Lesson I, Engineering Economy

8/3/2019 Lesson I, Engineering Economy

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Risk AnalysisCE 828

Pooyan Aslani, Ph.D.

Department of Civil Engineering

Fall 2008


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Syllabus

Grading For purpose of grading, the

performance of students enrolled in CE

828 will be assessed using thefollowing scoring system:

Class Participation 15%

Homework* 45%

Final Exam/ Project 40%


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Homework Assignments

Homework problems will be assigned weeklyand are due by the beginning of the classthrough drop box system in my poly. Allhomework must be done in Microsoft

Excel.Late homework will be given no credit.

Students are encouraged to discuss & workon homework problems with otherclassmates, but all problems must becompleted by the student her/himself; nocopying will be permitted.


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Options for Extra Credit: Project

You may complete a project of your own design.Your objective is to apply one or more of theconcepts in this course to a specific problem inyour area of interest. The application should be toa fresh problem and it should represent your work.

Do not simply summarize an application that is

described in the literature The report should be double-spaced, and it should

not exceed 10 pages in length, including figuresand tables. The report should be concise and

clear; the emphasis is on creativity and quality,not quantity. I have to confirm your project topic and the final

report and presentation is due December 5, 2005


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Examination

final exam is formally scheduled for thefollowing date:

Thursday 18/12/2008


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Text and Reader/Notes

Required Textbooks for this course are following: Making hard decisions Clemen, R. and Reilly, T.

2004 update. ISBN: ISBN 0-495-01508-3 Against the Gods, The Remarkable Story of Risk''

Peter L Bernstein ISBN: 9780471295631

Recommended Reading: Data analysis using Microsoft Excel Middleton, M.Third Edition. Published by Thompson. ISBN:0534402933

`Fooled By Randomness, The Hidden Role of Chancein Life and in the Markets,' Nassim Nicholas Taleb,

2nd Ed., ISBN: 978-0812975215 ``The Black Swan: The Impact of the HighlyImprobable,''Nassim Nicholas Taleb, ISBN: 978-0812975215

Wall Street Journal. You can get a student discount.


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Topics to be covered

See the Syllabus


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What about you?

Introduces yourself

What area of Civil Engineering are youinterested in?

What year are you in?

Full time or Part time?

Who do you work for?

Beside the fact that CE 828 is one of themandatory courses what do you expectfrom the course to learn?


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Thinking?!

Thinking is important to all of us in ourdaily life.

Good thinking is; therefore not

something that is forced upon us inschool: It is something that we all want to do,

Wants other to do,

To achieve our goals and theirs

This approach gives a special meaningto the term rationale.


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Rational

Rational does not mean, here, a kind ofthinking that denies motions anddesires.

It means, the kind of thinking we wouldall want to do, if we were aware of ourown best interest, in order to achieve

our goals.


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Decision

A decision is a choice of action- of whatto do or not to do.

Decisions may attempt to satisfy the

goals of others as well as the selfishgoals of the decision maker.

Decision depend on beliefs and goals,but we can think about beliefs andgoals separately, without evenknowing what decisions they willaffect.


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What is Risk?

A riskis an event that may possibly occur,and if it did occur would have a negativeimpact on the goals of the organisation.Thus a risk is composed of three elements:1. The scenario,2. Its probability of occurrence,3. The size of its impact if it did occur (either a

fixed value or a distribution).

The concept of risk is about our recognition of

future uncertainty.Risk implies that a given action has more than

one possible outcome.


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What is opportunity?

An opportunityis an event that maypossibly occur, and if it did occurwould have a positiveimpact on the

goals of the organisation. Thus anopportunity is composed of the samethree elements as a risk.


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Characteristics of Risk

Risk is either subjective or objective. Flipping a coin is an objective because

the odds are well known.

An objective risk can be describedprecisely based on theory, experiment,or common sense.

Describing the odds for rain nextThursday is not so clear cut, andrepresent a subjective risk.


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Subjective Risk

Given the same information, theory,computers, etc., weatherman A maythink odds of rain are 30% while

weatherman B may think the odds are65% and neither are wrong!

Describing a subjective risk is open-ended in the sense that you could

always refine your assessment withnew information, further study, or bygiving weight to the opinion of others.


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Deciding that something is risky requirespersonal judgment, even for objectiverisks.

Flipping a coin where you win $ 1 forhead and loose $1 for tail would not besignificant to most people.

If the stakes were $100,000 and -$100,000 respectively, most peoplewould find the situation to be quite risky!


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Risky actions and therefore risk arethings that we often can choose oravoid. Individuals differ in the amount

of risk they willingly accept.


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The Need for Risk Analysis InCivil Engineering

Construction Will the cost construction materials and labor be

as forecast?

Will a labor strike affect the construction

schedule?

Structural

Will the level of stress placed on the structure bypeak load crowds and nature be as forecast?

Will the structure ever be stressed to the point offailure?


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Assessing and Quantifying Risk

Recognizing a need for risk analysis.

How do you quantify the risk you haveidentified for a given uncertain

situation?


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Quantifying Risk

Means determining all possible values arisky variable could take anddetermining the relative likelihood of

each value. Suppose your uncertain situation is the

outcome from the flip of a coin. You couldrepeat the flip a large number of timesuntil you had established the fact that halfof the times it comes up tails and half ofthe times heads.


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Describing Risk

Summarize the risk using a probabilitydistribution.

A probability distribution is a device for

presenting the quantified risk for avariable.


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What is Risk Analysis?

Risk analysis is any method -qualitative and/or quantitative forassessing the impact of risk on

decision situations.


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WHAT IS ECONOMICS ?

The study of how limited resources isused to satisfy unlimited human wants.

The study of how individuals and

societies chooseto use scarceresources that nature and previousgenerations have provided.


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Resources

Land

Labor

Capital


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Land

All gifts of nature, such as:water, air, minerals, sunshine,

plant and tree growth, as wellas the land itself which isapplied to the production

process.


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Labor

The efforts, skills, andknowledge of people which are

applied to the productionprocess.


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Capital

Real Capital (Physical Capital ) Tools, buildings, machinery -- things

which have been produced which areused 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


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Origins of Engineering Economy

The perspective that ultimateeconomy is a concern to theengineer and the availability of

sound techniques to address thisconcern differentiate this aspect ofmodern engineering practice fromthat of the past.


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PRINCIPLES OF ENGINEERING

ECONOMY

1. Develop the Alternatives;

2. Focus on the Differences;

3. Use a Consistent Viewpoint;4. Use a Common Unit of Measure;

5. Consider All Relevant Criteria;

6. Make Uncertainty Explicit;

7. Revisit Your Decisions


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DEVELOP THE ALTERNATIVES

The final choice (decision) isamong alternatives. The

alternatives need to beidentified and then definedfor subsequent analysis.


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USE A CONSISTENT VIEWPOINT

The prospective outcomes of thealternatives, economic and other,should be consistently developed

from a defined viewpoint(perspective).

USE A COMMON UNIT OF


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USE A COMMON UNIT OF

MEASURE

Using a common unit ofmeasurement to enumerate as many

of the prospective outcomes aspossible will make easier theanalysis and comparison of

alternatives.

CONSIDER ALL RELEVANT


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CONSIDER ALL RELEVANT

CRITERIA

Selection of a preferred alternative(decision making) requires the useof a criterion (or several criteria).

The decision process shouldconsider the outcomes enumeratedin the monetary unit and thoseexpressed in some other unit ofmeasurement or made explicit in adescriptive manner.

MAKE UNCERTAINTY EXPLICIT


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MAKE UNCERTAINTY EXPLICIT

Uncertainty is inherent in projecting(or estimating) the future outcomesof the alternatives and should be

recognized in their analysis andcomparison.

REVISIT YOUR DECISIONS


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REVISIT YOUR DECISIONS

Improved decision making resultsfrom an adaptive process; to theextent practicable, the initial

projected outcomes of the selectedalternative should be subsequentlycompared with actual results

achieved.

ENGINEERING ECONOMY AND


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ENGINEERING ECONOMY AND

THE DESIGN PROCESS

An engineering economy study isaccomplished using a structuredprocedure and mathematical

modeling techniques. Theeconomic results are then used in adecision situation that involves two

or more alternatives and normallyincludes other engineeringknowledge and input.

ENGINEERING ECONOMIC


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ENGINEERING ECONOMIC

ANALYSIS PROCEDURE

1. Problem recognition, formulation, andevaluation.

2. Development of the feasible

alternatives.3. Development of the cash flows for eachalternative.

4. Selection of a criterion ( or criteria).

5. Analysis and comparison of thealternatives.

6. Selection of the preferred alternative.

7. Performance monitoring and post-evaluation results.


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LIFE-CYCLE COST

Life-cycle cost is the summation ofall costs, both recurring andnonrecurring, related to a product,

structure, system, or service duringits life span.

Life cycle begins with the

identification of the economic needor want ( the requirement ) and endswith the retirement and disposalactivities.

FIXED VARIABLE AND INCREMENTAL


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FIXED, VARIABLE, AND INCREMENTAL

COSTS

Fixed costsare those unaffected by changesin activity level over a feasible range ofoperations for the capacity or capabilityavailable.

Typical fixed costs include insurance andtaxes on facilities, general management andadministrative salaries, license fees, andinterest costs on borrowed capital.

When large changes in usage of resourcesoccur, or when plant expansion or shutdownis involved fixed costs will be affected.

RECURRING AND NONRECURRING


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RECURRING AND NONRECURRING

COSTS

Recurring costs are repetitive and occurwhen a firm produces similar goods andservices on a continuing basis.

Variable costs are recurring costsbecause they repeat with each unit ofoutput .

A fixed cost that is paid on a repeatablebasis is also a recurring cost:

Office space rental

$

DIRECT INDIRECT AND OVERHEAD


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DIRECT, INDIRECT AND OVERHEAD

COSTS

Direct costs can be reasonablymeasured and allocated to a specificoutput or work activity -- labor andmaterial directly allocated with a

product, service or constructionactivity;

Indirect costs are difficult to allocate to

a specific output or activity -- costs ofcommon tools, general supplies, andequipment maintenance ;

DIRECT INDIRECT AND OVERHEAD


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Overhead consists of plant operatingcosts that are not direct labor ormaterial costs indirect costs, overhead and burden are

the same; Prime Cost is a common method of

allocating overhead costs among

products, services and activities inproportion the sum of direct labor andmaterials cost ;

DIRECT, INDIRECT AND OVERHEADCOSTS

INTEREST & INTEREST RATE


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INTEREST & INTEREST RATE

The fee that a borrowerpays to a lender for the use

of his or her money. The percentage of money

being borrowed that is paidto the lender on some timebasis.

SIMPLE INTEREST


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SIMPLE INTEREST

The total interest earned or charged islinearly proportional to the initial amount ofthe loan (principal), the interest rate and

the number of interest periods for whichthe principal is committed.

When applied, total interest I may be

found by I = ( P ) ( N ) ( i ), where P = principal amount lent or borrowed

N = number of interest periods ( e.g., years )

i = interest rate per interest period

COMPOUND INTEREST


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COMPOUND INTEREST

Whenever the interest charge for any interestperiod is based on the remaining principalamount plus any accumulated interest chargesup to the beginningof that period.

Period Amount Owed Interest Amount Amount OwedBeginning of for Period at end of

period ( @ 10% ) period1 $1,000 $100 $1,100

2 $1,100 $110 $1,210

3 $1,210 $121 $1,331


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ECONOMIC EQUIVALENCE

Established when we are indifferent between afuture payment, or a series of future payments,and a present sum of money .

Considers the comparison of alternative options, or

proposals, by reducing them to an equivalentbasis, depending on:

interest rate;

amounts of money involved;

timing of the affected monetary receipts and/orexpenditures;

manner in which the interest , or profit on

invested capital is paid and the initial capital isrecovered.

ECONOMIC EQUIVALENCE FOR FOUR REPAYMENT


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Q

PLANS OF AN $8,000 LOAN

Plan #1: $2,000 of loan principal plus 10% of BOY principal paidat the end of year; interest paid at the end of each year isreduced by $200 (i.e., 10% of remaining principal)

Year Amount Owed Interest Accrued Total Principal Total endat beginning for Year Money Payment of Yearof Year owed at Payment( BOY ) end of

Year

1 $8,000 $800 $8,800 $2,000 $2,800

2 $6,000 $600 $6,600 $2,000 $2,600

3 $4,000 $400 $4,400 $2,000 $2,400

4 $2,000 $200 $2,200 $2,000 $2,200

Total interest aid $2 000 is 10% of total dollar- ears $20 000


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Plan #2: $0 of loan principal paid until end of fourthyear; $800 interest paid at the end of each year

Year Amount Owed Interest Accrued Total Principal Total end

at beginning for Year Money Payment of Yearof Year owed at Payment( BOY ) end of

Year

1 $8,000 $800 $8,800 $0 $8002 $8,000 $800 $8,800 $0 $800

3 $8,000 $800 $8,800 $0 $800

4 $8,000 $800 $8,800 $8,000 $8,800

Total interest paid ($3,200) is 10% of total dollar-years ($32,000)

ECONOMIC EQUIVALENCE FOR FOURREPAYMENT PLANS OF AN $8,000 LOAN

ECONOMIC EQUIVALENCE FOR FOUR


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REPAYMENT PLANS OF AN $8,000 LOAN

Plan #3: $2,524 paid at the end of each year; interestpaid at the end of each year is 10% of amount owedat the beginning of the year.



Year

1 $8,000 $800 $8,800 $1,724 $2,5242 $6,276 $628 $6,904 $1,896 $2,524

3 $4,380 $438 $4,818 $2,086 $2,524

4 $2,294 $230 $2,524 $2,294 $2,524




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REPAYMENT PLANS OF AN $8,000 LOAN

Plan #4: No interest and no principal paid for first three years. Atthe end of the fourth year, the original principal plusaccumulated (compounded) interest is paid.



Year

1 $8,000 $800 $8,800 $0 $0

2 $8,800 $880 $9,680 $0 $0

3 $9,680 $968 $10,648 $0 $0

4 $10,648 $1,065 $11,713 $8,000 $11,713


CASH FLOW DIAGRAMS / TABLE NOTATION


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CASH FLOW DIAGRAMS / TABLE NOTATION

i = effective interest rate per interest periodN = number of compounding periods (e.g., years)

P = present sum of money; the equivalent value of oneor more cash flows at the present time reference

pointF = future sum of money; the equivalent value of one or

more cash flows at a future time reference point

A = end-of-period cash flows (or equivalent end-of-

period values ) in a uniform series continuing for aspecified number of periods, starting at the end of thefirst period and continuing through the last period

G = uniform gradient amounts -- used if cash flowsincrease b a constant amount in each eriod

CASH FLOW DIAGRAM NOTATION


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1 2 3 4 5 = N

1

1Time scale with progression of time moving from left toright; the numbers represent time periods (e.g., years,months, quarters, etc...) and may be presented within atime interval or at the end of a time interval.



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1 2 3 4 5 = N

1


P =$8,000 2

2 Present expense (cash outflow) of $8,000 for lender.



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1 2 3 4 5 = N

1


P =$8,000 2


A = $2,524 3

3 Annual income (cash inflow) of $2,524 for lender.



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1 2 3 4 5 = N

1

1 Time scale with progression of time moving from left toright; the numbers represent time periods (e.g., years,months, quarters, etc...) and may be presented within atime interval or at the end of a time interval.

P =$8,000 2


A = $2,524 3


i = 10% per year4

4 Interest rate of loan.



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1 2 3 4 5 = N1

1Time scale with progression of time moving from left to right;the numbers represent time periods (e.g., years, months,quarters, etc...) and may be presented within a time interval orat the end of a time interval.

P =$8,000 2


A = $2,524 3


i = 10% per year4

4 Interest rate of loan.

5

5Dashed-arrow line indicates

amount to be determined.

RELATING PRESENT AND FUTURE EQUIVALENT


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VALUES OF SINGLE CASH FLOWS

Finding F when given P: Finding future value when given present

value

F = P ( 1+i ) N

(1+i)N single payment compoundamount factor

functionally expressed as F = ( F / P,

i%,N )

P

0

N =

F = ?



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Finding P when given F: Finding present value when given future

value

P = F [1 / (1 + i ) ] N (1+i)-N single payment present worth

factor

functionally expressed as P = F ( P / F,i%, N )

VALUES OF SINGLE CASH FLOWS

P = ?

0 N =F

RELATING A UNIFORM SERIES (ORDINARY


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RELATING A UNIFORM SERIES (ORDINARYANNUITY) TO PRESENT AND FUTURE EQUIVALENT

VALUES

Finding F given A:

Finding future equivalent income (inflow) valuegiven a series of uniform equal Payments

( 1 + i ) N - 1

F = A

i

uniform series compound amount factor in [ ] functionally expressed as F = A ( F / A,i%,N )

RELATING A UNIFORM SERIES (ORDINARY


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ANNUITY) TO PRESENT AND FUTURE EQUIVALENT

VALUES

Finding F given A:

Finding future equivalent income (inflow) value givena series of uniform equal Payments

( 1 + i )N

- 1F = A

i

uniform series compound amount factor in [ ]

functionally expressed as F = A ( F / A,i%,N )

predetermined values are in column 4 ofAppendix C of text F = ?

1 2 3 4 5 6 7 8 A =

RELATING A UNIFORM SERIES (DEFERRED ANNUITY)


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RELATING A UNIFORM SERIES (DEFERRED ANNUITY)

TO PRESENT / FUTURE EQUIVALENT VALUES

If an annuity is deferredjperiods, wherej < N

And finding P given A for an ordinary annuity isexpressed by:

P = A ( P / A, i%,N )This is expressed for a deferred annuity by:

A ( P / A, i%,N -j) at end of periodj

This is expressed for a deferred annuity by:A ( P / A, i%,N -j) ( P / F, i%,j)as of time 0 (time present)


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NOMINAL AND EFFECTIVE INTEREST RATES

Nominal Interest Rate - r - For rates compounded morefrequently than one year, the stated annual interestrate.

Effective Interest Rate - i - For rates compounded morefrequently than one year, the actual amount of interestpaid.

i = ( 1 + r / M )M - 1 = ( F / P, r / M, M ) -1

M - the number of compounding periods per yearAnnual Percentage Rate - APR - percentage rate per

period times number of periods.

APR = r x M

Effective Interest Rate


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Ex: the nominal rate is 16%/yearcompounded quarterly. What iseffective rate?

r= 16%/year divided by 4= 4%quarter.On an annual basis, this equals16.99%/year. The general formula is

ieff= (1+ r/M)M 1

ieff = (1+ 0.16/4)4 1= (1.04)4 1=1.1699-1= .01699= 16.99%



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A credit company advertises a nominalrate of 16% on unpaid balancescompounded daily. What is the

effective interest rate per year beingcharged?

r = 16%/year, M= 365 days/ year

ieff= (1+0.16/365)365-1=0.1735=17.35%



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In the beginning of this section, I wasdefined simply as the interest rate perinterest period. A more precise

definition, we know, is that Iis theeffective interest rate per period. Whencompounding is continuous, we havespecial case in which

ieff = er-1

PRESENT WORTH METHOD ( PW )


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PRESENT WORTH METHOD ( PW )

Based on concept of equivalent worth of allcash flows relative to the present as a base

All cash inflows and outflows discounted

to present at interest -- generally MARR PW is a measure of how much money

can be afforded for investment in excessof cost

PW is positive if dollar amount receivedfor investment exceeds minimumrequired by investors

FINDING PRESENT WORTH


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FINDING PRESENT WORTH

Discount future amounts to the present by using theinterest rate over the appropriate study period

PW = P Fk ( 1 + i ) k

i = effective interest rate, or MARR per compoundingperiod

k = index for each compounding period

Fk = future cash flow at the end of period k

N = number of compounding periods in study period

interest rate is assumed constant through project

The higher the interest rate and further into future a cash flowoccurs, the lower its PW

k = 0

N

Discount Rate


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Discount Rate

Three main factors must be considered: Investment opportunities: what alternative opportunities are

available for investment?

Risk: is the proposed project more or less risky than the otheroptions?

Inflation: how much will inflation reduce the future purchasingpower of our money?

Discount Rate


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Discount Rate

It is possible to think of the discount rate asbeing made up of three components relatedto these three factors:

The rate-of-return for risk-free investments, such

as bank accounts or government bonds (i%) A risk premium that reflects the amount of risk in

the project (r%)

A premium to offset the expected effects of

inflation (inf%)

DEPRECIATION


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DEPRECIATION

Decrease in value of physical propertieswith passage of time and use

Accounting concept establishing annualdeduction against before-tax income

- to reflect effect of time and use on assetsvalue in firms financial statements

- to match yearly fraction of value used byasset in production of income over assets

economic life

PROPERTY IS DEPRECIABLE IF IT


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MUST :

be used in business or held to produceincome

have a determinable useful life which is

longer than one year wear out, decay, get used up, become

obsolete, or lose value from naturalcauses

not be inventory, stock in trade, orinvestment property

DEPRECIATION CONCEPTS


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Adjusted cost basis -- allowableadjustment (increase or decrease) tooriginal cost basis, used to calculate

depreciation and depletion deductionsBasis, or cost basis -- also called

unadjusted cost -- initial cost of

acquiring an asset, plus sales tax,transportation, and normal costs ofmaking asset serviceable



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Market Value (MV) -- Amount paid by willingbuyer to willing seller for property where noadvantage and no compulsion to transact

-- approximates present value of what willbe received through ownership of property,including time-value of money (or profit)



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The following terms are used in the classical(historical) depreciation method equations:N = depreciable life of the asset in yearsB = cost basis, including allowable adjustmentsd k = annual depreciation deduction in year k (1< k


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( )

Simplest depreciation method:Assumes constant amount is depreciatedeach year over depreciable (useful) life

d k = ( B - SVN ) / Nd k* = kdk for 1 < k < N

BVk = B - d k*

This method requires an estimate of the finalSV ( also the final book value at the end ofyear N )

DECLINING BALANCE (DB) METHOD


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Sometimes called constant percentage method or

Matheson formulaAssumed annual cost of depreciation is fixedpercentage of BV at beginning of year

R is constantR = 2 / N when 200% declining balance

used R = 1.5 / N when 150% decliningbalance used

d 1 = B ( R )d k = B ( 1 - R )

k - 1 ( R )d

k*

= B [ 1 - (1 - R ) k ]BV k = B ( 1 - R )

kBV N = B ( 1 - R )

N Because declining balance method never reaches

BV = 0, its permissible to switch from this to straight-line method so assets SV

Nwill be zero or other

desired value

SUM-OF-THE-YEARS-DIGITS (SYD) METHOD


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Book value at the end of year k

2(B - SVN) (B - SV

N)

BVk = B - ----------------- k + ----------- k (k + 1 )N N (N + 1)

The cumulative depreciation through the kth year

d k* = B - BV k

( )


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Thursday 11th

Preliminary Data Analysis1. Read Against the Gods pp.1-

39

2. Homework posted at my.poly

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Lesson I, Engineering Economy

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