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Transcript of 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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Characteristics of Risk
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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Characteristics of Risk
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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ECONOMIC EQUIVALENCE FOR FOUR
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 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 $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
Total interest paid ($2,096) is 10% of total dollar-years ($20,950)
ECONOMIC EQUIVALENCE FOR FOUR
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ECONOMIC EQUIVALENCE FOR FOUR
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 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 $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
Total interest paid ($3,713) is 10% of total dollar-years ($37,128)
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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CASH FLOW DIAGRAM NOTATION
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.
CASH FLOW DIAGRAM NOTATION
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CASH FLOW DIAGRAM NOTATION
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.
P =$8,000 2
2 Present expense (cash outflow) of $8,000 for lender.
CASH FLOW DIAGRAM NOTATION
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CASH FLOW DIAGRAM NOTATION
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.
P =$8,000 2
2 Present expense (cash outflow) of $8,000 for lender.
A = $2,524 3
3 Annual income (cash inflow) of $2,524 for lender.
CASH FLOW DIAGRAM NOTATION
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CASH FLOW DIAGRAM NOTATION
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
2 Present expense (cash outflow) of $8,000 for lender.
A = $2,524 3
3 Annual income (cash inflow) of $2,524 for lender.
i = 10% per year4
4 Interest rate of loan.
CASH FLOW DIAGRAM NOTATION
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CASH FLOW DIAGRAM NOTATION
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
2 Present expense (cash outflow) of $8,000 for lender.
A = $2,524 3
3 Annual income (cash inflow) of $2,524 for lender.
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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RELATING PRESENT AND FUTURE EQUIVALENT
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 = ?
RELATING PRESENT AND FUTURE EQUIVALENT
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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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Effective Interest Rate
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%
Effective Interest Rate
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Effective Interest Rate
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%
Effective Interest Rate
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Effective Interest Rate
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
DEPRECIATION CONCEPTS
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DEPRECIATION CONCEPTS
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)
DEPRECIATION CONCEPTS
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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