

Some common equivalencies or cat~versions are as fallows:

Length: 100 centimeters = I meter 1000 meters = 1 kilometer I2 inches = 1 foot 3 feet = 1 yard 39.370 inches = I meter 'pressure: 1 atmosphere = 1 newtonlmete?

1 atmosphere = 10' = 1 kilopascal Many equivalent measures are a combination of two or more scales For example,

110 kilometers per hour (kph) is equivalen~ to 68 miles per hour (mph) or 1.133 miles per minute, basedon theequivalence that 1 mile = 1.6093 kilometers and 1 hour = 60 minutes We can funher conclude that driving at approni- mately 68 mph for 2 hours is equivalent to traveling a total of about 220 kilamc- tets, or 136 miles Three scales-time in hours, length in miles, and length in kilometers-arecombined to develop equivalent statements An additional use of these equivalencies is to estimate driving time in hours between two cities using twomaps, oneindicating distance in miles, asecond showing kilometers Note lhat throughout these statements the fundamental relation 1 mile = 1.6093 kilometers

is used If this relition changes, then the other equivalencies would be in error

16 CHAPTER I Faundvtlon~ of Engmeenng Economy

When considered together, the time value of money and the interest rate help

d e v e l o ~ the conceDl of economic equiwlence, which means that dtfferent sums

o f money at different times would be equal in economic value For example, if the interest rate is 6% per year, $100 today (present time) is equivalent ta $106 one year from taday

Amount accrued = 100 + lOU(0.06) = 100(1 + 0.06) = $106

So, if someone offered yo" a gift of $100 today or $106 one yea from taday, it wouldm~kenndifferencewhich offer youaccepted fromaneconomicperspective

In either case you have$106one yearfrnmtoday However, the two sums ofmoney are equivalent to each other only when the interest rate is 6% per year At a higher

or lower interest rate, $100 taday is not equivalent to $106 one year from today

In addition to future equivalence, we can apply the same logic to determine equivalence for previous years Atotal of$100 now is equivalent to $100/1.06 =

$94.34 one year aeo at an interest rate of 6% Derveur From these illustrations we

6 x 100% = 6% per year

$100 and

$5.6(, X 100% = 6% per year

$94 34 Figure 1-3 indicates the amount of interest each year necessary to make these three different amounts equivalent at 6% per year

SECTION Simple and Cornpuund

1.6 SIMPLE A N D COMPOUND INTEREST

The terms Ozrerert interest oeriod and interest ralc (introduced in Section 1.4)

an: 11~~!1111 111 c.lilll.!l,ll: :., I,,\ .Ic"~ hUIII, >I "lOllU! IN .IIlC Il,lr:crl , > c ~ , I I t t l l i ' C - 1

1>.1,t LINI ,IIW pcrt0.1 (1.c i u t ~ c ~ ; Ildw:! zr, i,>r ~ n h ~ r ? ci>:!n mt, $nk.r:\[ 1pe,1& t h

~ c r t n , ,,,n/>Ie, it!,, m J ,, W / > ~ , ! ~ < I , I u.1e ,< ,! l>c.wnt; tt~q>orc.,~t

.SunpIe t , , , ~ r ~ ~ t I~L:IICUILI:J ust412 the pr~~t l> l ~ > l ) gnd<.n: ",I> ~I>~:I:,I :

r w J tn nre~.: lhrht! > I I ~ C < : \ I n:rdocl~ I lhc ld:#I \!<!t~>l: L ~ , L c ~ ~ A I .,\? ,e\crdl o.mdl> -

1s computed as

Interest = (principal)(number of periods)(interest rate) [1.5]

where the Interest rate is expressed m decrmal form

19'11 (~1z.t ISJIJIII!)(IE~~~)U! P J ~ J J J B 118 + j c d p a ! ~ d ) = ) S ~ J J I ~ ~

sc palelnqez s! popad aun lo, IsaJalu! arll

A ~ O N 'osle Isazalu! aql uo Aauoru~o anlsn am!] aql JO IsaJJa all1 s13ayal ~ s a a ~ u ! punoduro3 'Isaralu! jo do1 ua salalu! sueam 1 s a ~ a s ! punodluo~ ' s n q ~ -spu!~ari snmnard [lo t palolntrrn~~a Jraralrr!/o ~tniou,u lo801 ay, srrjd ,ad!3u!rd aql uo

Palcln31== s! po!~ad isalalu! q x a JOJ PJWJJP I S ~ ~ I U ! aql ?raarrq pa,zodtrro? J O ~

CHAFTER 1 Foundarlona of Englnecnng Ecanomy I SECTION 1 6 Sllnplc md Compound Inleie\t

Another and shorter way to calculate the total amount due after 3 years in

Example 1.8 is to combine calculations rather than perform them on a yearby-

year basis The total due each year is as follows:

Year 1: $1000(l.05)1 = $1050.00 ,

Year2: $1000(1.05)' = $1 102.50 Year 3: $1000(1.05)' = $1157.63 The year 3 total is calculated directly; it does not require the 2 total In gen-

eral formula form

Total due after a number of years = principal(1 + interest rate)"Ol"becY'y"EY'

This fundamental relation is used many times in upcoming chapters

We combine the concepts of interest rate, simple inlerest, compound interest,

and equivalence to demonstrate that different loan repayment plans may be

equivalent, but differ substantially in monetary amaunts from one year to an-

other This also shows that there are many ways to take into account the time

Vdlue of money The follawing example illustrates equivalence for five different

loan repayment plans

1.1, i>cmoi.suaa 1112 cun:rpc I tq~,~aleu;r ~ # n : lhc J ~ i i c r m t I j.,n z~~Iu).JI~.~N

plan% Jr%.nk.l hcluw P1:h plrl rep:%) r jS(n!D lol! t m 5 )c.x, z R'i .I, '.m,c

!f.e eo I 'f ye.# 5 Ic8tcrc.d ,c: 81nt8Iac~~~cd;c ." (h: l,c#ttc~g~.~l "1:

I.*

- Plan 2: O~lnpu~mnd intcrest,la? a l l a t end So inwrcr( .r ir.scoprl I p.8~

? -.?I81 (he end of ! e x 5 lnlcrsrt mulac lac ~ j z h yrrr ou rl>e I I I 11 u i pnt,.~

p d r8.J d ;~;:nll*l mtcrcv

(i

: Pbn): S i m p l t i n t c m l paid annuallv, principal w p r i d at end I i c m r l

mtere,, #>pa! l c ~ c ~ )eu,~ndth< :ott,c pnnc~pdl ccpd#J.~ ~ h e c t ~ ~ ,,t ) < , ~ r j

I'lan ?: (:nmpuunal inlerr4 nlld l l n n i u n ul prinripdl re(vn~8t m n u ~ l l !

'lhc ~ : c m : l #t>tcre<c A ~ L J ,~ne.fifch c i t l t ~ p n ~ ~ : p : t l j l < L j) t * r ~ ~ ~ i ~ , , , l

I

I The equalions and piocedurcs of engineeriug economy utilize the following

terms and symbols Sample units are illdicated

r

i P % I,,<! r 't,,,<l,,.t d l tnd":! :,.,I,, < < I ~ , , ~ " ~ L \ I - \ 11,: p,:\<,,t %.<

I I ~ I ~ V 1, \ 1 1 % r:i~,,<cJ , )a% pr.\c 81, u,,rth I*\\ , prct:~, !,,l.c

1 capitalized cost (CC); dollars

I f = value or amount of money at some future time.Also F i s called

~ ~ future worth (FW) and future value (FV); dollars

n =number of intercst periods; ycars, months, days

i = interest rate or rate ofreturn per rime period: pcrcent per y e a ,

percent per moolll; percent per day

t = time, stated in periods; y e a s , months, days The symbols P and f represeni one-time occurrences: A occuis with the same value once each interest period for a specified number of periods It should bc clear that a prcsenl value P iepresents a single sum of money at some lime prior lo a future value F or prior to the first occurrence of an equivalent series amount A

It is important to note that the symbol A always represents a uniform amount (i.e., the same amount each period) that extends through consect~rR,e

& t e r e ~ < p g o d > , B ~ t l ~ = o n d i t i " " s !m>stenist before the seiics_c_an~be~ rcpre:~~ ~ ~ -~

senled by A

The illterest ntB i is assumed to bc a compound rule, unless specifically stated

as simple interest The rate i is expressed in perccnl per interest period, for enample, 12% per year Unless stated olherwise, assume that the rate applies throughout the cntire n years or interest periods The decimal equivalent for i is always used in engineering economy computations

All engineering economy problems involve the element of time n and interest rate i In general cvery problem will invalvc at least four of the symbols P, f, A,

tr, and i, with at least three of them estimated or known

CHAPTER i FoundaUonr of Engmeenng Economy

In Examples 1.10 and 1.11, the P value is a receipt to the borrower, and F o r

A is a disburseinent from the borrower I t is equally correct to use these symbols

in thc reverse roles

CHAPTER I Fouodatioia of Engineering Economy

1.8 INTRODUCTIONTO SOLUTION BY COMPUTER

The functions on a computer spreadsheet cun greatly reduce the amount of hand

and calculator work lor equivalency computations involving conrpou,,d hcferesf

and the tenns P , F, A, i, and s The power of the electronic spreadsheet often

makes it possible to enter a predefined spreadsheet function into one cell and

obtain the final answer immediately Any spreadsheet systcm can be used-ne

off the shelf, such as Microsaft Excelo, ar one specially dcvelopcd with built-in

financial functions and operators Excel is used througi~out Uus b w k because it

is rcadilv available and easv , m ~~ inse ~-

Appendix A is a primer on using spreadsheets and Excel The functions used

in engineering economy are described there in detail, with explanations of all the

parameters (also called arguments) placed between parentheses after thc function

identifier The Excel online lhelp function provides similar information Appen-

dix A also includes a section on spreadsheet layout that is useful when the eco-

nomic analysis is presented to someone else-a coworker, a bass, or a professor

A total of six Excel functions can pcrform most of the fundalnental engineer-

ing economy calculations However, these functions are no substitute for know-

ing how the time value of money and compound interest work The functions are

great supplemental tools, but they do not replace the understanding of engineer-

ing economy relations, assumptions, and techniques

Using the symbols P, F,A, i, and ,t exactly as defined in the previous section,

the Excel functions mast used in engineering cconomic analysis are formulated

as follows

To find the present valuc P : PV(i%,rz,A,F)

To find the future value F: FV(i%,rz,A,P)

To find the equal, periodic value A: PMT(i%,tj,P,E)

To lind the number of periods ,r: NPER(i%,A,P.F)

Ib findthe compound interest rate i: RATE(r,,A,P,F)-' -

To find the compound interest rate i: IRR(first_cell:last_cell)

To find the present value P of any series: NPV(W, secand~cell:last_ceU) +

first~ccll

If some of the parameters don't apply to a particular problem, they can be

omitted and zero is assumed If the p-mcler omitted is a n interior one, the

comma must be entererl The last two functions require that a series of numbers

beentered into contiguous spreadsheet cells, but the first fivecan beused with no

supportingdata Inall cases, the function must be preceded by an equals sign (=)

in the cell whcre the answer is to be displayed

Each of these functions will be inuoduced and illustmled at the point in this

tent where they are most useful However, to gel an idea of how they work, look

back at E n a m ~ l e s 1.10 and 1.11 In Enamole 1.10 the future amount ~ ~~~ ~ F is ~ ~nn-

known, as indicated by F = ? i n the solution In the next chapter, we will learn

how the time value of money is uied to find F, given P, i, and n To find F in this

example using a spreadsheet, simply enter the FV function preceded by an equals

SECTION 1.8 - ~ntrodvction to Solution by Computer 27 ;$

of the Excel spreadsheet with the FV function entered into cell B2 The answer

of 6-14.693.28 is displayed l b e answer is in red on the actual Excel screen to

indicate a negative amount from the borrower's perspective to repay the loan after 5 years The W function is shown in the formula bar above the worksheet itself Also, we have added a cell tag to show the format of the W function

In Example 1.11, the uniform annual amount A is sought, and P , i, and n are known Find A, using the function PMT(i%,n,P) or, in this example,

PMT(7%,10,2000) Figure 1-56 shows the result in cell C4 The format of the

FV function is shown in the formula bar and the cell tag

I l a n d 14

ili

CHAPIER I Foundations of Engineering Ecmomy

I3c:3u\c lllsje i u n ~ t o n ~ c : ~ n h: ussJ sos:trtl) ~nd rdplJl), u c all1 J~.ta11 ~ ~ C I I I

~n many uf thr i.x.tmplcr IIIIJU;II.IIII the 1h81~l, A q)e;lal chc:kcrell-tll: ~:m

u ttl~ @-5vl\, (tor q ~ c k ~ ~ l u t n , u J prlnte.1 ,I, 11, 1, plxc:J ill the in:,rvin u,nco~ tu.t

one function is needed to get ananswer In the introductory chapfen of ~ e v e l

One, the entire spreadsheet and detailed functions are shown In succeeding

chapters, the Q-Solv icanis shown in the margin, and the spreadsheet function is

contained within the solution of the example

When the power of the computer is used to salve a more complex problem utilizin~ several functions and oossiblv an Excel c h m (eraoh) the icon in the

example is always presented after the Solution bv and As menliokd earlier

1.9 M I N I M U M ATTRACTIVE RATE OF RETURN

For any investment to be profitable, the investor (corporate orindividual) expects

to receive more money than the amount invested In other words, a fair rote of

rerun:, or relron on invest?ne,rt, must be realizable The definition of ROR in

Equation 11.41 is used in this discussion, that is, amount earned divided by the

original mount

Engineering alternatives are evaluated upon the prognosis that a reasonable ROR can be expected Therefore, some reasonable rate must be established for

the selection criteria phase of the engineering economy study (Figure I-I) The

reasonable rate is called the Minimum Allmctive Rate of Return (MARRI and i s

sometimes used as the benchmark safe rate

The MARR is also referred to as the hurdle rare for projects: that is, to be considered financially viable theexpected ROR must meet or exceed the MARR

or hurdle rate Note that the MARR is not a rate that is calculated like a ROR

The MARR is establiihed by (financial) managers and is used as s criterion

against which an alternative's ROR is measured, when making the acceptlreject

decision

To develop a foundation-level understanding of how a MARR value is estab-

lished and used, we must return to the term capital introduced in Section 1.1

Capital is also referred to its capital fi<n<ls [sand capitol investment mo,,e)i it

always costs money in the form of interest to mise capital The interest, stated as

a percentage rate, is called the cort of car,irnl For examole if vou want to nur-

SECTION 1.9 Attractive Rate af Return

"TIYCS

I l p e c s d rate of return on

r ncw pmposrt

nav off the balance on a monthly basis This aoorovch will probably cost you at

ing In analogous ways, corporations estimate the cost oC capital from different

sources to raise funds for engineering projects and other types of projects

In general, capital is developed in two ways-quity financing and debt financing Acomhinatian of these two is very common for mast projects Chap- ter 10 covers these in greater detail, but a snapshot description follows

Equity financing The corporation uses its own funds from cash on hand, stock sales, or retained earnings Individuals can use their own cash, saw

ings, or investments In the example above, using money fiom the 5%

savines account is eauitv financinn

Table 1-3 Sources ofdebt capital may be bonds, loans, mortzages, venture capital pools, and many others Individuals, too, can utilize debt sources, such as the credit card and credit union options described in the music sys- tem example

Combinations ofdebt-equity financingmean that a weighted average cost ofcap- ital (WACC) resulls If the lnusic system is purchased with 40% credit card money at 18% pel year and 60% savings account funds earning 5% per year, the weighted averagecost of capital is 0.4(18) + 0.6(5) = 10.2% per year

For a corporation, the esiablishedMARR used as a criterion to accept or reject

an alternntive will always be higher than the tr,eiglired overage cosr ofcripitul

that the corporation must be= to obtain the necessary capital funds So the in- eaualitv

SECTION 1.10 Cash Flows: TheiiEstirnation and Diqramlnino

Samples ol Cash Inflow Estimatcr

Revenues (usually increnzerttal resulting from an alternative)

Operating cost reductions (resulting fmm an alternative)

Asset salvage value

Receipt of loan principal

Income tan savings

Receipts from stock and bond sales

ROR r MARR > cost of capital

Construction and facility cost savings

11.71 1 Savine or return of coreorate c a ~ i t a l funds

must be correct for an accepted project Exceptions may be government-regulated Corh oa~JIo,vs, or disbursements, may be comprised of the fallowing, again

~~~

~ ~

~~~ requirements (safely, security, environmental, legal, etc.), economically lucrative depending upon the nature of the activity and type of business

ventures expected to lead to other opportunities, etc Value-added engineering projects usually follow Equation [1.7]

Often there are many alternatives that are expected to yield a ROR that ex- ceeds the MARR as indicated in Figure 1-6, but there may not bc sufficient capital available far all, or the project's risk may be estimated as too high to take the investment chance Therefore, new projects that arc undertaken are usually those projects that have an expected return at least as great as the re- turn on another alternative not yet funded Such a selected new project would

be a proposal represented by the top ROR arrow in Figure 1 4 For example, assume MARR = 12% and proposal 1 with an expected ROR = 13% cannot

be funded due to a lack of capital funds Meanwhile, proposal 2 has a ROR = 14.5% and is funded from available capital Since proposal 1 is not undertaken due to the lack of capital, its estimated RORof 13% is referred to as the

oi,poHenify cosf; that is, b e opportunity to make an additional 13% return is forgone

~ - ~ ~

1.10 CASH FLOWS: THEIR ESTIMATION AND DIAGRAMMING

In Section 1.3 cash flows are described as the inflows and outflows of money

These cash flows may be estimates or observed values Every person or company

has cash receipts-revenue and income (inflows): and cash disbursernents- expenses, and costs (outflows) These receipts and disbursements are thc cash flows, with u plus sign representing cash inflows and a minus sign represent- ing cash outflows Cash flows occur during specified periods of time, such as

1 month nr 1 vnar

~ ~ ,

Of all the elements of the engineering economy study approach (Figure 1-1)

cash flow estimation is likely the most difficult and inexact Cash flaw estimates are just that-stimates about an uncertain future Once estimated, the tech- niques of this book guide the decision making process But the time-proven accuracy of an alternative's estimated cash inflows and outflows clearly dictates the quality of the economic analysis and conclusion

Cash i n j o w ~ , or receipts, may be comprised of the following, depending upon the nature of the proposed activity and the type of business involved

San~ples of Cash Outflow Estimatec First cost of assets

Engineering design costs

Operating casts (annual and incremental)

Periodic maintenance and rebuild cosLs

Loan interest and principal payments

Major expected/unexpected upgrade costs

Income taxes Expenditure of corporate capital funds

Background information for estimates may be available in departments such as accounting, finance, marketing, sales, engineering, design, manufacturing, pro- duction, field services, and computer services The accuracy of estimates is largely dependent upon the experiences of the person making the estimate with

similar situations Usually point estimates are made; that is, a single-value esti- mate is developed for each economic element of an'altemative If a statistical ap=- proach to the engineering economy study is undetlaken, a range estimate or dis-

rribuiiorz estimnte may be developed Though more involved camputatianally, a statistical study provides mare complete results when key estimates are expected

to vary widely We will use paint estimates throughout most of this book Final chapters discuss decision m a z n g under risk

Once the cash inflow and outflow estimates are developed, the net cash flaw can be determined

Net cash Row = rceeipts - disbursements

= cash inflows - cash outflows 11.81 Since cash flows normally take place at varying times within an interest period,

a simplifying assumption is made

,

T h e end-of-period convertlion means that all cash Rows are assumed t o

':I bursemenis occur within a given interest period, the net cash flow is

assumed t o occur a t the end of the interest period

~*

However, it should be understood that, although F o r A amounts are located at the end of the interest period by convention, the end af the period is not neces-

sarily December 31 In Example 1.12 the deposit took place on July 1, 2002, and the withdrawals will take place on July 1 of each succeeding year far

10 yean Thus, endof rheperiodrneans end of interestperiod, ,tot mdof colendnr yea,:

The cash flow diagram is a very important tool in an economic analysis, es- pecially when the cash flow series is complex It is a graphical representation

of cash flows d n w n on a time scale The diagram includes what is known, what is estimated, and what is needed That is, once the cash flow diagram is complete, another person should be able to work the problem by looking at the diagram

Cash flow diagram time r = 0 is the present, and t = 1 is the end of time period 1 We assume that the periods are in years for now The lime scale of Figure 1-7 is set up for 5 yea& Since the end-of-year convention places cash flows at the end of years, theyl" marks the end of year 1

While it is not necessary tp use an exact scale on the cash flow diagram, you will probably avoid errors ifyou make a neat diagram to approximate scale for both time and relative cash flow magnitudes

The direction of the arrows an the cash flow diagram is imponant A vertical

amow pointing up indicates a positive cash flow Conversely, an arrow pointing down indicates a negative cash flow Figure 1-8 illustrates areceipt (cashinflow)

at the end of year 1 and equal disbursements (cash outflows) at theend of years 2 and 3

The perspective or vantage point must be determined prior to placing a sign

on each cash flow and diagammingit.As an illustration, if you borrow $2500 to buy a $2000 used Harley-Davidson for cash, and you use the remaining $500 for a new paint job, there may be several different perspectives taken Possible

Example ofpostiive and

negative cash flows I 4

SECTION I LO

perspectwes, cash flow signs, and amounts are as follows

Perspective Cash Flow 6

You as borrower i25OO YO" as purchaser - 2 0 0 and as prrnt customer 5 0 Used cycle dealer + 2 0 O

CHATTER I Foundrt~ona of Eng~neenng Economy t SECTION I I1 Rule 01 72 EIllrnvtxng Doubling T~me and Interert Rate 35

1.11 RULE OF 72: ESTIMATING DOUBLING TIME AND INTEREST RATE

Sornetimes it is helpful to estimate thc number of years n or the rate of return i required for a single c a ~ h Bow amount ta double in size The rule of 72 for com- pound interest rates can be used to estimate i or a, gi\,en the other value The estimation is simple; the time required for an initial single amount to double in size with compound interest is approximately eqttal lo 72 divided by the rate of return in percent

72

- For example, a t a rate of 5% per ycar, it would take approximately 7215 =

14.4 years for a current amount to double (The actual time required is 14.3 years, us will be shown in Chapter 2.) Table 1 4 compares the times estimated from the rule of 72 to the actual rimes required for doubling at several com- pounded rates As you can see, very good estimates are obtained

Alternatively, the compound rate i in percent required for money to double in

a specifiedperiod of time ?z can be estimated by dividing 72 by the specified n

If the interest is simple, a rule of 100 may be used in the same way In this case

the answers obtained will always be exactly correct As illustrations, money dou-

bles in exactly 12 y e a s at 100/1? =-833%simple interest Or, at 5% simple i n - ~ terest it takes exactly 10015 = 2 0 years to double

CHAPTER I Foundrliuns of Engineering Economy

CASH FLOW ESTIMATES

Thc example below demonstrates how an Excel spreadsheet can be used to

obtain eauivalcnt futurevalues.Akev featureis the useof mathematical relations

developed in the cells to perform sensitivity analysis for changing cash Row

estimates and the interest rate To answer these basic questions using hand solu-

tion can be timeconsurning; the spreadsheet makes it much easier

ferto Figure I-l?olu

rrion bur tile coU v

SECTION 12 Spreadsheet AppI~cat~onStmple andcompound

I SECTION 1.12 Sprcvdsllcct Applicainn-Simple mil Compound b~ts~ert 39

ADDITIONAL EXAMPLES

CHAPTER 1 Foundvllona of Eng~meenng Economy CHAFER SUMMARY

The MARR is a reasonable rate of return established as a hurdle rate to deter- rninc if an alternative is economicallv viable The MARR is slwavs hieher than

i Also, we learned about cash flows:

i Difficulties with their estimation

I Difference between estimated and actual villue End-of-year convention for cash flow location

3 yeus Haw would the cash Row diagram appev if i = 8 i Different perspectives in determining the cash flow sign

i Construction of a cvsh flow diagram

42 CHAPTER I Foundal~onr Economy

X 1 I z x

PROBLEMS

1.1 What is meant by the term tinre value of rate on the loan?

1.2 List three intangible factors pleted apipeline project wherein he tom-

pany realized a profit of $2.3 million in 1.3 ( 0 ) What is meantby evaluationcriterion? I year If the amount of money ihe com-

(b) What i s theprimaryevaluationcrite- pany had invested was $6 million, what

rion llsed in economic analysis? was the rate of return on the investment?

1.6 What is the difference between simple and 1 1 4 A publicly traded cot~stnrction company

compound interest? reported that it just paid off a losn that it

received 1 v e x earlirlier If thc total ~~ ~~ arnoilnr ~~~~~~~~~

1.7 What is meant by minimum attractive rate of money the company paid was $1.6 mil-

10% per year, how much money did the 1.8 What is the difference between debt and company borrow 1 year ago?

equity Gnancing?Giveane~am~leofeach 1.15 A comoilnv , has estah- ~ ~

lished a goal of makiug at least s 35% per

I n t e r s t Rate a n d R a t e of Return year

~~~ rate of return -~ ~~ ~ on its investment Ifthe 1.9 Tntcking giant Yellow Corp agreed to pur- company acquired $5&illion i n ientGe

chase rival Roadway for $966 million in capital, how much did it have to earn in

order to reduce so-called back-office costs the first year?

(eg payroll and insurance) by $45 mil-

lion per Year If the savings were realized

as plamed, what would be the rate of

return an the investment?

1.10 11 Ford Motor Company's profits in-

creased from 2 2 cents per share to 29 cents

Per share in the April-June quarter com-

pared to the previous quarter, what was the

rate of increase in p m L s for that quarter?

1.11 A broadband service company borowcd

$2 million for new equipment and repaid

the principal of the loan plus $275,000

Equivalence

1.17 A medium-size consulting engineering firm is trying to decide whether it should replace its office furniture now or wait and doit I year from now If it waits I year, the cost is expected to be $16,000 At an inter- est rate of 10% per year, what would be the equivalent cost now?

1.18 An investment of $40,000one year ago and $50,000 now are equivalent at what interest rate?

1.19 At what intcresl mte would $100,000 now

be equivalent to $80,000 one year ago?

Simple a n d Compound Interest Certain certificates of deposit accumulate interest at 10% per y e a simplc interest If

a commny invests $240.000 now in lhcse ccnificates for the purchase of a new ma- chine 3 vevrs from now how much will the company have at the end of the 3-year period?

1.21 A local bank is offering to pay cornpound interest of 7% per y e a on new savings accounts An e-bank is offering 7.5% per year simple interest on a 5-year cenificate

of deposit Which offer is mare attractive

to a canlpany that wants to set aside

$1,000,000 now for a plant expansion

5 years from now?

1.22 Badger Pump Company invested

$500.000 five years aeo in a new oroduct

pound interest basis?

1.23 How long will it L&e for an investment to

double at 5% per year (a) simple interest and (B) compound interest?

1.24 A company that manufactures regencra- live thermal oxidizers made an investment

10 yearsago that isnow worth$l,300,000

How much was the initial investment at

an interest rate of 15% per ycar (u) simple

interest and (b) compound interest?

1.25 Compmies frequently borrow money under an arrangement that requires them

to make periodic payments of only interest and then pay the principal of the loan all at

.26 A company that manufactures in-line mix- ers for bulk manufacturing is considering borrowing $1.75 million to update a pro- ductionline Ifitborrows themoney now,it

can do so at an interestrate of7.5% peryear simpleintcrcstfar5 years Ifitborrowsncxt vex the interest rvte will be 8% oer v e x

thc company borrow now or I year from now?Assume the total amount due will be paid when tlieloan is due in either case

Symbols and Spreadsheets

1.27 Define the sytnbols involved when a con-

struction compiny wants to know how much money it can spend 3 years fmln

1

~ now i n lieu of spending $50,000 now to purchasc a new truck, when i6iiompo""d~

.28 State the purpose for each of the following built-in Excel functions:

44 CHAFTER 1 Foundations of Engineering ljconorny

1.30 Write the engineering economy symbol

that corresponds to each of the following

1.31 In a built-in Excel function, if a certain

pammeter does not apply, under what

circumstances can it be left blank? When

must a comma be entered in its place?

MARR and Cast of Capital

1.32 Identify each.of the following as either a

safc investment or a risky one

i d ) Government bond

(e) Relative's "get-rich-quick" idea

1.33 Identify each of the following as either

equity or debt financing

( a ) Money from savings

(b) Money from a certificate of deposit

( c ) Money from a relative who is a part-

ner in the business

( d ) Bank loan

( e ) Credit card

1.34 Rank the following from highest to lowest

rate of return or interest rate: government

bond, corporate bond, credit card, bank

loan to new business, interest on checking

account

1.35 Rank the following from highest to lowest

interest rate: cost of capitdl, acceptable

rate of return on a risky investment, mini-

mum attractive rate ofreturn, rate of return

on a safe investment, interest on checking

account, interest on savings account

1.36 Five separate projects have calculated

rates of return of 8, 11, 12.4, 14, and 19%

per year An engineer wants to know which projects to accept on the basis of rate of return She learns from the finance department that company funds, which have a cost of capital of 18% per year, are commonly used to fund 25% of all capital projects Later, she is told that borrowed money is currently costing 10% per year

If the MARR is established at exactly the weighted average cost of capital, which projects should she accept?

Cash Flows 1.37 What is meant by the end-or-period con- vention?

1.38 Identify the following as cash inflows or outflows to Daimler-Chrvsler: income

vices, cost reductions

1.39 Construct a cash flow diagram for the fol- lowing cash flaws: $10,000 outflow at time zero,$3000per year outflow in ycars

1 through 3 and $9000 inflow in years 4

through 8 at an interest rate of 10% per year, and an unknown future amount in year 8;

1.40 Construct a cash flow diagram to find the present worth of a future outflow of

$40,000 in year5 at an interest rate of 15%

per year Doubling the Value 1.41 Use the rule of 72 to estin~ate the time it would take for an initial investment of

$10,000 to accumulate to $20,000 at a compound rate of 8% per year

1.42 Estimate the time it wauld take (according

to the ~ l e of 72) for money to quadruple

in value at a compound interest mte of 9% per year

1.43 Use the rule of 72 to estimate the interest rate that wauld be required for $5000 to accumulate to $10,000 in 4 years

1.44 If you now have $62,500 in your retire-

I rnent account and you want to retire when

1.45 An example of an intangible factor is

(c) 15 years

( d ) 20 years

the account is worth $2 million, estimate the rate of return that the account must eam if you want to retire in 20 years without adding any more money to the account

comoound rate of return earned on the in- vestment is closest to

(c) Costs the least

( d ) Is most politically correct 1.47 At a compound interest rate of 10% per 1.50 The cost of tuition at a certain public uni-

year, $10,000 one year ago is now equiva- versity was $160 per credit-hour 5 years

(c) 8%

1.48 An investment of $10,000 nine years ago ( d ) 10%

has accumulated to $20,000 now The

m

-EXTENDED EXERCISE

EFFECTS OF COMPOUND INTEREST

In an effan to maintain compliance with noise emission standards on the pro- cessing floor, National Semiconductors requires the use of noise-measuring in- struments The company plans to purchase new portable systems at the end of next year at a cost of $9000 each National estimates the maintenance cost to be

$500 per year for 3 years, after which they will be salvaged for $2000 each

46 CHAPTER I Foundatmns Englneenng Economy

Questions

I Construct the cash Row diagram Far a compound interest rate of 8% per

Esolro year, find the equivalent Fvalue after 4 years, using calculations by hand

2 Find the F value in question 1, using a spreadsheet

3 Find the F value if the maintenance costs are $300, $500, and $1000 for each of the 3 years By how much has theFvalue changed?

4 Find the Fvalue in question 1 in terms of dollars needed in the future with

an adjustment for innation of 4% per year This increases the interest rate from 870 to 12.32% per year

Factors: How Time and

Interest Affect Money

In the previous chapter we learned the basic concepts of engineering econ-

omy and their role in decision making The cash flow is fundamental t o every

economic study Cash flows occur in many configurations and amounts-

isolated single values, series that are uniform, and series that increase or

decrease by constant amounts or constant percentages This chapter devel-

ops derivations for all the commonly used engineering economy factors that

take the time value of monev into ,, accaunt~ ~~~ ~~

The application of factors is illustrated using their mathematical forms and

a standard notation format Spreadsheet functions are introduced in orderto

rapidly work with cash flow series and to ~ e r i o r m sensitiviw analvsis , ,

The case study focuses on the slgnlf~cant Impacts that compound interest

and tlme make on the value and amount of money

This chapter will heip you:

2 Derive and use the uoHorm serier present worth and capital

5 , ~~~i~~ and "se the arithmetic gradient present wonh and

I uniform series factors

6 Derive and use the gradient series foimulas

I

7 Determine the interest rate (rate of return) for a sequence of

cash flows

of years required for equivaience in a

to perform basic seosit\vity analysis

Facton: How Time 2.1 SINGLE-PAYMENT FACTORS ( F I P A N D P / F ) The most fundamental factor in engineering economy is the one that determines the amount of money F accumulated after n years (or periods) from a single pre- sent worth I: with interest compounded one time peryear (or period) Recall that compound interest refen to interest paid on top of interest Therefore, if an amount P is invested at time f = 0, the anlount F, accumulated 1 year hence at

an interest rate of i percent per year will be

where the interest w e is expressed in decimal form At the end of the second year, the amount accumuliltcd F2 is the amount after year 1 plus the interest from the end of year 1 to the end of year 2 on t l ~ e entire F,

This is the logic used in Chapter I for compound interest, specifically in Exam- ples 1.8 and 1.18 The amount F, can be expressed as

Similarly, the amount of money accumulated at the end of year 3, using Equa- tion [2.1], will be

The expression is brackets is known as the sirrgle-poyme,~tprcsenf >vonh/actor

(SPPWF), or the P I F factor: This expression determines the present worth P of

a given future amount Fafter n years at interest rate i The cvsh flow diagnm is shown in Figure 2-16,

Note thacthe two factors derived here &e for sirrglepaynzerrlc that is, they are used to find the present or future amount when only one payment or receipt is involved

A standard natation has been adopted for all factors The natation includes two cash flow symbols, the interest rate, and the number of periods It is always

in the general form (X/Y,i,n) The letter X represents what is sought, while the letter Yrepresents what is given For exilmple, F I P m e i l n s j n d F when given F!

The i is the interest mte in percent, and n rcpresentsthe number of periods in- volved Thus, (FIP,6%,20) represene the factor chat is used to calculate the future amount Faccumulvted in 20 periods if the interest rate is 6% per period

The P is given The standard notation, simpler to use than formulas and factor

To simplify routine engineeri.ng economy calculalions, tables of factor values have been prcpaied for interest rates from 0.25 to 50% and time periods from 1

to large ,I values, depending on the i value These tables, found at the rear of the

52 C H A F E R 2 Factois: How Timeand lnter$stAffect Money I SECTION 2.1 Single-Payment Factors ( F I P and P I F ) 53

book, are arranged with factors across the top and the number of periods n down the left The ward discrete in the title of each table emphasizes that these tables utilize the end-af-period convention and that interest is compounded once each interest period For agiven factor, interest rate, and time, the comect factor value

is found at the intersection of the factor name and n For example, the value of the factor (PIF,5%,10) is found in the PIF column of Table 10 at period 10 as 0.6139 This value is determined by using Equation [2.3]

1 (P/F,5%,10) =

For solution by compute,: the F value is calculated by the W function &ing the

5 4