## Engineering Economy

## Applying Theory to Practice

Third Edition

### Ted Eschenbach

## Table of Contents

**Part One: Basic Concepts and Tools**

**Chapter 1. Making Economic Decisions**

1.1 What Is Engineering Economy?

1.2 Principles for Decision Making

Common Measure

Include All Consequences

Only Differences Matter

Make Separable Decisions Separately

Adopt a Systems Viewpoint

Use a Common Planning Horizon

Address Uncertainty

1.3 The Decision-Making Process

1. Define Problem

2. Choose Objective(s)

3. Identify Alternatives

4. Evaluate Consequences

5. Select

6. Implement

7. Audit

Summary of the Decision Process

1.4 The Environment for Decisions

Nonlinear Process

Iterative Modeling and Spreadsheets

One Decision in a Continuing Stream

Importance of Communication Skills

Analysis vs. Action

Private and Public Politics

1.5 Ethics and Decision Making

Gaining Knowledge and Building Trust vs. Favors for Influence

Cost, Quality, and Functionality

The Environment We Live In

Safety and Cost

Emerging Issues and "Solutions"

Importance of Ethics in Engineering and Engineering Economy

1.6 The Role of Engineering Economy

Problem too Small to Merit Engineering Economy

Time Period too Short to Merit Engineering Economy

Engineering Economy Dominates Decision Making

Engineering Economy Is One Factor in Decision Making

1.6 Operational Economics

1.7 Summary

**Chapter 2. The Time Value of Money**

2.1 What Is Interest?

Interest Rates Vary

2.2 Simple vs. Compound Interest

Simple Interest

Compound Interest

2.3 Cash Flow Diagrams

Categories of Cash Flow

Timing of Cash Flows

It Is Better Not to Simplify the Cash Flow Diagrams

Drawing Cash Flow Diagrams with a Spreadsheet

2.4 Equivalence for Four Loans

Equivalence Defined

Calculating the Interest for Each Year

Finding an Equivalent Present Worth

2.5 Limits on Equivalence

Equivalence Depends on the Interest Rate

Equivalence with Respect to Time Value of Money Only

2.6 Compounding Periods Shorter than a Year

Compounding Periods Are M per Year

Nominal vs. Effective Interest

Continuous Compounding

2.7 Summary

**Chapter 3. Equivalence Ä a Factor Approach**

3.1 Definitions and Assumptions

Assumptions

Definitions

Reality and the Assumed Uniformity of A and G

3.2 Tables of Engineering Economy Factors

Factor Notation

Expanded Factors as Calculator Functions

Names of the Engineering Economy Factors

Format for the Interest Rate

Interpolation

Formulas vs. Factors

3.3 Single Payment Factors (Ps and Fs)

Formula Development

Tabulated Factors

(P/F) and (F/P) as a Function of i and N

3.4 Uniform Flows

Formula Development

Tabulated Factors

Calculating an Interest Rate

(A/P), (A/F), (P/A), and (F/A) vs. i and N

3.5 Combining Factors

Deferred Annuities

Annuities Due for Prepaid Expenses and Other Beginning-of-Year Cash Flows

Constructing Formulas from Cash Flow Diagrams

Deriving One Factor's Formula From Another's

3.6 Arithmetic Gradients

Definition

Using the Arithmetic Gradient Factors

Arithmetic Gradient Formulas

3.7 Geometric Gradients

Geometric Gradients Change at a Constant Rate

The Basic Geometric Formula

The Four Geometric Rates

Inflation

Mathematical Model for PW

Present Worth Formula for a Single Geometric Gradient

Using Equivalent Discount Rates for Geometric Gradients

3.8 Summary

**Chapter 4. Spreadsheets and Economic Analysis**

4.1 Using Spreadsheets for Economic Analysis

Why Use Spreadsheets

Reality and the Flexibility of Spreadsheet Models

The Elements of a Spreadsheet

Relative and Absolute Addresses

4.2 Spreadsheet Modeling

Using a Data Block

Defining Variables in a Spreadsheet

Use Relative and Absolute Addresses in Your Formulas

Explaining and Labeling Your Formulas

Formatting Your Spreadsheets

4.3 Financial Functions in Spreadsheets

Spreadsheet Annuity Functions

Spreadsheet Block Functions

4.4 Examples Show Spreadsheet Models Can Be More Realistic

4.5 Using Spreadsheets to Get a Project Funded

Sensitivity Analysis

Creating Graphs

Documenting Data Sources

4.6 Summary

**Part Two: Analyzing a Project**

Chapter 5. Present Worth

5.1 The Present Worth Measure

Is PW > 0?

Standard Assumptions

5.2 Examples of When to Use Present Worth

5.3 Rolling Back Irregular Cash Flows for PW Calculations

5.4 Salvage Values

5.5 Capitalized Cost and Perpetual Life

5.6 Staged Projects

5.7 Cost of Underutilized Capacity

5.8 Spreadsheets and Shorter Periods

5.9 Spreadsheets and More Exact Models

5.10 Summary

**Chapter 6. Equivalent Annual Worth**

6.1 The Equivalent Annual Worth Measure

6.2 Assumptions and Sign Conventions

6.3 Examples of Annual Evaluations

6.4 Finding the EAC of "Irregular" Cash Flows

EAC of a Single Interior Cash Flow

Deferred Annuities to Regular Annuities

6.5 EAC Formulas for Salvage Values and Working Capital

Capital Recovery with Salvage Values

Working Capital

6.6 Perpetual Life

Assumptions and Formulas

N vs. Infinity

Arithmetic Gradients and Perpetual Life

6.7 Repeated Renewals

Repetition for Every Subperiod

Capitalized Costs

Repeated Renewals with Neither an Initial nor a Final Cash Flow

6.8 Spreadsheets and Analyzing Loan Repayments

Finding the Balance Due

Shortening the Time to Payoff by Increasing Payments

How Much Goes to Interest? How Much Goes to Principal?

6.9 Summary

**Chapter 7. Rate of Return**

7.1 The Internal Rate of Return

7.2 Assumptions

Loans

Investments

Multiple Sign Changes

Reinvestment Assumption

Applying the IRR Measure

7.3 Finding the IRR

Hints and Shortcuts for Finding the IRR

7.4 Loans and Leases

7.5 Spreadsheets and the IRR

RATE Investment Function

IRR Block Function

7.6 Multiple Sign Changes

Mineral Extraction

Environmental Restoration

Staged Construction or Expansion

Summary of Multiple Sign Change Consequences

7.7 Project Balances over Time

7.8 Modified Internal Rate of Return (MIRR)

7.9 Summary

**Chapter** **8. Benefit/cost Ratios and Other Measures**

8.1 Measures of Economic Attractiveness

Conceptual Definitions

Frequency and Patterns of Use

8.2 Benefit/Cost Ratio

8.3 Present Worth Indexes

Mathematical Definition of PW Indexes

8.4 Future Worth

8.5 Payback Period

Difficulties with Payback Period

When Can Payback Be Used?

8.6 Discounted Payback

Why to Use or Not Use

Examples of Use

8.7 Breakeven Volume

8.8 Summary

**Part Three: Comparing Alternatives and Projects**

Introduction to mutually exclusive and constrained budget problems.

**Chapter 9. Mutually Exclusive Alternatives**

9.1 Applying Engineering Economy to Engineering Design

9.2 Key Assumption Is the Interest Rate or Minimum Attractive Rate of Return

Common Assumptions

9.3 Comparing Alternatives with Lives of the Same Length

9.4 PWs and Explicitly Comparing Different-Length Lives

Approaches For Defining a Problem Horizon

Choosing the Best Horizon

Mutually Exclusive Alternatives without a Common Horizon

9.5 EAWs and EACs and Implicitly Comparing Different-Length Lives

9.6 Using EAC for Different-Length Lives Is a Robust Approach

Robustness Due to Discounting

Robustness Due to Estimated Lives

9.7 Benefit/Cost and IRR Comparisons of Mutually Exclusive Alternatives Require Incremental Analysis

9.8 Defender/Challenger Analysis

9.9 PW, EAW, and IRR Have the Same Interest Rate Assumption

9.10 Using Spreadsheet GOAL SEEK Tool to Calculate Incremental IRRs

9.11 Summary

**Chapter 10. Replacement** **Analysis**

10.1 Why Is Equipment Replaced, Retired, or Augmented?

Reduced Performance

Altered Requirements

Obsolescence

Risk of Catastrophic Failure or Unplanned Replacement

Lease or Rental vs. Ownership

Summary of Reasons for Replacement

10.2 Old and New Are Mutually Exclusive

Different-Length Lives

Economic Life

10.3 Sunk Costs, Risks, and Short-Term Cost Savings

Sunk Costs

Risks of the New often Far Exceed Those of Extending the Old

Short-term Cost Savings Are Not Enough to Compare Repair vs. Replace

10.4 Optimal Challengers

Challenger's Optimal or Economic Life

Cost Curve for the Challenger's Economic Life

Spreadsheets for Challenger's Economic Life

10.5 Optimal Defenders

Typical Defender's Economic Life

Incorrect Assumptions for Minimizing the Defender's EAC

When to Calculate the Defender=s Best EAC

Flowchart to Summarize the Decision Rules

10.6 Optimal Capacity Problems

10.7 Estimating Future Challengers

A Simple Rule of Thumb

MAPI

10.8 Replacement and Repair Models

Classifying Replacement Models

Block Replacement

10.9 Summary and Conclusions

**Chapter 11. Constrained Project Selection**

11.1 The Constrained Project Selection Problem

Mutually Exclusive Choices vs. Constrained Project Selection

Budgets and Project Selection

Problem Size

Budget Flexibility and Contingency Allowances

11.2 Ranking Projects

Investment Opportunity Schedule

Ranking by PW or EAW Does Not Work

Strengths and Weaknesses of IRR

11.3 Determining the Minimum Attractive Rate of Return Using the Opportunity Cost of Capital

Minimum Attractive Rate of Return (MARR)

11.4 A Theoretically Optimal Approach for Determining the Capital Budget

11.5 Capital Limits in the Real World

Why Capital Are Imposed

Budget Limits and the Cost of Capital

11.6 Matching Assumptions to the Real World

Assumption of Indivisible Projects and Increments of Financing

Assumption of Project Independence

Assumption of Simultaneous Evaluation

Stability and Reinvestment Assumptions

11.7 Present Worth Indexes and Benefit/Cost Ratios

11.8 Using the SORT Spreadsheet Tool

Using Spreadsheet Investment and Block Functions

Using the SORT Tool

11.9 Summary

Appendix 11A Mathematical Programming and Spreadsheets

Using Spreadsheets to Solve Linear Programs

Disadvantages of Mathematical Programming Models

**Part Four: Enhancements for the Real World**

Chapter 12. Depreciation

12.1 Introduction

Definitions

12.2 Basic Depreciation Methods

Straight-Line Method

Declining Balance Method

SOYD Method

Units-of-Production Method

12.3 Modified Accelerated Cost Recovery System (MACRS)

Based on Accelerated Cost Recovery System (ACRS)

MACRS

Alternate MACRS

12.4 Gains and Losses on Sales and Recaptured Depreciation

12.5 Optimal Depreciation Strategies

12.6 PW of a Depreciation Schedule

Straight-Line Method

Declining Balance Method

SOYD Method

MACRS

12.7 Depletion of Resources

Cost Depletion

Percentage Depletion

12.8 Section 179 Deduction and Bonus Depreciation

Section 179

Recapture for Section 179 Assets

Bonus Depreciation

12.9 Spreadsheet Functions for Depreciation

Using VDB for MACRS

12.10 Summary

**Chapter 13. Income Taxes**

13.1 Principles of Income Taxes

Income, Property, Sales, and Value Added Taxes

Point of View

Principles of Calculation

13.2 Progressive Marginal Tax Rates

Effective Tax Rate for State, Local, and Federal Taxes

13.3 Finding Taxable Income When Depreciation Is Included

Categorizing Before-Tax Cash Flows

13.4 Calculating After-Tax Cash Flows and EACs Using Tables or Spreadsheets

Selecting an After-Tax Interest Rate

13.5 Calculating After-Tax Cash Flows and EACs using Formulas

Straight-Line Depreciation

MACRS Depreciation

Sum-of-the-Years'-digits (SOYD) Depreciation

13.6 Investment Tax Credits (ITC) and Capital Gains

History of ITC

Computing and using an ITC

Capital Gains

13.7 Interest Deductions and an After-Tax IRR

Leverage

13.8 Summary

Appendix 13A: Personal Income Taxes

**Chapter 14. Public Sector Engineering Economy**

14.1 Defining Benefits, Disbenefits, and Costs

Agencies t)That Do Not Serve the Public Directly

Benefits to Whomsoever They Accrue

14.2 Why Are Public-Sector Problems Difficult?

Quantifying and Valuing Benefits

Long Problem Horizons

Probabilities of Rare Events

Multiple Objectives That May Conflict

Interest Groups with Differing Perspectives

Selecting an Interest Rate

Summary

14.3 Correct Methods and Interest Rates

Evaluating a Single Project

Criteria for Mutually Exclusive Alternatives

Criteria for Constrained Project Selection

Deferred Maintenance

14.4 Whose Point of View?

What Is Internal? What Is External?

Federal Subsidies

Consumers' Surplus

14.5 Allocating Costs to Benefit Recipients

14.6 Valuing the Benefits of Public Projects

A Life's Present Value

Standards of Federal Agencies

Risk and Valuing Public Benefits

14.7 Cost Effectiveness

14.8 Summary

**Chapter 15. Inflation**

15.1 Defining and Measuring Inflation and Deflation

The Consumer Price Index (CPI)

Annual Inflation Rate

Producer Price Indexes

15.2 Consistent Assumptions for Interest Rates and Cash Flow Estimates

Inflation Terminology

Matching Interest Rates to Inflation Assumptions

Differential Inflation

Estimating Differential Inflation

Accuracy of Inflation Estimates

15.3 Solving for PW or EAC When Inflation Is Included

15.4 Inflation Examples with Multiple Inflation Rates

15.5 Leases and Other Prepaid Expenses

15.6 Depreciation and Loan Payments

15.7 Inflation and Other Geometric Gradients

The Four Geometric Gradients

Formulas Based on the Equivalent Discount Rate

15.8 Summary

**Part Five: Decision Making Tools**

Chapter 16. Estimating Cash Flows

16.1 Introduction

Importance of Cost Estimating

The Impact of Early Project Decisions

16.2 Cash Flow Estimating and Life-Cycle Stages

Hidden Costs

Costs during the Project Life Cycle

16.3 Cash Flow Estimating Standards

Stages of Cash Flow Estimating

Conceptual Design

Preliminary Systems Design

Final Systems Design

Cost Estimate Definitions and Accuracy

16.4 Design Criteria and Specifications

Design Criteria

Specifying Performance

16.5 Modeling the Base Case

16.6 Using Indexes for an Order-of-Magnitude Estimate

16.7 Using Capacity Functions for Order-of-Magnitude Estimates

16.8 Using Growth Curves

16.9 Using Learning Curves

16.10 Using Factor Estimates

16.11 Summary

**Chapter 17. Sensitivity Analysis**

17.1 What Is Sensitivity Analysis?

Sources of Uncertainty

Breakeven Charts

Why Do Sensitivity Analysis?

17.2 Uncertain Data and Its Impact

Defining the Limits of Uncertain Data

Estimating Sensitivities

17.3 Techniques for Sensitivity Analysis

Scenarios

The Relative Sensitivity of the Economic Criteria to Different Variables

Tabulating Relative Sensitivity Analysis

Tornado Diagram

Spiderplot

More Advanced Techniques

17.4 Spiderplots

Defining Spiderplots

Interpreting a Spiderplot

17.5 Constructing a Spiderplot

By Hand

Using a Spreadsheet

Choosing a y-axis

17.6 Constructing Tornado Diagrams

Tornado Diagrams with Positive Values Only

Tornado Diagrams with Positive and Negative Values

Using the Tornado Diagram Template

17.7 Multiple Alternatives

Spiderplots

Scenarios

17.8 Sensitivity Analysis with Multiple Variables

17.9 Summary

**Chapter 18. Uncertainty and Probability**

18.1 Probabilities

18.2 Computing Expected Values

18.3 Choosing Alternatives Using Expected Values

18.4 Economic Decision Trees

Sequential Decisions

Cash Flows That Occur over Time

18.5 Risk

18.6 Risk/Return Tradeoffs

Buying Insurance

Balancing Risks and Returns

Efficient Frontier for Risk/Return Trade-offs

Approaches to Risk/Return Tradeoffs

18.7 Real Options

18.8 Probability Distributions for Economic Outcomes

Probability Distributions with Multiple Independent Variables

N and i Need Complete Distributions for Exact Answers

Continuous and Discrete Probability Distributions

Simulation

18.9 Summary

**Chapter 19. Multiple Objectives**

19.1 Multiple Attributes

Definitions and Trade-offs

Attribute Categories

Selecting Multiple Objectives

Summary

19.2 The Process of Evaluating Multiple Objectives

Eliminating Dominated and Unsatisfactory Alternatives

Decision Rules for Choosing the Best Alternative

19.3 Identifying the Attributes

19.4 Evaluating the Alternatives

19.5 Graphical Techniques

Shaded Circles and Squares

Polar Graph

19.6 Numerical Scales for Evaluation

Numerical Variables

Choosing the Best and the Worst Case

Verbal Variables

Missing Values

19.7 Additive Models

Direct Assignment of Weights

Subjective Assignment of Importance Ratings

Tabular Additive Models

Graphical Additive Models

Closing Comment on Additive Models

19.8 Hierarchical Attributes and Objectives

19.9 Summary

Appendixes

A. Accounting

A.1 Role of Accounting

A.2 General Accounting

Business Transactions

A.3 The Balance Sheet

Assets

Liabilities

Equity

Financial Ratios Derived from Balance Sheet Data

A.4 Income Statement

Definition

Financial Ratios Derived from Income Statement Data

Linking the Balance Sheet, Income Statement, and Capital Transactions

A.5 Traditional Cost Accounting

Direct and Indirect Costs

Indirect Cost Allocation

Problems with Traditional Cost Accounting

A.6 Activity Based Costs (ABC)

Definition

ABC Provides More Accurate Costs

Using ABC

Economic Justification Using ABC Data

Timely and Accurate Data

A.7 Summary

B. Time Value of Money (TVM) and Calculators

B.1 Advantages and Types of TVM Calculators

B.2 Notation for TVM Calculators

B.3 Examples with TVM Calculators & Tabulated Factors

C. End-of-Period Compound Interest Tables

D. Fundamentals of Engineering (FE) Exam Practice Problems