Assignment 7

554 Chapter 19 More on Variation and Decision Making under Risk

CHAPTER SUMMARY
To perform decision making under risk implies that some parameters of an engineering alterna-
tive are treated as random variables. Assumptions about the shape of the variable’s probability
distribution are used to explain how the estimates of parameter values may vary. Additionally,
measures such as the expected value and standard deviation describe the characteristic shape of
the distribution. In this chapter, we learned several of the simple, but useful, discrete and con-
tinuous population distributions used in engineering economy—uniform and triangular—as well
as specifying our own distribution or assuming the normal distribution.
Since the population’s probability distribution for a parameter is not fully known, a random
sample of size n is usually taken, and its sample average and standard deviation are determined.
The results are used to make probability statements about the parameter, which help make the
final decision with risk considered.
The Monte Carlo sampling method is combined with engineering economy relations for a
measure of worth such as PW to implement a simulation approach to risk analysis. The results of
such an analysis can then be compared with decisions when parameter estimates are made with
certainty.

PROBLEMS
Certainty, Risk, and Uncertainty

19.1 Identify the following variables as either discrete
or continuous:
(a) The number of times heads comes up in 100

tosses of a coin
(b) The number of accidents occurring in a spec-

ified section of a freeway
(c) The weight of boxes shipped from an Ama-

zon warehouse
(d) The concentration of carbon dioxide in the

air of San Diego versus time
(e) Optimistic, most likely, and pessimistic esti-

mates of salvage value

19.2 For each situation below, determine (1) if the
variable(s) is(are) discrete or continuous, and (2) if the
information involves certainty, risk, and/or uncertainty.
(a) A friend in real estate tells you the price per

square foot for new houses will go up slowly
or rapidly during the next 6 months.

(b) Your manager informs the staff that there is
an equal chance that sales will be between 50
and 55 units next month.

(c) Jane got paid yesterday and $800 was taken
out in income taxes. The amount withheld
next month will be larger because of a pay
raise between 3% and 5%.

(d) There is a 20% chance of rain and a 30%
chance of snow today.

(e) The first cost of a new front-end loader is
$34,000 or $38,000 depending on the size
purchased.

19.3 In the recent past, the production output has been
between 10,000 and 20,000 units per week 75% of

the time; however, it may fall below 10,000 or go
above 20,000 more frequently in the future. The
production manager wants to use E(output) to
make a decision about upgrading automation soft-
ware. Identify at least two additional pieces of in-
formation that must be obtained or assumed to
finalize the output information for this use.

Probability and Distributions

19.4 The cost of flood damage from significant storms
varies as a function of the severity of the storm.
Estimate the expected flood damage due to the
next significant storm.

Flood Flow,
Million Acre-ft

Flood Damage,
$ Millions Probability

0.5 19 0.35
1.0 41 0.36
1.5 97 0.20
>2.0 210 0.09

19.5 AAA car-buying service surveyed 1000 households
to determine the number of operating vehicles
owned by residents at the same address. Use the
results below to estimate the percentage of house-
holds that own (a) one or less vehicles, (b) one or
two vehicles, and (c) more than three vehicles.

Number of Cars, C Number of Households

0 120
1 560
2 260
3 32
4 22

5 or more 6

bla23437_ch19_528-560.indd 554 18/11/16 11:29 am

Front Cover
Title page
Copyright page
CONTENTS (with direct page links)
Preface to Eighth Edition
LEARNING STAGE 1 – THE FUNDAMENTALS
1. Foundations of Engineering Economy
1.1 Why Engineering Economy and the Time Value of Money are Important
1.2 Performing an Engineering Economy Study
1.3 Professional Ethics and Economic Decisions
1.4 Interest Rate and Rate of Return
1.5 Terminology and Symbols
1.6 Cash Flows: Estimation and Diagramming
1.7 Economic Equivalence
1.8 Simple and Compound Interest
1.9 Minimum Attractive Rate of Return
1.10 Introduction to Spreadsheet Use
Chapter Summary
Problems
Exercises for Spreadsheets
Additional Problems and FE Exam Review Questions
Case Study—Cost of Electricity with Renewable Sources Added

2. Factors: How Time and Interest Affect Money
PE: Progressive Example—The Steel Plant Case
2.1 Single-Amount Factors (F/P and P/F )
2.2 Uniform Series Present Worth Factor and Capital Recovery Factor (P/A and A/P)
2.3 Sinking Fund Factor and Uniform Series Compound Amount Factor (A/F and F/A)
2.4 Factor Values for Untabulated i or n Values
2.5 Arithmetic Gradient Factors (P/G and A/G)
2.6 Geometric Gradient Series Factors
2.7 Determining i or n for Known Cash Flow Values
Chapter Summary
Problems
Exercises for Spreadsheets
Additional Problems and FE Exam Review Questions
Case Study—The Amazing Impact of Compound Interest

3. Combining Factors and Spreadsheet Functions
3.1 Calculations for Uniform Series That Are Shifted
3.2 Calculations Involving Uniform Series and Randomly Placed Single Amounts
3.3 Calculations for Shifted Gradients
Chapter Summary
Problems
Exercises for Spreadsheets
Additional Problems and FE Exam Review Questions
Case Study—Preserving Land for Public Use

4. Nominal and Effective Interest Rates
PE: Progressive Example—The Credit Card Offer Case
4.1 Nominal and Effective Interest Rate Statements
4.2 Effective Annual Interest Rates
4.3 Effective Interest Rates for Any Time Period
4.4 Equivalence Relations: Payment Period and Compounding Period
4.5 Equivalence Relations: Single Amounts with PP ≥ CP
4.6 Equivalence Relations: Series with PP ≥ CP
4.7 Equivalence Relations: Single Amounts and Series with PP < CP 4.8 Effective Interest Rate for Continuous Compounding 4.9 Interest Rates That Vary Over Time Chapter Summary Problems Exercises for Spreadsheets Additional Problems and FE Exam Review Questions Case Study—Is Owning a Home a Net Gain or Net Loss Over Time? LEARNING STAGE 2 - BASIC ANALYSIS TOOLS 5. Present Worth Analysis PE: Progressive Example—Water for Semiconductor Manufacturing Case 5.1 Formulating Alternatives 5.2 Present Worth Analysis of Equal-Life Alternatives 5.3 Present Worth Analysis of Different-Life Alternatives 5.4 Future Worth Analysis 5.5 Capitalized Cost Analysis Chapter Summary Problems Exercises for Spreadsheets Additional Problems and FE Exam Review Questions Case Study—Comparing Social Security Benefits 6. Annual Worth Analysis 6.1 Advantages and Uses of Annual Worth Analysis 6.2 Calculation of Capital Recovery and AW Values 6.3 Evaluating Alternatives by Annual Worth Analysis 6.4 AW of a Permanent Investment 6.5 Life-Cycle Cost Analysis Chapter Summary Problems Exercises for Spreadsheets Additional Problems and FE Exam Review Questions Case Study—Annual Worth Analysis—Then and Now 7. Rate of Return Analysis: One Project 7.1 Interpretation of a Rate of Return Value 7.2 Rate of Return Calculation Using a PW or AW Relation 7.3 Special Considerations When Using the ROR Method 7.4 Multiple Rate of Return Values 7.5 Techniques to Remove Multiple Rates of Return 7.6 Rate of Return of a Bond Investment Chapter Summary Problems Exercises for Spreadsheets Additional Problems and FE Exam Review Questions Case Study—Developing and Selling an Innovative Idea 8. Rate of Return Analysis: Multiple Alternatives 8.1 Why Incremental Analysis Is Necessary 8.2 Calculation of Incremental Cash Flows for ROR Analysis 8.3 Interpretation of Rate of Return on the Extra Investment 8.4 Rate of Return Evaluation Using PW: Incremental and Breakeven (Two Alternatives) 8.5 Rate of Return Evaluation Using AW 8.6 Incremental ROR Analysis of Multiple (More than Two) Alternatives 8.7 All-in-One Spreadsheet Analysis Chapter Summary Problems Exercises for Spreadsheets Additional Problems and FE Exam Review Questions Case Study—Peforming ROR Analysis for 3D Printer and IIoT Technology Case Study—How a New Engineering Graduate Can Help His Father 9. Benefit/Cost Analysis and Public Sector Economics PE: Progressive Example—Water Treatment Facility #3 Case 9.1 Public Sector Projects 9.2 Benefit/Cost Analysis of a Single Project 9.3 Incremental B/C Analysis (Two Alternatives) 9.4 Incremental B/C Analysis of Multiple (More than Two) Alternatives 9.5 Service Sector Projects and Cost-Effectiveness Analysis 9.6 Ethical Considerations in the Public Sector Chapter Summary Problems Exercises for Spreadsheets Additional Problems and FE Exam Review Questions Case Study—Highway Lighting Options to Reduce Traffic Accidents EPILOGUE: Selecting the Basic Analysis Tool LEARNING STAGE 3 - MAKING BETTER DECISIONS 10. Project Financing and Noneconomic Attributes 10.1 MARR Relation to the Cost of Capital 10.2 Debt-Equity Mix and Weighted Average Cost of Capital 10.3 Determination of the Cost of Debt Capital 10.4 Determination of the Cost of Equity Capital and the MARR 10.5 Effect of Debt-Equity Mix on Investment Risk 10.6 Multiple Attribute Analysis: An Introduction 10.7 Evaluation Measure for Multiple Attributes Chapter Summary Problems Exercises for Spreadsheets Additional Problems and FE Exam Review Questions Case Study—Expanding a —Debt vs. Equity Financing? 11. Replacement and Retention Decisions PE Progressive Example—Keep or Replace the Kiln Case 11.1 Basics of a Replacement Study 11.2 Economic Service Life 11.3 Performing a Replacement Study 11.4 Additional Considerations in a Replacement Study 11.5 Replacement Study over a Specified Study Period 11.6 Replacement Value Chapter Summary Problems Exercises for Spreadsheets Additional Problems and FE Exam Review Questions Case Study—A Pumper System with an ESL Problem 12. Independent Projects with Budget Limitation 12.1 An Overview of Capital Rationing among Projects 12.2 Capital Rationing Using PW Analysis of Equal-Life Projects 12.3 Capital Rationing Using PW Analysis of Unequal-Life Projects 12.4 Capital Budgeting Problem Formulation Using Linear Programming 12.5 Additional Project Ranking Measures Chapter Summary Problems Additional Problems and FE Exam Review Questions 13. Breakeven and Payback Analysis 13.1 Breakeven Analysis for a Single Project 13.2 Breakeven Analysis Between Two Alternatives 13.3 Payback Analysis 13.4 More Breakeven and Payback Analysis on Spreadsheets Chapter Summary Problems Exercises for Spreadsheets Additional Problems and FE Exam Review Questions Case Study—Water Treatment Plant Process Costs LEARNING STAGE 4 - ROUNDING OUT THE STUDY 14. Effects of Inflation 14.1 Understanding the Impact of Inflation 14.2 Present Worth Calculations Adjusted for Inflation 14.3 Future Worth Calculations Adjusted for Inflation 14.4 Capital Recovery Calculations Adjusted for Inflation Chapter Summary Problems Additional Problems and FE Exam Review Questions Case Study—Inflation Considerations for Stock and Bond Investments 15. Cost Estimation and Indirect Cost Allocation 15.1 Understanding How Cost Estimation Is Accomplished 15.2 Unit Method 15.3 Cost Indexes 15.4 Cost-Estimating Relationships: Cost-Capacity Equations 15.5 Cost-Estimating Relationships: Factor Method 15.6 Indirect Cost Rates and Allocation: The Traditional Method 15.7 Activity-Based Costing (ABC) for Indirect Costs 15.8 Making Estimates and Maintaining Ethical Practices Chapter Summary Problems Additional Problems and FE Exam Review Questions Case Study—Indirect Cost Analysis of Medical Equipment Manufacturing Costs Case Study—Deceptive Acts Can Get You in Trouble 16. Depreciation Methods 16.1 Depreciation Terminology 16.2 Straight Line (SL) Depreciation 16.3 Declining Balance (DB) and Double Declining Balance (DDB) Depreciation 16.4 Modified Accelerated Cost Recovery System (MACRS) 16.5 Determining the MACRS Recovery Period 16.6 Depletion Methods Chapter Summary Appendix 16A.1 Sum-of-Years-Digits (SYD) and Unit-of-Production (UOP) Depreciation 16A.2 Switching between Depreciation Methods 16A.3 Determination of MACRS Rates Problems Additional Problems and FE Exam Review Questions Appendix Problems 17. After-Tax Economic Analysis 17.1 Income Tax Terminology and Basic Relations 17.2 Calculation of Cash Flow after Taxes 17.3 Effect on Taxes of Different Depreciation Methods and Recovery Periods 17.4 Depreciation Recapture and Capital Gains (Losses) 17.5 After-Tax Economic Evaluation 17.6 After-Tax Replacement Study 17.7 After-Tax Value-Added Analysis 17.8 After-Tax Analysis for International Projects 17.9 Value-Added Tax Chapter Summary Problems Additional Problems and FE Exam Review Questions Case Study—After-Tax Analysis for Expansion 18. Sensitivity Analysis and Staged Decisions 18.1 Determining Sensitivity to Parameter Variation 18.2 Sensitivity Analysis Using Three Estimates 18.3 Estimate Variability and the Expected Value 18.4 Expected Value Computations for Alternatives 18.5 Staged Evaluation of Alternatives Using a Decision Tree 18.6 Real Options in Engineering Economics Chapter Summary Problems Additional Problems and FE Exam Review Questions Case Study—Sensitivity to the Economic Environment Case Study—Sensitivity Analysis of Public Sector Projects—Water Supply Plans 19. More on Variation and Decision Making under Risk 19.1 Interpretation of Certainty, Risk, and Uncertainty 19.2 Elements Important to Decision Making under Risk 19.3 Random Samples 19.4 Sample Estimates: Mean and Standard Deviation 19.5 Monte Carlo Sampling and Simulation Analysis Chapter Summary Problems Additional Problems and FE Exam Review Questions Case Study—Using Simulation and Three-Estimate Sensitivity Analysis APPENDICES: A: Using Spreadsheets and Microsoft Excel® A.1 Introduction to Using Excel A.2 Organization (Layout) of the Spreadsheet A.3 Spreadsheet Functions Important to Engineering Economy (Alphabetical Order) A.4 Goal Seek—A Tool for Breakeven and Sensitivity Analysis A.5 Solver—An Optimizing Tool for Capital Budgeting, Breakeven, and Sensitivity Analysis A.6 Error Messages B: Basics of Accounting Reports and Ratios B.1 The Balance Sheet B.2 Income Statement and Cost of Goods Sold Statement B.3 Ratios C: Code of Ethics for Engineers D: Alternate Methods for Equivalence Calculations D.1 Using Programmable Calculators D.2 Using the Summation of a Geometric Series E: Glossary of Concepts and Terms E.1 Important Concepts and Guidelines E.2 Symbols and Terms Reference Materials Factor Tables INDEX A B C D E F - G H - I L M - N O - P R S T - U V - W - X - Y Format for Spreadsheet Functions on Excel Relations for Discrete Cash Flows with End-of-Period Compounding