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Lebanese University –
Faculty of Engineering
Engineering
Economics
Introduction to Engineering
Economics
Chapter 1
1
Mikhael TANNOUS, Ph.D. in Computational Mechanics
What is Economics ?
A social science of how limited resources are used to satisfy unlimited
human wants
What is Engineering ?
Engineering is the profession in which knowledge of the mathematical &
natural sciences gained by study, experience & practice is applied with
judgment to develop ways to use, economically, the forces of nature for the
benefit of humankind. (ABET)
2
Engineering Economics
Engineering
Economics
ENGINEERING ECONOMICS
Resources
3
All gifts of nature, such as: water, air, minerals,
sunshine, plant and tree growth, as well as the land
itself which is applied to the production process.
The efforts, skills, and knowledge of
people which are applied to the
production process.
LAND OR NATURAL
RESOURCES
LABOR
Real Capital (Physical Capital )
Tools, buildings, machinery -- things which have been produced
which are used in further production
Financial Capital
Assets and money which are used in the production
process
Human Capital
Education and training applied to labor in the production
process.
CAPITAL
$$
Engineering Economics, previously known as engineering
economy, is a subset of economics for application to engineering
projects
4
$$
$$
$$
$$
WHY DO ENGINEERS NEED TO LEARN
ABOUT ECONOMICS?
5
Engineers must decide if the benefits of a project exceed its costs, and must
make this comparison in a unified framework. The framework within which to
make this comparison is the field of engineering economics, which strives to
answer exactly these questions, and perhaps more.
Ages ago, the most significant barriers to engineers were technological. The
things that engineers wanted to do, they simply did not yet know how to do, or
hadn't yet developed the tools to do. There are certainly many more challenges
like this which face present-day engineers
Natural resources (from which we
must build things) are becoming more
scarce and more expensive
Negative side-effects of engineering
innovations (such as air pollution from
automobiles)
➢ Engineering Economics is about making decisions
➢ Engineering Economics assesses the appropriateness of
a given project, estimates its value, and justifies it from
an engineering standpoint
➢ Engineering Economics is the application of economic
techniques to the evaluation of design and engineering
alternatives
What is Engineering Economics?
6
Engineering
Assessing the worth of these
products in economic terms
Produce products and services
depending on physical Laws
Physical
Environment
Economic
Environment
Physical Efficiency =
System Output
System Input
Economic Efficiency=
System Worth
System Cost
How Engineering is composed of physical
and economic components
7
Engineering Economics: Origins
• The development of Engineering Economics methodology is relatively
recent
• A pioneer in the field was Arthur Wellington, a civil engineer, who at the
end of 19th century addressed the role of economic analysis in engineering
projects (his area of interest was railroad building in the USA)
• This early work was followed by other contributions in which the emphasis
was put on techniques that depended on financial mathematics. In 1930,
Eugene Grant published a textbook which was a milestone in the
development of engineering economy as we know it today (economic point
of view of engineering)
• In 1942 Woods and DeGarmo wrote a book, later titled Engineering
Economy
8
• Cost Concepts
• Time Value of Money
• Cash-Flow Concepts
• Comparing Alternatives
• Evaluating Projects
• Benefit-Cost Analysis
• Depreciation and Income Taxes
• Inflation and Price Changes
• Dealing with Uncertainty
Course Topics
9
Chapter 1: Engineering Economics Overview
1. Rational decision-making process
2. Economic decisions
3. Predicting future
4. Role of engineers in business
5. Large-scale engineering projects
6. Types of strategic engineering economic decisions
Topics dealt with in chapter 1
10
T1. Rational decision-making process
(what engineers do)
– Recognize a decision
problem
– Define the goals or
objectives
– Collect all the relevant
information
– Identify a set of feasible
decision alternatives
– Select the decision
criterion to use
– Select the best alternative
11
T2. Engineering economic decisions
Planning
Marketing
Manufacturing Profit
Investment
12
T3. Predicting the future
- Estimating a required
investment
- Forecasting a product
demand
- Estimating a selling
price
- Estimating a
manufacturing cost
- Estimating a product
life
13
T4. Role of engineers in business
Create & design
engineering projects
Evaluate
expected
profitability
timing of
cash flows
degree of
financial risk
Evaluate
impact on
financial statements
firm’s market value
stock price
Analyze
production methods
engineering safety
environmental impacts
market assessment
14
Accounting vs. engineering economics
Evaluating past
performance
Evaluating & predicting
future events
Accounting Engineering economy
past future
present
15
What Kinds of Questions Can
Engineering Economics Answer?
ENGINEERING ECONOMICS INVOLVES:
FORMULATING, ESTIMATING, AND EVALUATING
ECONOMIC OUTCOMES
WHEN CHOICES OR ALTERNATIVES ARE AVAILABLE
16
How Does It Do This?
BY USING SPECIFIC
MATHEMATICAL RELATIONSHIPS
TO COMPARE THE CASH FLOWS OF THE DIFFERENT
ALTERNATIVES
(typically using spreadsheets)
17
Where Do I Get the Data?
• Engineering economics is based mainly on estimates of future
costs and benefits:
• So it has to deal with risk and uncertainty
• The costs, benefits, and other parameters are typically
unknown, and can vary over time:
• The values of these parameters will dictate a particular
numerical outcome
• And therefore a particular decision!
• Sensitivity analysis can be used to explore how the decision
changes as our estimates change
18
Time & uncertainty are the
defining aspects of any
engineering
economic decision 19
T5. A large-scale engineering project
– Requires a large sum of
investment
– Takes a long time to see
the financial outcomes
– Has uncertainty in
predicting the revenue &
cost streams
20
T6. Types of strategic engineering economic
decisions in manufacturing sector
– Service improvement
– Equipment & process selection
– Equipment replacement
– New product & product expansion
– Cost reduction
21
Fundamental principles of engineering economics
1. A nearby dollar is worth more than a distant dollar
2. All that counts are the differences among
alternatives
3. Marginal revenue must exceed marginal cost
4. Additional risk is not taken without the
expected additional return
22
Principle 1: A nearby dollar is worth more than
a distant dollar
today 6-month later
23
Principle 2: All that counts are the differences
among alternatives
Option Monthly
fuel cost
Monthly
mainten-
ance
Cash
outlay at
signing
Monthly
payment
Salvage
value at
end of
year 3
Buy $960 $550 $6,500 $350 $9,000
Lease $960 $550 $2,400 $550 0
Irrelevant items in decision making
24
Principle 3: Marginal revenue must exceed
marginal cost
Manufacturing cost
Sales revenue
Marginal
cost
1 unit
Marginal
revenue
1 unit
Ignore sunk costs 25
Principle 4: Additional risk is not taken
without expected additional return
Investment
class
Potential
risk
Expected
return
Savings
account (cash)
Low/none 1.5%
Bond (debt) Moderate 4.8%
Stock (equity) High 11.5%
26
Principles of Engineering Economy
1. Develop the Alternatives
• Creativity and innovation are essential to the process
• The alternatives need to be identified and then defined for subsequent analysis
• Consider the status quo, but do not focus on it(i.e., doing nothing)
2. Focus on the Differences
• Only the differences among alternatives are relevant to comparison and decision
3. Use a Consistent Viewpoint (perspective)
4. Use a Common Unit of Measure
• Use it for enumerating as many possible outcomes as possible, since it simplifies
the analysis of alternatives
5. Consider All Relevant Criteria
• Consider both those that can be measured in monetary terms and “non-monetary”
criteria
6. Make Uncertainty Explicit
7. Revisit Your Decisions: compare initial projected outcomes with actual results achieved
27
Engineering economic analysis procedure
1. Problem recognition, definition, and evaluation
2. Development of the feasible alternatives
• Searching for potential alternatives
• Screening them to select a smaller group of feasible
alternatives
3. Development of the cash flows for each alternative (or of prospective
outcomes)
4. Selection of a criterion ( or criteria)
5. Analysis and comparison of the alternatives
6. Selection of the preferred alternative
7. Performance monitoring and post-evaluation results: helps to do
better analysis and improves the operations in organization
28
Simpler procedure for formulating
engineering economic decisions
Four essential steps in formulaing engineering economic decisions
are:
• Creative step: find an opening through a barrier of economic and
physical limitations. Opportunities are not made, they are
discovered.
• Definition step: define all factors associated with each alternative
originated in creative step
• Conversion step
• Decision step
29
Creative step
30
The creative step consists of finding an opening
through a barrier of economic and physical
limitations (ex. aluminum discovery or mining)
We explore, investigate and research aiming at
finding new opportunitites
Many successful ideas are simply new
combinations of known facts
Definition step
31
In the definition step, we define the alternatives originated or
selected for comparison
Choice is always between alternatives, but we also need to
choose which alternatives to consider
Is it better to spend more time defining more possible
alternatives or to take the decision fast considering only few?
Conversion step
32
In order to be able to
compare the alternatives we
need to convert them to a
common measure
We express each alternative
in terms of cash flows at
specified date in the future,
and state also those
considerations that cannot
be reduced to money terms
Decision step
33
Having done all the abovementioned, we
need to decide what to choose
Consider multiple criteria
Cancel out identical factors and stress the
attention on differences
When facts are missing use judgement
Making the decision
What Kinds of Questions Can Engineering Economics Answer?
Example:
•Engineering economics is needed for many kinds of
decision making
•Example: Buying a car
•Alternatives:
•$18,000 now, or
•$600 per month for 3 years
•Which is better?
34
Engineering Economics Helps Make
Cash Flow Comparisons!
Example:
Buying a car
• Alternatives:
• $18,000 now, or
• $600 per month for 3 years
(= $21,600 total)
• Which is better?
• It depends!
• Issue: how much is money now worth compared to
money in the future?
• Leads to idea of time value of money!
35
Time Value of Money
• Would you rather have:
• $100 today, or
• $100 a year from now?
• Basic assumption:
• Given a fixed amount of money, and
• A choice of having it now or in the future,
• Most people would prefer to have it sooner rather than later
36
Time Value of Money
Most people would prefer to have it sooner. Why???
Reasons:
• Security ?
• Interests ?
• Inflation?
• Currency strength ?
• Uncertainty ?
37
Time Value of Money
One consequence of the time value of money:
• Suppose you are willing to exchange a certain amount now for
some other amount later
• Then the later amount has to be larger or smaller?
38
Time Value of Money
• The time value of money centers around the idea
of an interest rate (if projecting into the future):
• Or, equivalently, a discount rate (if rolling back
to the present)
39
Time value of money deals with changes in the value of
money over some period of time (due to investment
opportunities, uncertainty, etc.)
This is a key concept in engineering economics!
– Money has a time value
because it can earn more
money over time (earning
power).
– Money has a time value
because its purchasing power
changes over time (inflation).
– Time value of money is
measured in terms of
interest rate.
– Interest is the cost of money
a cost to the borrower & an
earning to the lender
40
Time value of money
What Does This Mean for Us?
41
In this course, we will
learn methods to:
• Compare different
cash flows over
time
Using the interest
rate or discount rate:
• How much more a
dollar today is
worth compared to
a dollar in one year
For example, if the
interest rate is 5%:
• $1 today is worth
as much as $1.05
next year
Interest rates
42
Interest factor: The ratio between an amount one
period in the future and an equivalent amount now.
• Example: If you are indifferent between $5 now and $6 one
period in the future, the interest factor is 6/5 = 1.20 (per
period)
Interest rate = interest factor – 1
• In above example, it’s 0.20 = 20%
– Time value of money
– Risk
– Overhead costs
– Inflation
– Supply of & demand for funds
43
What determines interest rate?
44
Money supply & demand
Simple interest: the practice of charging an interest
rate only to an initial sum (principal amount).
Compound interest: the practice of charging an
interest rate to an initial sum & to any previously
accumulated interest that has not been withdrawn.
45
Methods of calculating interest
P = Principal amount
i = Interest rate
N = Number of interest
periods
Example:
P = $1,000
i = 8%
N = 3 years
End of
year
Beginning
balance
Interest
earned
Ending
balance
0 $1,000
1 $1,000 $80 $1,080
2 $1,080 $80 $1,160
3 $1,160 $80 $1,240
46
Simple interest
F = P+(iP)N
where
P =Principal amount
i =simple interest rate
N =number of interest periods
F =totalamountaccumulatedat theendofperiodN
F = $1,000 + (0.08)($1,000)(3)
= $1,240
47
Simple interest formula
The practice of charging an interest rate to
an initial sum & to any previously
accumulated interest that has not been
withdrawn.
48
Compound interest
P = Principal amount
i = Interest rate
N = Number of
interest periods
Example:
P = $1,000
i = 8%
N = 3 years
End
of
year
Beginning
balance
Interest
earned
Ending
balance
0 $1,000
1 $1,000 $80 $1,080
2 $1,080 $86.40 $1,166.40
3 $1,166.40 $93.31 $1,259.71
49
Compound interest
F = P(1+ i)N
SOME BASIC ECONOMIC
CONCEPTS
50
Value and
Utility
51
Value is the worth that a person
attaches to a good or service
Value is inherent in a regard a person
has for it, not in the item itself
Value is not the cost of the item
Utility is a power to satisfy human
wants and is determined subjectively
Utility is the satisfaction that a person
derives from an item
Exchange
52
Without the subjectivity of the
concepts “value” and “utility” there
would hardly be any room for
exchange between people. Why?
Through exchange we can increase
the total utility of the goods and
services. How?
Exchange is possible when it is
mutually benefitial
What If I Don’t Like the Answers?
• Remember:
• “Tools” don’t make decisions
• People make decisions, based on values
• Engineering economics is just a set of tools:
• It can help in decision making
• But it won’t make the decision for you
• Which alternative is “best” is up to you!
53

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CHAP1.pdf

  • 1. Lebanese University – Faculty of Engineering Engineering Economics Introduction to Engineering Economics Chapter 1 1 Mikhael TANNOUS, Ph.D. in Computational Mechanics
  • 2. What is Economics ? A social science of how limited resources are used to satisfy unlimited human wants What is Engineering ? Engineering is the profession in which knowledge of the mathematical & natural sciences gained by study, experience & practice is applied with judgment to develop ways to use, economically, the forces of nature for the benefit of humankind. (ABET) 2 Engineering Economics Engineering Economics ENGINEERING ECONOMICS
  • 3. Resources 3 All gifts of nature, such as: water, air, minerals, sunshine, plant and tree growth, as well as the land itself which is applied to the production process. The efforts, skills, and knowledge of people which are applied to the production process. LAND OR NATURAL RESOURCES LABOR Real Capital (Physical Capital ) Tools, buildings, machinery -- things which have been produced which are used in further production Financial Capital Assets and money which are used in the production process Human Capital Education and training applied to labor in the production process. CAPITAL $$
  • 4. Engineering Economics, previously known as engineering economy, is a subset of economics for application to engineering projects 4 $$ $$ $$ $$
  • 5. WHY DO ENGINEERS NEED TO LEARN ABOUT ECONOMICS? 5 Engineers must decide if the benefits of a project exceed its costs, and must make this comparison in a unified framework. The framework within which to make this comparison is the field of engineering economics, which strives to answer exactly these questions, and perhaps more. Ages ago, the most significant barriers to engineers were technological. The things that engineers wanted to do, they simply did not yet know how to do, or hadn't yet developed the tools to do. There are certainly many more challenges like this which face present-day engineers Natural resources (from which we must build things) are becoming more scarce and more expensive Negative side-effects of engineering innovations (such as air pollution from automobiles)
  • 6. ➢ Engineering Economics is about making decisions ➢ Engineering Economics assesses the appropriateness of a given project, estimates its value, and justifies it from an engineering standpoint ➢ Engineering Economics is the application of economic techniques to the evaluation of design and engineering alternatives What is Engineering Economics? 6
  • 7. Engineering Assessing the worth of these products in economic terms Produce products and services depending on physical Laws Physical Environment Economic Environment Physical Efficiency = System Output System Input Economic Efficiency= System Worth System Cost How Engineering is composed of physical and economic components 7
  • 8. Engineering Economics: Origins • The development of Engineering Economics methodology is relatively recent • A pioneer in the field was Arthur Wellington, a civil engineer, who at the end of 19th century addressed the role of economic analysis in engineering projects (his area of interest was railroad building in the USA) • This early work was followed by other contributions in which the emphasis was put on techniques that depended on financial mathematics. In 1930, Eugene Grant published a textbook which was a milestone in the development of engineering economy as we know it today (economic point of view of engineering) • In 1942 Woods and DeGarmo wrote a book, later titled Engineering Economy 8
  • 9. • Cost Concepts • Time Value of Money • Cash-Flow Concepts • Comparing Alternatives • Evaluating Projects • Benefit-Cost Analysis • Depreciation and Income Taxes • Inflation and Price Changes • Dealing with Uncertainty Course Topics 9
  • 10. Chapter 1: Engineering Economics Overview 1. Rational decision-making process 2. Economic decisions 3. Predicting future 4. Role of engineers in business 5. Large-scale engineering projects 6. Types of strategic engineering economic decisions Topics dealt with in chapter 1 10
  • 11. T1. Rational decision-making process (what engineers do) – Recognize a decision problem – Define the goals or objectives – Collect all the relevant information – Identify a set of feasible decision alternatives – Select the decision criterion to use – Select the best alternative 11
  • 12. T2. Engineering economic decisions Planning Marketing Manufacturing Profit Investment 12
  • 13. T3. Predicting the future - Estimating a required investment - Forecasting a product demand - Estimating a selling price - Estimating a manufacturing cost - Estimating a product life 13
  • 14. T4. Role of engineers in business Create & design engineering projects Evaluate expected profitability timing of cash flows degree of financial risk Evaluate impact on financial statements firm’s market value stock price Analyze production methods engineering safety environmental impacts market assessment 14
  • 15. Accounting vs. engineering economics Evaluating past performance Evaluating & predicting future events Accounting Engineering economy past future present 15
  • 16. What Kinds of Questions Can Engineering Economics Answer? ENGINEERING ECONOMICS INVOLVES: FORMULATING, ESTIMATING, AND EVALUATING ECONOMIC OUTCOMES WHEN CHOICES OR ALTERNATIVES ARE AVAILABLE 16
  • 17. How Does It Do This? BY USING SPECIFIC MATHEMATICAL RELATIONSHIPS TO COMPARE THE CASH FLOWS OF THE DIFFERENT ALTERNATIVES (typically using spreadsheets) 17
  • 18. Where Do I Get the Data? • Engineering economics is based mainly on estimates of future costs and benefits: • So it has to deal with risk and uncertainty • The costs, benefits, and other parameters are typically unknown, and can vary over time: • The values of these parameters will dictate a particular numerical outcome • And therefore a particular decision! • Sensitivity analysis can be used to explore how the decision changes as our estimates change 18
  • 19. Time & uncertainty are the defining aspects of any engineering economic decision 19
  • 20. T5. A large-scale engineering project – Requires a large sum of investment – Takes a long time to see the financial outcomes – Has uncertainty in predicting the revenue & cost streams 20
  • 21. T6. Types of strategic engineering economic decisions in manufacturing sector – Service improvement – Equipment & process selection – Equipment replacement – New product & product expansion – Cost reduction 21
  • 22. Fundamental principles of engineering economics 1. A nearby dollar is worth more than a distant dollar 2. All that counts are the differences among alternatives 3. Marginal revenue must exceed marginal cost 4. Additional risk is not taken without the expected additional return 22
  • 23. Principle 1: A nearby dollar is worth more than a distant dollar today 6-month later 23
  • 24. Principle 2: All that counts are the differences among alternatives Option Monthly fuel cost Monthly mainten- ance Cash outlay at signing Monthly payment Salvage value at end of year 3 Buy $960 $550 $6,500 $350 $9,000 Lease $960 $550 $2,400 $550 0 Irrelevant items in decision making 24
  • 25. Principle 3: Marginal revenue must exceed marginal cost Manufacturing cost Sales revenue Marginal cost 1 unit Marginal revenue 1 unit Ignore sunk costs 25
  • 26. Principle 4: Additional risk is not taken without expected additional return Investment class Potential risk Expected return Savings account (cash) Low/none 1.5% Bond (debt) Moderate 4.8% Stock (equity) High 11.5% 26
  • 27. Principles of Engineering Economy 1. Develop the Alternatives • Creativity and innovation are essential to the process • The alternatives need to be identified and then defined for subsequent analysis • Consider the status quo, but do not focus on it(i.e., doing nothing) 2. Focus on the Differences • Only the differences among alternatives are relevant to comparison and decision 3. Use a Consistent Viewpoint (perspective) 4. Use a Common Unit of Measure • Use it for enumerating as many possible outcomes as possible, since it simplifies the analysis of alternatives 5. Consider All Relevant Criteria • Consider both those that can be measured in monetary terms and “non-monetary” criteria 6. Make Uncertainty Explicit 7. Revisit Your Decisions: compare initial projected outcomes with actual results achieved 27
  • 28. Engineering economic analysis procedure 1. Problem recognition, definition, and evaluation 2. Development of the feasible alternatives • Searching for potential alternatives • Screening them to select a smaller group of feasible alternatives 3. Development of the cash flows for each alternative (or of prospective outcomes) 4. Selection of a criterion ( or criteria) 5. Analysis and comparison of the alternatives 6. Selection of the preferred alternative 7. Performance monitoring and post-evaluation results: helps to do better analysis and improves the operations in organization 28
  • 29. Simpler procedure for formulating engineering economic decisions Four essential steps in formulaing engineering economic decisions are: • Creative step: find an opening through a barrier of economic and physical limitations. Opportunities are not made, they are discovered. • Definition step: define all factors associated with each alternative originated in creative step • Conversion step • Decision step 29
  • 30. Creative step 30 The creative step consists of finding an opening through a barrier of economic and physical limitations (ex. aluminum discovery or mining) We explore, investigate and research aiming at finding new opportunitites Many successful ideas are simply new combinations of known facts
  • 31. Definition step 31 In the definition step, we define the alternatives originated or selected for comparison Choice is always between alternatives, but we also need to choose which alternatives to consider Is it better to spend more time defining more possible alternatives or to take the decision fast considering only few?
  • 32. Conversion step 32 In order to be able to compare the alternatives we need to convert them to a common measure We express each alternative in terms of cash flows at specified date in the future, and state also those considerations that cannot be reduced to money terms
  • 33. Decision step 33 Having done all the abovementioned, we need to decide what to choose Consider multiple criteria Cancel out identical factors and stress the attention on differences When facts are missing use judgement Making the decision
  • 34. What Kinds of Questions Can Engineering Economics Answer? Example: •Engineering economics is needed for many kinds of decision making •Example: Buying a car •Alternatives: •$18,000 now, or •$600 per month for 3 years •Which is better? 34
  • 35. Engineering Economics Helps Make Cash Flow Comparisons! Example: Buying a car • Alternatives: • $18,000 now, or • $600 per month for 3 years (= $21,600 total) • Which is better? • It depends! • Issue: how much is money now worth compared to money in the future? • Leads to idea of time value of money! 35
  • 36. Time Value of Money • Would you rather have: • $100 today, or • $100 a year from now? • Basic assumption: • Given a fixed amount of money, and • A choice of having it now or in the future, • Most people would prefer to have it sooner rather than later 36
  • 37. Time Value of Money Most people would prefer to have it sooner. Why??? Reasons: • Security ? • Interests ? • Inflation? • Currency strength ? • Uncertainty ? 37
  • 38. Time Value of Money One consequence of the time value of money: • Suppose you are willing to exchange a certain amount now for some other amount later • Then the later amount has to be larger or smaller? 38
  • 39. Time Value of Money • The time value of money centers around the idea of an interest rate (if projecting into the future): • Or, equivalently, a discount rate (if rolling back to the present) 39 Time value of money deals with changes in the value of money over some period of time (due to investment opportunities, uncertainty, etc.) This is a key concept in engineering economics!
  • 40. – Money has a time value because it can earn more money over time (earning power). – Money has a time value because its purchasing power changes over time (inflation). – Time value of money is measured in terms of interest rate. – Interest is the cost of money a cost to the borrower & an earning to the lender 40 Time value of money
  • 41. What Does This Mean for Us? 41 In this course, we will learn methods to: • Compare different cash flows over time Using the interest rate or discount rate: • How much more a dollar today is worth compared to a dollar in one year For example, if the interest rate is 5%: • $1 today is worth as much as $1.05 next year
  • 42. Interest rates 42 Interest factor: The ratio between an amount one period in the future and an equivalent amount now. • Example: If you are indifferent between $5 now and $6 one period in the future, the interest factor is 6/5 = 1.20 (per period) Interest rate = interest factor – 1 • In above example, it’s 0.20 = 20%
  • 43. – Time value of money – Risk – Overhead costs – Inflation – Supply of & demand for funds 43 What determines interest rate?
  • 45. Simple interest: the practice of charging an interest rate only to an initial sum (principal amount). Compound interest: the practice of charging an interest rate to an initial sum & to any previously accumulated interest that has not been withdrawn. 45 Methods of calculating interest
  • 46. P = Principal amount i = Interest rate N = Number of interest periods Example: P = $1,000 i = 8% N = 3 years End of year Beginning balance Interest earned Ending balance 0 $1,000 1 $1,000 $80 $1,080 2 $1,080 $80 $1,160 3 $1,160 $80 $1,240 46 Simple interest
  • 47. F = P+(iP)N where P =Principal amount i =simple interest rate N =number of interest periods F =totalamountaccumulatedat theendofperiodN F = $1,000 + (0.08)($1,000)(3) = $1,240 47 Simple interest formula
  • 48. The practice of charging an interest rate to an initial sum & to any previously accumulated interest that has not been withdrawn. 48 Compound interest
  • 49. P = Principal amount i = Interest rate N = Number of interest periods Example: P = $1,000 i = 8% N = 3 years End of year Beginning balance Interest earned Ending balance 0 $1,000 1 $1,000 $80 $1,080 2 $1,080 $86.40 $1,166.40 3 $1,166.40 $93.31 $1,259.71 49 Compound interest F = P(1+ i)N
  • 51. Value and Utility 51 Value is the worth that a person attaches to a good or service Value is inherent in a regard a person has for it, not in the item itself Value is not the cost of the item Utility is a power to satisfy human wants and is determined subjectively Utility is the satisfaction that a person derives from an item
  • 52. Exchange 52 Without the subjectivity of the concepts “value” and “utility” there would hardly be any room for exchange between people. Why? Through exchange we can increase the total utility of the goods and services. How? Exchange is possible when it is mutually benefitial
  • 53. What If I Don’t Like the Answers? • Remember: • “Tools” don’t make decisions • People make decisions, based on values • Engineering economics is just a set of tools: • It can help in decision making • But it won’t make the decision for you • Which alternative is “best” is up to you! 53