CCP_SEC6_Economic Analysis Statistics and Probability and Risk

EECONOMICCONOMIC AANALYSIS,NALYSIS,
SSTATISTICS,TATISTICS, PPROBABILITY ANDROBABILITY AND RRISKISK
Hisham Haridy, PMP, PMI-RMP, PMI-SP
CCP_Section VI

1. Financial & Cash Flow Analysis
2. Practical Corporate Investment Decision-Making Guide
3. Statistics & Probability
4. Optimization
5. Risk Management Fundamentals
CContentontent
5. Risk Management Fundamentals
6. Risk Management Practical Guide
7. Total Cost Management Overview
8. The International System of Units (SI)
ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK

FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS
Time Value of money
The monetary costs and benefits must be calculated at a
single point in time.
In this way can compare projects that have very different
time profiles of benefits and costs.
Compounding
Future ValuePresent Value
Compounding
Discounting
A value expressed in dollars
received immediately
A value expressed in
dollars received at
some future time
n
i1PVFV )(* +=n
i1
FV
PV
)( +
=

Simple Interest Compound Interest
Interest Interest Rate
The amount earned or paid for the
use of money.
The % of the principal earned or paid
per unit of time.
The amount paid only on the
principal.
The interest that is earned on both the
principal and any interest that has
been previously earned.
Principal
The amount of money borrowed or deposited.

$100 $100
I = 10%
0 1 2
EOY 1 EOY 2
Principal = $1,000
3
Total @EOY3 with
simple interest =
$1,300
Year EOY 3
Principal = $1,000
Simple
Interest
I = 10%
0 1 2
EOY 1 EOY 2
Principal = $1,000
3
Total @EOY3
with simple
interest =
$1,331
Year EOY 3
$100 $110
Total @EOY3
with simple
interest =
$1,210
Total @EOY3
with simple
interest =
$1,100
$121
Compound
Interest

Nominal Interest Rate Effective Interest Rate Continuous Interest Rate
The customary
type of interest
rate designation
on an annual basis
without
An interest rate for a
stated period (per year
unless otherwise
specified) that is the
equivalent of a smaller
Discrete compounding
occurs when interest
payments are made at
the end of finite
compounding periods.
consideration of
compounding
periods.
A frequent basis
for computing
periodic interest
payments.
rate of interest that is
more frequently
compounded.
K =1 “Annual”
K=2 Semi-Annual”
K=12 “Monthly”
EIR, i = 1 +
r k
- 1
k
i = e
r
- 1

Rates of Return (ROR)
it is the effective annual interest rate earned on an investment.
Minimum attractive rate of return (MARR)
The lowest ROR at which a company will consider investing.
It is not usually stated as an option, it is a constraint or decision criteria that
applies to all investment considerations.
The selection of an appropriate MARR depends generally upon the cost of
The selection of an appropriate MARR depends generally upon the cost of
capital, However, the highest one of the following three values:
1. Cost of borrowed money from banks,
insurance companies, etc.
2. Cost of capital or the composite value for
the capital structure of the firm.
3. Opportunity cost or the rate-of-return of the
best project that is rejected.

BANK
Loans Share capital
Methods of Financing
Debt Financing Equity Financing
Interest on loans Shareholders return
Money raised through loans or
by an issuance of bonds
Capital is coming from either
retained earnings or funds raised
from an issuance of stock

Cost Of Capital
The rate the firm must pay to various sources for the use of capital
Cost of Debt
Cost associated
with borrowing
capital from
creditors
Costofcapital
Cost of Equity
Opportunity cost
associated with
using
shareholders’
capital
creditors
Costofcapital

Workshop
A firm is evaluating the feasibility of a design and construction project and needs to
know what interest rate should be used in the study.
The following data has been compiled:
i. Cost of borrowed money, loan A = 9%
ii. Investment opportunity, project B = 16%
iii. Cost of capital = 20%

Discount Rate
The rate of interest reflecting the investor's time value of money, used to
determine discount factors for converting benefits and costs occurring at different
times to a base time.
The discount rate may be expressed as nominal or real
The equivalent amount X given amount Y,
Interest rate i
(X/Y, i, n)
Interest rate i
The number of discounting or compounding periods n.

P Present Value
A single lump sum occurring at time zero, the first of n time
periods.
A Annual Value
Annual amount or annuity.
A uniform series of end-of-period payments or receipts.
Annual Compounding
F Future Value
A single lump sum value occurring at the end of the last of n time
periods
G Gradient Value
Uniform or arithmetic gradient amount;
A constant increase or decrease in funds flow at the end of each
period.

Discount Factors for Discrete Compounding

55%%
66%%

Cash flow
Inflow and outflow of funds within a project.
A time-based record of income and expenditures, often presented graphically
Year Income Expense
0 $20,000
Cash Flow Table
0 $20,000
1 $5,000 $500
2 $5,000 $600
3 $5,000 $700
4 $5,000 $800
5 $5,000 $900

$5,000
0 1 2 3
$5,000 $5,000 $5,000 $5,000
4 5
Cash Flow Diagram
$500 $600 $700 $800 $900$20,000
Cash Flow Conventions

Cash Flow Notation
Salvage Value (S)
In many studies there may be a residual value resulting in income at the end of
the useful life of an asset.
It is shown as an upward arrow on the cash flow diagram.
If the salvage value is low with respect to other cash flow, it is usually omitted.

CASH FLOW ANALYSIS METHODS
There are two fundamental approaches to the analysis of a given cash flow,
1. Equivalent value
2. Rate-of-return
Equivalent Net Value
The equivalent net value method simply converts to one of the basic forms, (i.e.,
The equivalent net value method simply converts to one of the basic forms, (i.e.,
the equivalent present value, or annual value, using discount factors and the
required MARR).
The "net" is the difference between all costs and all benefits (savings and other
gains).
Thus, the Net Present Value (NPV) takes into account the time value of money
adjusting to expenditures and returns, as they occur over time, so they can be
evaluated equally.

Equivalent Net Present Value (NPV)
A contractor is considering the acquisition of a piece of equipment with
anticipated financial impact as shown in Table. If the contractor’s MARR is 6%,
should the investment be made?

1. P = P0 + P1 + P2
2. P0 = -$38,000
3. P1 = - G (P/G,i,n)=-$1,000 (P/G, 6 %, 4) = -$4,945
4. P2 = A (P/A,i,n)=$11,000 (P/A, 6 %, 4) =$38,115
5. P = -$38,000 - $4,945 + $38,115 = -$4,830

Equivalent Net Future Value
Using the cash flows of the previous example calculate the net future value at
EOY4.
The future value method uses the end of the planning horizon as a reference
point.
1. F = F0 + F1 + F2
2. F0 = -P (F/P, i, n)= - $38,000 (F/P, 6%, 4) = -$47,956
3. F1 = -G (P/G, i, n) (F/P, i,n) = -$1,000 (P/G, 6%, 4) (F/P, 6%, 4) = -$6,241
4. F2 = A (F/A,i,n) = $11,000 (F/A, 6 %t, 4) = $48,125
5. F = -$47,956 - $6,241 + $48,125 = -$6,072

Equivalent Annual Value
The basis of this method is the conversion of all cash flows to an Equivalent
Uniform Annual Value (EUAV).
Approach (1)
1. A = A0 + A1 + A2
2. A0 = P (A/P, i, n) = -$38,000 (A/P, 6 %, 4) = -$10,967
3. A1 = G (A/G, i,n) = -$1,000 (A/G, 6 %, 4) = -$1,427
3. A1 = G (A/G, i,n) = -$1,000 (A/G, 6 %, 4) = -$1,427
4. A2 = $11,000
5. A = -$10,967 - $1,427 + $11,000 = -$1,394
Approach (2)
1. Convert P or F as determined previously to annuity
2. P = - $4,830
3. A = P (A/P, i, n) = -$4,830 (A/P, 6%, 4) = -$4,830 (.2886) = -$1,394
4. F = - $6,075
5. A = F (A/F, i, n) = -$6,075 (A/F, 6 percent, 4) = -$6,075 (.2286) = -$1,389

Capitalized Cost
The present sum of money (P) that would have to be set aside now, at a given
interest rate (i), to provide a perpetual uniform cash flow (A).
For example, in governmental analysis of permanent structures such as roads,
dams, and pipelines, the required maintenance can be spread over an infinite
period ( n = 8) .
Example: What is the capitalized cost of a public works project that will cost
$15,000,000 now and will require $1,000,000 in annual maintenance? The
effective annual interest rate is 10%.
P = $15,000,000 + $1,000,000/.10 = $25,000,000
P=
A
i

Internal Rate of Return (IRR)
Discount rate of required return such that the NPV = 0
It’s the rate of return internally generated by the project (Finance definition).
The discount rate that will equal all cash flow to the initial investment (Math definition).
0 = ∑
FV
- Initial investment
(1+i)n
Where:
Although the project B has a smaller duration than project A does not matter because
time is already taken into account in IRR calculations
Example
You have two projects to choose from; Project A with an IRR of 21 percent will be
completed in 4 years or Project B with an IRR of 15 percent will be completed in one year.
Which one would you prefer?
i : Rate of return

The higher IRR is better if it’s multiple project. However, we always compare with the WACC
and we ONLY accept the project which produce IRR > WACC.
In case conflict, we should use NPV that we can trust NPV!!! BUT WHY?
When compared to NPV, each of the alternative ways of assessing profitability that we will
examine is flawed in some key way; so NPV is the preferred approach in principle, if not
always in practice.
There are three conditions or keys:
1. Take all cash flow into consideration.
2. Average modification for risk.
3. Precise value of the project.
Firstly, estimating the future cash flows we expect the new business to produce.
Appling our basic discounted cash flow procedure to estimate the present value of those cash
flows.
Estimating NPV as the difference between the present value of the future cash flow and the
cost of the investment. “discounted cash flow (DCF) valuation”

Benefit Cost Ratio (BCR)
A comparison of revenue to costs. Greater than 1 is good.
BCR of > 1 means that benefits (i.e. expected revenue) is greater than the
cost. Hence it is beneficial to do the project.
BCR=
PV “Benefits”
PV “Costs”
Project “A”
Example
Project A has an investment of $ 500,000 and BCR of 2.5 Project B has an
investment of $ 300,000 and BCR of 1.5 Using the Benefit Cost Ratio criteria,
which project will you select?
Although the project B has a smaller investment than project A will not impact
the selection

Workshop
1. If a monthly interest rate is compounded to yield an effective 12.00 percent
annual rate of return, then that monthly interest rate must be…
2. The following chart shows end-of-period cash flows for expenses. The interest
rate is 10%:
What is the net present value of this cash flow?

Workshop
3. To finance part of an owner’s new manufacturing facility, the board of directors
decides to issue 2,000 bonds with a face value of $1,000, all of which are due in
15 years. The bond coupons shall pay 8% per annum, and the coupons are
payable semiannually. If buyers expect a compounded 10% rate-of-return on their
investment, what should they pay for the bonds?

Workshop
A chemical engineer obtains a 17-year patent for a new process and determines to
sell it, intending to invest the proceeds for his eventual retirement. A company
desires to purchase the patent and offers the engineer either of two options:
a. Sell the patent rights for royalties of $20,000 per year for four years, followed
by $10,000 per year for four additional years.
b. Immediately sell the patent rights for a lump-sum of $85,000.
The engineer estimates the weighted average annual return after taxes on his
retirement investment accounts to be 11%. His effective income tax rate will be 40%
for the lump-sum option and 35% for periodic payments.

Workshop
1. The cash inflows for option “a” could be viewed equivalently as:
A. $10,000 per year for years 1 through 8, plus $10,000 per year for years 1
through 4
B. $20,000 per year for years 1 through 4, plus $10,000 per year for years 5
through 8
C. Both A and B
D. None of the above
2. The 11% discount rate is properly applied:
A. After expected income taxes are deducted from the cash inflows each year
B. Before expected income taxes are deducted from the cash inflows each year
C. Both A and B are correct due to equivalence
D. None of the above
3. The NPV of the after-tax cash flow for year 4 of option “a” is????

Multiple Alternatives
Three simple rules will help identify the preferred alternative when using the
net equivalent value methods:
1. Compute the net present value of each alternative at the required MARR.
2. Rank the alternatives.
3. Select the alternative having the highest net present value
Example
Example
Given the mutually-exclusive alternatives A, B, C, and a minimum attractive rate
of return (MARR) of five percent, which one would be chosen?
1. PVA = - $2,500 + $3,100 (P/F, 5%, 5) = -$2,500 + $3,100 (.7835) = -$71
2. PVB = - $2,700 + $650 (P/A, 5%, 5) = -$2,700 + $650 (4.329) = $114
3. PVC = - $3,000 + $350 (P/G, 5%, 5) = -$3,000 + $350 (8.237) = -$117

Incremental Analysis
This technique is based on the paired comparison of alternatives.
The following steps should be followed in an incremental rate-of return analysis:
1. Identify all alternatives.
2. Calculate the ROR for each alternative and discard any alternative with ROR <
MARR.
3. Arrange remaining alternatives in ascending order of initial cost.
3. Arrange remaining alternatives in ascending order of initial cost.
4. Calculate the ROR on the difference between the first two (lowest initial cost)
alternatives (if this ∆ROR = MARR, retain the higher cost alternative, otherwise
retain the lower cost alternative).
5. Select the retained alternative from the previous step, compare it to the next
higher alternative using the calculation of step 4 and calculate the rate-of-return
on their difference (if this ∆ROR = MARR, retain the higher cost alternative,
otherwise retain the lower cost alternative).
6. Repeat this process until all alternatives have been evaluated.

PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE
Capital is financial assets or financial value of assets.
Capital is a limited resource, and there are numerous projects that are
competing for funding.
Investment decision makers review many projects and options to evaluate
what is best for the company.
The Project Assessment Document (PAD) facilitate the review process.
There are three important elements required by investment decision makers:
There are three important elements required by investment decision makers:
1. Value to the Company
2. Effect on Cash Flow
3. Transparency of Risk to the Company

i. Value to the Company
Company’s market and operating condition.
A project aligned with the core values (strategic vision) of the company.
Business lines that are difficult to sustain and that pull a company away from its
strategic vision will erode the cash flow of the company over time.
ii. Effect on Cash Flow
Cash flow analysis is generally more important than profit analysis.
Cash flow analysis is generally more important than profit analysis.
It is important to determine the viability of company.
Projects must support and improve the cash flow of a company.
Not all projects generate profit, but they can improve the cash flow of a company.
iii. Transparency of Risk to the Company
A transparent, clear, and realistic accounting of risks is vital to assessing a project.
It is far better to fund a well-defined (but less profitable) project than to fund
(gamble on) a highly profitable project with uncertain risks.

Forms of Business Organizations
1. Proprietorship
2. Partnership
3. Corporation
20%
9%
71%
Proprietorship Partnership Corporation

Corporate Organization

Goals of the Corporation
Primary Goal
MAXIMIZE Stockholder Wealth = MAXIMIZE Stock Price
Managerial Incentives
Controlled by competitive forces
Controlled by competitive forces
Social Responsibility
Must be mandated initially to reduce disadvantages
Stock Price Maximization and Social Welfare
Maximizing stock = benefiting society

Front-End Engineering and Design (FEED)
It helps establish a well-defined scope, budget, schedule, and identifies
risks, resulting in greater success during implementation and start-up.
By undertaking FEED at the beginning of any project, you can minimize your
overall project risks.
Benchmark studies show benefits of up to 30% reduced cost and shorter
project execution times when FEED studies are performed.

Front End Loading (FEL) or Pre-Project Planning (PPP)
Defining the project scope and plans in a way that assures the best practical
level of definition is achieved as needed to support a project decision gate.
FEL is pre-project planning to develop sufficient strategic information to
assess risks to make decisions concerning resources and insure success.
The optimal critical success factors that define FEL are determined based upon
the project’s outcome as assessed by the key performance indicators.
the project’s outcome as assessed by the key performance indicators.
The key performance indicators
By which an organization can measure the progress being made to ensure that
the critical success factors are being achieved.

Average Annual Rate of Return (AARR)
The measure (%) of profitability of an asset over a period of time.
It is the average yearly profit over the operating lifecycle of a facility and
dividing it by the final cost of the project.
It compares to the corporate discount rate of a company.
Investment
Investment
The act of contributing money or capital into an enterprise with the expectation
of future profit.
Investments have a limited decision time-frame to determine the impact of a
20-year life cycle on the company cash flow.

Executive Summary
There are 7 key elements to an executive summary:
1. Statement of the problem that the project addresses “how the project aligns
with their strategic investment portfolio”
2. Project Summary “what the project is, why it s important, and what the
value is to the investor”
3. Key Project Drivers “summarizes the key factors that influence the
3. Key Project Drivers “summarizes the key factors that influence the
economic indicators and cash flow for the company”
4. Primary Risks and Uncertainties
5. Capital Cost Variance
6. Average Annual Rate of Return Variance
7. Cash Flow Analysis

Capital Cost variance

Cash Flow Analysis
Cash flow = Cash Receipts - Cash Payments
1. Operations = Revenue generated by operations – Materials – Labor
2. Financing = Loan + Cash Received from equity or issue of debt/shares - Loan
repayment – Taxes – Dividends - Share repurchase
3. Investments = Sale of Assets + Purchase Capital – Acquisitions
Common elements that directly affect the cash flow of a project and
corporation:
Economic Risks
Financial Risks
Political Risks

Project Drivers
Capital Revenue Expense Schedule
Project Drivers
Drivers:
Drivers are specific influencing factors to a project’s success, and are often
based on research from the corporation or project team.
Drivers
Technical
Issues
Commercial
Issues

1. Capital Drivers
The ultimate investment decision for the company must consider the total cost
of the project along with other cost drivers.
i. Technical Issues (The technical design alternatives need to be quantified in
terms of capital cost)
ii. Commercial Issues (Cost of land, cost of capital, credit risk, and taxation).
2. Revenue Drivers
The primary revenue drivers for any commercial project are production (rate
and volume) and prices.
i. Technical Issues (Product strategy)
ii. Commercial Issues (keep the product viable over the planned life cycle and
keep the cash flow positive).

3. Expense Drivers
The primary expense cost components are fixed operating costs, variable
operating costs, utilities, and fuel.
i. Fixed Operating Cost
ii. Variable Operating Cost
iii. Utilities
iv. Tariffs
iv. Tariffs
v. Regulations or regularity issues
4. Schedule Drivers
The technical, commercial and political factors that contribute to the project
schedule and any uncertainty and risk.
i. Late Change to Scope or Design
ii. Force Majeure

Economic Summary
If the completed project is not meeting the economic indicators in the
future, then it is important to review the basis of the original economic premises
to determine what changed.
Base Case Economic Indicators
The project needs to declare the NPV, AARR on both a gross cost basis and net
cost basis.
cost basis.
Basic economic indicators should be considered to evaluate the project on a
near-term and long-term basis.
i. The Profitability Index (PI)
ii. The Return On Capital Employed (ROCE)

i. The Profitability Index (PI)
PI > 1 means that benefits (i.e. expected revenue) is greater than the cost. Hence it is
beneficial to do the project. ACCEPTED.
Easy to understand and communicate for market agents or market clients.
Profitability Index (PI)=
∑ PVCF
Initial Investment
The amount of value the project creates per each 1$ of investment
Also called the benefit cost ratio
Example
XYZ Corporation is undertaking a project at a cost of $50 million which is expected to
generate future net cash flows with a present value of $65 million. Calculate the profitability
index.
Profitability Index (PI)=
$65
= 1.3
$50
PI greater than one means the project should be considered.

ii.The Return On Capital Employed (ROCE)
The Return On Capital Employed (ROCE)=
Operating Income
Assets Employed
How efficient a company is to generating profit out of capital
The Return On Capital Employed (ROCE)=
Sales
(Assets Employed - liabilities)
(ROCE)=
(Sales / Assets Employed) X [(Operating Income before
taxes and interest)/Sales]
Example
Company A that realizes a profit of 40 million USD and has 600 million in assets while
Company B that makes the same profit with 800 million USD in assets. Both companies have
the same liabilities.
ROCE=
40
= 6.67%
600
ROCE=
40
= 5%
800
Company A Company B
(ROCE)=
taxes and interest)/Sales]

Risks to Revenue Generation
Cash flow is an extremely important assessment to a corporation.
Projects are funded and built to address the corporation cash flow.
It is important to understand the risks to the cash flow.
A tornado diagram can be used to depict the magnitude of the risks to the
project’s revenue.
The variance on
annual revenue
generated

STATISTICS & PROBABILITYSTATISTICS & PROBABILITY
Statistics
The field of study where data are collected for the purpose of drawing conclusions and
making inferences.
Descriptive statistics Inferential statistics
The summarization and description of The estimation, prediction, and/or
data generalization about the population based on
the data from a sample.
‫معلومات‬ ‫جمع‬
‫و‬ ‫تنظيمھا‬
‫عرضھا‬
‫إستخراج‬ ‫و‬ ‫تحليلھا‬
‫منھا‬ ‫مقاييس‬

Population Sample
The collection of all elements from which
statistical inferences are to be developed.
The size of the population is usually
denoted by N.
A subset of data randomly selected
from a population.
The size of a sample is usually denoted
by n.
Data Information
Raw facts about physical phenomena Data that has been converted into
meaningful and useful context.

Quantitative
Discrete
Continuous
Describing Data
Qualitative Data Quantitative data
Graphic methods Numerical methods
Frequency
Distribution
Stem and Leaf
Plots
Histogram
Measures of
Location
Mean
(Average)
Median
Mode
Measures of
Dispersion
Range
Variance
Standard
Deviation
Relative
Standing
Percentile
Z-scores
T- Scores

Graphic Methods
Frequency
Distribution
Stem and Leaf Plots Histogram
The stem-and-leaf plot
It shows data arranged by place value.
It shows data arranged by place value.
Display data in an organized way that allows you to see each value.
Example
4 2
To write 42 in a stem-and-leaf plot, write each digit in a separate column.
Stem Leaf

Example
Use the data in the table to make a stem-and-leaf plot.
Test Scores
75 86 83 91 94
88 84 99 79 86
Stems
Test Scores
Leaves
7
8
9
5 9
3 4 6 6 8
1 4 9
9 1 4 9
Frequency
Class
Frequency
10 - 19 2
20 - 29 2
30 - 39 4
40 - 49 3
Example:
Suppose you have the following list of values: 12, 13, 21, 27, 33, 34,
35, 37, 40, 40, 41

Example
The following average training hours for every employee are selected
from the Jan. 20, 2003 “The 100 Best Companies to Work For” from
Fortune magazine, only the Top 50 company.

The sum of measurements
divided by the number of
measurements
Measures of Location
(Central Tendency)
Mean (Average) Median Mode
The middle
number, when the data
observations are
arranged in either
The measurement that
occurs most often in the
data set
The mode = 40 hours
Population mean is
denoted by µ = ∑X/N
Sample mean is denoted
by x‾ = ∑X/n
(Ungrouped data) or x‾
x‾ = ∑fX/∑F (Grouped
data)
The mean = 2,445/50 =
48.9 hours
arranged in either
ascending or descending
order.
If the number n of
measurements is
even, the median is the
average of the two
middle measurements in
the ranking.
The median= 40 hours
The mode = 40 hours

For symmetric data set, the mean = the median
If the median < the mean, the data set is skewed to the right
If the median > the mean, the data set is skewed to the left.

The difference
between the largest
and the smallest
Measures of
Dispersion
Range Variance Standard Deviation
The average of the
squared deviations
from the mean
The positive square root
of the variance.
The population standardand the smallest
values of the data
set.
The range = 160 - 20
= 140 hours.
from the mean The population standard
deviation is denoted by σ
The sample standard
deviation is denoted by s
The sample standard
deviation s =

Relative Standing
Percentile Z-scores
pth percentile: In any data set, the
pth percentile is the number with
exactly p percent of the measurements
fall below it and (100-p) percent fall
A z-score is the number of
standard deviations a point is
above or below the mean of a set
of data.
fall below it and (100-p) percent fall
above it when the data are arranged in
ascending or descending order.
of data.
The population z-score for a
measurement x is z = (x- µ)/ σ
The sample z-score for a
measurement x is z = (x-‾X)/s
Lowest Highest

Example
The following observation training hours for every employee are selected from
the Jan. 20, 2003 “The 100 Best Companies to Work For” from Fortune
magazine, only the Top 50 company.
Percentile of 50?????
Number of observation less than/total number of observations X 100
Percentile of observation 50 =32/50= 64% 50 under P64%

Example
You take the SAT and score 1100. The mean score for the SAT is 1026 and the
standard deviation is 209. How well did you score on the test compared to the
average test taker?
Z = (x- µ)/ σ
Z= (1100-1026)/209= 0.354
Z= (1100-1026)/209= 0.354
This means that your score was 0.354 standard deviation above the mean
Look up your z-value in the z-table to see what percentage of test-takers scored
below you is 63.68%.

Random variable
A numerical value to each outcome of a particular experiment
1. Discrete random variable can assume a countable number of values.
Number of sales
Number of calls
Shares of stock
People in line
People in line
Mistakes per page
2. Continuous random variable can assume any value along a given interval of a
number line.
Length
Depth
Volume
Time
Weight

Probability
Distributions
Discrete Continuous
The probability that the random
variable X will equal is P(x)
Binomial
Poisson
Normal
Distribution
Standard Normal
Distribution
‫ذو‬‫الحدين‬

1. Discrete Probability Distribution
The probabilities of the values of a discrete random variable may be derived
by means of probability tools such as tree diagrams or by applying one of the
definitions of probability, so long as these two conditions apply:
Population mean
The population mean is the weighted average of all of its values.
The weights are the probabilities.
This parameter is also called the expected value of X and is represented by
E(X).

Population variance
It is calculated similarly.
It is the weighted average of the squared deviations from the mean.
Standard deviation
The standard deviation is the same as before:

Example
Probability distributions can be estimated from relative frequencies.
Consider the discrete (countable) number of televisions per household from US
survey data.
1. What is the probability there is at least one television but no more than three in
any given household?
P(1 ≤ X ≤ 3) = P(1) + P(2) + P(3) = .319 + .374 + .191 = .884

2. Find the mean, variance, and standard deviation for the population of the number
of color televisions per household.
Mean:
= 0(.012) + 1(.319) + 2(.374) + 3(.191) + 4(.076) + 5(.028) = 2.084
Variance:
Standard Deviation
= (0 – 2.084)2(.012) + (1 – 2.084)2(.319)+…+(5 – 2.084)2(.028)= 1.107

Binomial distribution ‫فقط‬ ‫نتيجتان‬ ‫لھا‬ ‫تجربة‬
It is the probability distribution that results from doing a “binomial experiment”.
Binomial experiments have the following properties:
1. n identical trials
2. Two outcomes: Success or Failure
3. P(S) = p; P(F) = q = 1 – p
3. P(S) = p; P(F) = q = 1 – p
4. Trials are independent ‫نتيجه‬‫مستقله‬‫ال‬‫تتأثر‬‫باالخرى‬
5. x is the number of Successes in n trials.
xnx
qp
x
n
xP −






=)(
The number of ways of
getting the desired results
The probability of getting the
required number of successes
The probability of getting the
required number of failures

Example
Say 40% of the class is female.
Mean
Variance
Standard Deviation
2
np
npq
npq
µ
σ
σ
=
=
=
What is the probability that 6 of the first 10 students walking in will be female?
1115
1296004096210
64
6
10
qp
x
n
xP
6106
xnx
.
))(.(.
))(.(.
)(
=
=






=






=
−
−
nCx=n!/x!(n-x)!

2. Continuous Probability Distribution
A continuous random variable is one that can assume an uncountable number
of values.
We cannot list the possible values because there is an infinite number of
them.
Continuous probability distributions, used extensively in modeling and
simulation represent the uncertainty in values such as durations of schedule
activities and costs of project components.
There are five different types of Continuous Distribution:
1. Normal Distribution (standard deviations)
2. Uniform Distribution (values equally probable, scenarios where no obvious)
3. Beta Distribution
4. Triangular Distribution (three-point estimates)
5. Lognormal distribution (standard deviations, random values)

Probability density function
A function f(x) is called a probability density function (over the range a ≤ x ≤
b if it meets the following requirements:
a) f(x) ≥ 0 for all x between a and b, and
f(x)
b) The total area under the curve between a and b is 1.0
xba
area=1
‫الكليه‬ ‫االحتماالت‬ ‫مجموع‬

Normal Distribution
The normal distribution is the most important of all probability distributions.
The probability density function of a normal random variable is given by:
It looks like this: Bell shaped,
Symmetrical around the mean µ
The normal distribution is fully defined by two parameters: its standard
deviation and mean.

Standard deviation is a statistical calculation used to measure and describe how data is
organized.
68.25% of the values will fall within 1σ from the mean.

Standard Normal Distribution
It is a normal distribution whose mean is zero and standard deviation is one.
0
1
1
Any normal distribution can be converted to
a standard normal distribution

Example
The return on investment is normally distributed with a mean of 10% and a
standard deviation of 5%. What is the probability of losing money?
We want to determine P(X < 0). Thus,
5
100X
P)0X(P 




 −
<
σ
µ−
=<
0228.
4772.5.
)2Z0(P5.
)2Z(P
5
P)0X(P
=
−=
<<−=
−<=




<
σ
=<

Regression Analysis
Regression analysis is a statistical process for estimating the relationships among
Regression Analysis
Simple Multiple
‫متغير‬ ‫أثر‬ ‫تحليل‬ ‫و‬ ‫دراسه‬
‫أخر‬ ‫كمى‬ ‫متغير‬ ‫على‬ ‫كمى‬
‫المتغيرين‬ ‫أحدى‬ ‫لقياس‬ ‫رياضية‬ ‫معادلة‬ ‫صياغه‬
‫األخر‬ ‫على‬
‫على‬ ‫كمى‬ ‫متغير‬ ‫أثر‬ ‫تحليل‬ ‫و‬ ‫دراسه‬
‫أخرى‬ ‫كميه‬ ‫متغيرات‬ ‫عدة‬
y = α + β1x1 + β2x2 + β3x3 + …. + βkxk + εy = α + βx + ε
Regression analysis is a statistical process for estimating the relationships among
variables.
The benefit of performing regression analysis is in the ability of predicting or
estimating a dependent variable from given independent variables using a
probability model developed from a group of known sampled data.
The model that yields the minimum sum of squared error “SSE” is chosen as the
best fit.
This is known as the “Least Square Approach’ to fit a model.

y = Deterministic component + Random error
y = (α + ßx) + e
Where:
y = Dependent variable (variable to be modeled) ‫متأثر‬
x = Independent variable (variable used as a predictor of y) ‫مستقل‬
e (epsilon) = Random error component due to the deviation from the true value
e (epsilon) = Random error component due to the deviation from the true value
‫عوامل‬‫أخرى‬‫تؤثر‬‫فى‬‫المتغير‬‫المتأثر‬
α = y-intercept of the line, i.e., point at which the line intercepts or cuts through
the y- axis ‫ثابت‬‫اإلنحدار‬
= [Σy/n] - ß [Σx/n]
ß = Slope of the line, i.e., amount of increase (or decrease) in the deterministic
component of y for every unit change in x. ‫مﻌامل‬‫اإلنحدار‬
= Σ [ (xi - x)(yi - y) ] / Σ [ (xi - x)2]

Linear Regression
Last year, five randomly selected students took a math aptitude test before they
Student 1 2 3 4 5
Aptitude Test (X) 95 85 80 70 60
Statistics Grades (Y) 85 95 70 65 70
began their statistics course.
1. What linear regression equation best predicts statistics performance, based on
math aptitude scores (X)?
2. If a student made an 80 on the aptitude test, what grade would we expect her to
make in statistics?

Student xi yi (xi - x) (yi - y) (xi - x)2 (yi - y)2 (xi - x)(yi - y)
1 95 85 17 8 289 64 136
2 85 95 7 18 49 324 126
3 80 70 2 -7 4 49 -14
4 70 65 -8 -12 64 144 96
5 60 70 -18 -7 324 49 126
Sum 390 385 730 630 470
The regression equation is a linear equation of the form: ŷ = b0 + b1x .
To conduct a regression analysis, we need to solve for b0 and b1.
b1 = Σ [ (xi - x)(yi - y) ] / Σ [ (xi - x)2] b1 = 470/730 = 0.644
b0 = [Σy/n] - b1 [Σx/n] b0 = 77 - (0.644)(78) = 26.768
1. Therefore, the regression equation is: ŷ = 26.768 + 0.644x .
2. ŷ = 26.768 + 0.644x = 26.768 + 0.644 * 80 = 26.768 + 51.52 = 78.288
Sum 390 385 730 630 470
Mean 78 77

Correlation (r)
Correlation
Pearson’s Correlation
Coefficient
Spearman’s Rank Correlation
Coefficient
Pearson’s Correlation Coefficient
Strong Moderate Weak Weak Moderate Strong
-1 ≤ r ≤ 1
-1 1
DirectInverse
Pearson’s Correlation Coefficient
r =
nΣxy- (Σx)(Σy)
[ (nΣx2)- (Σx)2] 0.5 * [ nΣy2- (Σy)2] 0.5

OPTIMIZATIONOPTIMIZATION
Optimization is the process of determining the BEST performance for a system.
Models are simplified representations of reality by simple or complex systems
used to optimize the performance of the real system.
There are numerous techniques for optimization such as;
1. Linear Programming
2. Monte Carlo Simulation
3. Sensitivity Analysis

1. Linear Programming (1947)
An efficient mathematical method for determining an optimal
strategy for optimizing a linear objective function subject to a set
of linear constraints.
The goal of linear programming is to determine the level for all
the activities, sometimes referred to as variables, of the system
which:
George B. Dantzig
(1914 – 2005)
which:
Restrict the activities to be non-negative
Balance the constraint Equations
Optimize the Objective Function
The Optimization Theory:
To maximize or minimize (optimize) a linear objective function (profit or cost))
depends on the variables of the problem (X, Y, the number of products) -------
we use the corners of the solution area!!!!

Example
The RCC Development Company wants to maximize its profits in a new housing
development.
The RCC Company has two types of homes, a three-bedroom model and a four-
bedroom model.
The Company has ten lots available in the new development, Mountaineer
Estates.
Estates.
The maximum funding from the bank for the project is $2,400,000.
How many homes of each type should RCC Development Company
construct?
It means the value of x and y that maximize z.
Four-bedroom home (x) Three-bedroom home (y)
Profit $40,000 $30,000
Cost $300,000 $200,000

Objective Function: 40x + 30y = Z (maximum profit in thousand dollar units)
Under the following Constraints:
x + y ≤ 10 (lots available for development)
300x + 200y ≤ 2,400 (available funds from bank in thousand dollar units)
1. x + y = 10
at x=0 ------- y=10 ------------ (0, 10)
at y=0 ------- x =10 ------------ (10, 0) (10, 10)
at y=0 ------- x =10 ------------ (10, 0) (10, 10)
2. 300x + 200y = 2,400
at x=0 ------- y= 12 --------- (0, 12)
at y=0 ------- x =8 ------------ (8, 0) (8, 12)
3. Intersection point
x + y = 10 ------------ (1)
300x + 200y = 2,400 ------------- (2) (4, 6)

300x + 200y ≤ 2,400
x + y = 10
X , y 40x + 30y = Z
(8, 0) 320
(0, 10) 300
(4, 6) 340

2. Monte Carlo Simulation (1949)
It uses the generation of a series of random numbers to simulate
a population followed by statistical analysis to make predictions.
Useful in studying complex systems with significant uncertainty
in the inputs, such as in estimating costs.
It is used in investment analysis to evaluate the risk in making investments.
There are numerous commercial computer software programs available to perform
Stanisław M. Ulam
(1909 - 1984)
There are numerous commercial computer software programs available to perform
Monte Carlo Simulations such Crystal Ball, @Risk, Risk Solver, Arena, and
GoldSim.

3. Sensitivity Analysis
A technique used to quantify the variation in the solution with respect to the
variables and the constants used in the formulation of the problem.
Sensitivity analysis is done to investigate the impact of changes in variables and
assumptions made for constants used upon the solution obtained, often referred
to as the base case.
The purpose is to determine which variables and constants have the most
The purpose is to determine which variables and constants have the most
influence upon the solution.

RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS
Risk
AACE Recommended Practice 10S-90
1. The possibility of suffering harm or loss (American Heritage Dictionary,
Houghton Mifflin Co.)
2. Uncertainty of an event which if occurred would result in a negative
or positive effect on the project (Project Management Institute).
AACE Recommended Practice 10S-90, Cost Engineering Terminology, 2009
AACE Recommended Practice 10S-90, Cost Engineering Terminology, 2009
1. An ambiguous term that can mean any of the following:
All uncertainty (threats + opportunities)
Undesirable outcomes (uncertainty = risks + opportunities)
The net impact or effect of uncertainty (threats – opportunities).
2. Probability of an undesirable outcome.
3. In total cost management, an uncertain event or condition that could
affect a project objective or business goal.

Risk Management (TCM 7.6.1 Description)
Risk management is the process of identifying risk factors (risk assessment),
analyzing and quantifying the properties of those factors (risk analysis), treating
the impact of the factors on planned asset or project performance and developing a
risk management plan (risk treatment), and implementing the risk management
plan (risk control).
The goal of risk management is to increase the probability that a planned asset or
The goal of risk management is to increase the probability that a planned asset or
project outcome will occur without decreasing the value of the asset or project.
Risk management presumes that deviations from plans may result in unintended
results (positive or negative) that should be identified and managed.

Fundamental Approach to Risk Management
When we perform risk management we should keep in mind the following:
1. You do not need an advanced degree in mathematical theory to perform risk
management.
2. Risk management can be applied in different ways suitable to project needs
from easy/simple to complex.
3. One of the more important elements of risk management is to establish a
3. One of the more important elements of risk management is to establish a
process of dealing with risks.
The approach to risk management is similar to the classic approach to management
and project management.
Plan Implement Monitor Control

Project Risk Management Processes
To establish Risk
Management
objectives.
By monitoring,
communicating
and enhancing Risk
Management
To identify and
analyze risk.
Management
effectiveness.
analyze risk.
By planning and
implementing
risk responses.

RISK MANAGEMENT PRACTICAL GUIDERISK MANAGEMENT PRACTICAL GUIDE
• Identify the
threats/opportuniti
es and analyze
them to determine
potential impact to
project outcomes
and determine
appropriate
treatment
priorities.
• Identify the key
elements of the
project risk
management
plan including
objectives, roles
and
responsibilities,
level and
frequency of risk
analysis, risk
register updates,
Plan Asses
TCM Risk Management Steps
• Plan and
implement the
treatment of the
identified risks
• Monitor the
implementation
of risk treatment
actions, report
on status, and
adjust actions
according to
results.
register updates,
and reporting.
TreatControl

1. Risk Planning
Establish the approach, form, content
Define results of risk management
Define key terms
Establish criteria for risk identification and assessment, analysis approaches and
general risk treatment strategies
The outline of the risk management implementation should be in the project
The outline of the risk management implementation should be in the project
plan at the start of basic engineering.
The final version of the risk management plan should be reviewed and
approved early in detailed engineering.
The first workshops should take place during project development (prior to the
start of detailed design).
The earlier a project can recognize and implement risk management treatment
the more effective it will be.

2. Risk Assessment
a) Risk Identification
b) Risk Analysis (Qualitative and Quantitative)
The steps:
1. The risk management lead notifies the participants and schedules the
meetings and interviews.
2. Meetings and interviews to identify threats and opportunities are conducted,
2. Meetings and interviews to identify threats and opportunities are conducted,
based on the risk management criteria formulated in planning, approved by
management, and distributed to participants (i.e., risk identification).
3. Threat or opportunity items and any additional needed resources are
quantified and evaluated by the appropriate subject matter experts. The
results of analysis are prepared to support the treatment phase (i.e., risk
analysis).

a) Risk Identification
Threat Or
Opportunity
Causes
Effects
(Negative or
Positive)
Opportunity Threat
A project risk that has a positive effect A project risk that has a negative effect is
A project risk that has a positive effect
is referred to as an opportunity.
A project manager will proactively
manage opportunities to the project and
look for ways to exploit, enhance, or
share the opportunity.
A project risk that has a negative effect is
referred to as a threat.
A project manager will proactively manage
threats to the project and look for ways to
reduce the probability or impact of the
threat (Mitigate) or eliminate the threat
all together (avoid) or transfer to
another party.

Identification tools
2) Interviewing
1) Brainstorming
3) Delphi Technique
2) Interviewing
4) Root Cause Analysis

Risk Categories
Technical,
Quality and
Performance
Project
Management
Organizational External
Higher
performance goals
Technology shifts
Poor time
allocation
Poor budget
Weak
infrastructure
Unclear
Legal challenges
Shifting customer
goals
Technology shifts
Platform changes
New industry
standards
Complex
technology
Unproven
technology
Poor budget
planning
Poor resource
allocation
Poor time planning
Unclear
organizational
objectives
Intra-
organizational
resource conflicts
Shifting funding
availability
goals
Natural disasters
Legal shifts

Risk register
The outputs from risk identification.
Status: Whether a risk is an active risk, a dormant risk, or a retired risk.
ID#: The identification for the risk.
Date Identified & Project Phase: When a risk was identified and what project
phase (preconstruction or construction) the risk was identified in.
Functional Assignment: The capital delivery functions (planning, design,
Functional Assignment: The capital delivery functions (planning, design,
environmental, construction, etc.) which are impacted by the risk.
Risk Event: What the risk event is to the project with detailed description using
the SMART technique
Potential Responses
Root Causes of Risks
Risk Trigger: warning signs that indicate the risk is likely to occur or imminent
that used to determine when response strategies will be implemented.

b) Risk Analysis (Qualitative and Quantitative)
The overall objective of perform Qualitative Risk Analysis and Quantitative Risk
Analysis processes is to determine which RISKS warrant a response.
Risk analysis is in two broad areas:
i. Qualitative Risk Analysis
ii. Quantitative Risk Analysis
ii. Qualitative Risk Analysis
ii. Qualitative Risk Analysis
Subjectively evaluate the probability and impact of each risk.
Create a short list of risks by determining the top or critical risks that you will
quantify further and/or address in Plan Risk Responses process.
Assess the quality and reliability of the information you are working with.
Risk probability assessment investigates the likelihood that each specific risk will
occur.

Risk impact (consequence) assessment investigates the potential effect on a
project objective such as schedule, cost, quality, or performance, including both
negative effects for threats and positive effects for opportunities.
Probability Scale
Scale Rang
VL < 20
L 20-40
M 40-60
Impact Scale (for an objective)
Scale Rang
VL < 10
L 10-20
M 20-30
Risk
Identification
Cost
Impact
Schedule
Impact
Performance
Impact
Criticality
Score
Risk 1 L L L L
Risk 2 H H H H
Risk 3 H L L M
Risk 4 VL VL H H
M 40-60
H 60-80
VH >80
M 20-30
H 30-60
VH >60

Evaluation of each risk’s importance and, hence, priority for attention is
typically conducted using a look-up table or a probability and impact
matrix.
P-I matrix can be based on ordinal ‫(ترتيبي‬very low, low, medium, high, and
very high ) or cardinal ‫/1.(الﻌدد‬ .3/ .5/ .7/ .9 or 1/ 2/ 3/ 4/ 5) scales.
The organization should determine which combinations of probability and
impact result in a classification of high risk “red condition”, moderate risk
impact result in a classification of high risk “red condition”, moderate risk
“yellow condition”, and low risk “green condition”.
For consistency with other risk assessment terms, a 1-5 scale for
probability is used.

ii. Quantitative Risk Analysis
Quantitative risk analysis is the application of mathematical techniques and
models to numerically establish the probability of risk and the consequences of
risk.
Objectively evaluate the probability and impact of each risk.
Decide which risks warrant a response.
Determine the level of risk the project currently has and whether that level of
Determine the level of risk the project currently has and whether that level of
risk is acceptable for the expected gain from the product of the project.
Determine how much the project will cost and how long it will take if no further
risk management actions are taken to decrease project risk.
Determine which risk require response planning.
Determine the probability of achieving cost or schedule objectives for the
project.

The most common of these techniques are
a) Simulation
b) Sensitivity analysis
c) Decision tree analysis.
Frequency
CumulativeProbability0.5
0.6
0.7
0.8
0.9
1.0
0.08
0.10
0.12
0.14
0.16
Completion Date
Frequency
CumulativeProbability
3/11/31 4/5
0.1
0.2
0.3
0.4
0.5
0.02
0.04
0.06
0.08

Date: 7/11/2004 2:24:06 PM
Samples: 1000
Completion Std Deviation: 8.36 d
95% Confidence Interval: 0.52 dSteps
a) Simulation (Monte Carlo)
A simulation is the development of a model of the uncertainties of project, in
terms of cost or time, and the effect on the project.
Simulations are typically performed using the Monte Carlo technique.
The Monte Carlo process, as applied to risk management,
Unique ID: 1
Name: Project
Each bar represents 3 d
Completion Date
Frequency
CumulativeProbability
3/11/31 4/5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16 Completion Probability Table
Prob ProbDate Date
0.05 2/10
0.10 2/15
0.15 2/17
0.20 2/18
0.25 2/22
0.30 2/23
0.35 2/24
0.40 2/25
0.45 2/28
0.50 3/1
0.55 3/2
0.60 3/3
0.65 3/4
0.70 3/7
0.75 3/9
0.80 3/11
0.85 3/14
0.90 3/17
0.95 3/21
1.00 4/5
1. Develop a model
2. Select the group for
analysis
3. Identify uncertainty
4. Analyze the model with
simulation
5. Generate reports and
analyze information

b) Sensitivity analysis
Sensitivity analysis helps to determine which risks have the most potential impact
on the project.
It examines the extent to which the uncertainty of each project element affects
the objective being examined when all other uncertain elements are held at their
baseline values.
Tornado diagram is the most useful way to represent the results of a Sensitivity
Tornado diagram is the most useful way to represent the results of a Sensitivity
Analysis.
A tornado diagram in which a bar
represents each risk and the range of the
impact it could have, from negative to
positive impact.
The length of each bar represents the relative
impact of each risk - the bars are ordered in
sequence from greatest impact to least.

c) Decision tree analysis
Decision tree analysis is usually structured using a decision tree diagram that
describes a situation under consideration, and the implications of each of the
available choices and possible scenarios.
Solving the decision tree
provides the Expected Monetary
Value for each alternative, when
Value for each alternative, when
all the rewards and subsequent
decisions are quantified.
The decision tree analysis
technique for making decisions in
the presence of uncertainty can
be applied to many different
project management situations

Risk Management Software
1. Cost Risk Analysis
Crystal Ball, Oracle Corp.
@Risk, Palisade Corp.
Risk Solver, Frontline Systems Inc.
2. Schedule Risk Analysis
@Risk for Project, Palisade Corp.
@Risk for Project, Palisade Corp.
Primavera, Oracle Corp.

Contingency
An amount added to an estimate to allow for items, conditions, or events for which
the state, occurrence, or effect is uncertain and that experience shows will likely
result, in aggregate, in additional costs.
Typically, estimates using statistical analysis or judgment, based on past asset or
project experience.
Contingency usually excludes:
Contingency usually excludes:
Major scope changes such as changes in end product specification, capacities,
building sizes, and location of the asset or project.
Extraordinary events such as major strikes and natural disasters.
Management reserves.
Escalation and currency effects.

3. Risk Treatment
The risk management team and other members would develop recommendations
and decisions on how to treat those risks.
Risks should be assigned risk owners who will be responsible for overseeing the
implementation of the risk treatment action, which should be reflected in a risk
register.
Key actions performed during the risk treatment phase include (TCM Framework ):
Key actions performed during the risk treatment phase include (TCM Framework ):
1. Evaluating all appropriate response strategies.
2. Selecting an appropriate risk response plan strategy (or combination of strategies).
3. Developing action items in support of the selected response.
4. Validating proposed actions with assigned actionees, including dates for implementation.
5. Ascertaining post-response targets and gains.
6. Ascertaining response plan resource requirements.
7. Updating project schedule or budget if the anticipated treatment value gain is positive.
8. Identifying any secondary threats or opportunities that may arise from the response.

4. Risk Control
Risk control is a vital step in the risk management process cycle.
The original risk
occurs and is
acted upon
consistent with
the original plan.
Risk
assumptions,
analysis, and
treatment
strategies may
need to be
mod
Events or
developments
will highlight
new risks that
need to be
assessed.

Risk reassessment
Additional Risk Identification, Qualitative Risk Analysis, Quantitative Risk Analysis,
and Risk Response Planning.
Control Risks often results in identification of new risks, reassessment of
current risks, and the closing of risks that are outdated.
Project risk reassessments should be regularly scheduled.
The results of such reassessments may include newly identifications, additional
The results of such reassessments may include newly identifications, additional
qualitative or quantitative risk analysis, and further risk response planning.
There are two major times when a risk reassessment might occur:
a) When new risks are identified.
b) When changes occur on the project.

Risk Audit
Risk audits examine and document the effectiveness of risk responses in dealing
with identified risks and their root causes, as well as the effectiveness of the risk
management process.
It is arranged by project manager and results in identification of lessons learned for
the project and for other project in the organization.
Risk audits are evidence of how seriously risk should be taken on a project.
Risk audits are evidence of how seriously risk should be taken on a project.
A risk audit includes:
a) Reviewing if the right risk owners have been assigned to each risk
b) Determining if the risk owners are effective.
c) Examining and documenting the effectiveness of contingency plans and
fallback plans

Risk Management Closure
Key steps in risk management closure are:
Collect and
Debrief
Evaluate and
Document
Archive
All appropriate records
and documentation
The plans, actual
results and
A central archiving
system that is
and documentation
should be collected.
Reports, analysis, and
a comprehensive risk
register or data base
should be preserved.
results and
observations of the
participants should
be summarized in a
form usable for
future projects and
risk practitioners.
system that is
accessible to future
projects is
essential.

Integrate with
Project
management
Open and
Honest
Communication
Organizational
Commitment
Risk Effort
Scaled to
Project
Risk
Management
Success
Value Risk
Management
management Project
Responsibility

TOTAL COST MANAGEMENT OVERVIEWTOTAL COST MANAGEMENT OVERVIEW
Total Cost Management (TCM) is described as the “sum of the practices and
processes that an enterprise uses to manage the total lifecycle cost
investment in its portfolio of strategic assets”.
TCM attempts to illustrate the integration of all the various skills and knowledge
areas that are required for processes to support overall management of both
strategic assets as well as the individual projects, undertaken to create and
develop those assets.
develop those assets.
TCM is accomplished through the application of:
Cost engineering and cost management principles
Proven methodologies
The latest technologies in support of the management process

Strategic Assets are physical or intellectual property that has long-term or lasting
value to an enterprise.
They are expected to provide a positive economic benefit and are created
through the investment of money, time, and resources. Examples include:
Buildings
Software applications
Retail products
Retail products
Theater production
It is important to note that TCM recognizes the term “cost” as going beyond the
traditional monetary definition to include any investment of resources in the
enterprise’s assets.
TCM is a comprehensive approach to managing the total resource investment in
assets.

Total Cost Management Processes
Plan-Do-Check-Act (PDCA) Management Cycle
Often referred to as the Deming or Shewhart Cycle
Generally accepted, quality driven, continuous improvement model.
The AACE International Total Cost Management process is divided into two (2)
aspects:
1. Strategic Asset Management (SAM) Process
1. Strategic Asset Management (SAM) Process
The macro process of managing the total lifecycle cost investment of resources in
an enterprise’s complete portfolio of strategic assets.
This process focuses on initiating and managing the overall portfolio of projects in
a way that addresses the strategic objectives of the enterprise.
This process is typically business-led.

2. Project Control Process
This is a technical-led a process for controlling the investment of resources in an
asset during project execution.
Project Control is the recursive process nested within the “DO” step of the
Strategic Asset Management (SAM) Process cycle.
Unlike SAM, which is always ongoing, a project is a temporary undertaking with a
defined beginning and an end. Projects are how asset investment decisions are
defined beginning and an end. Projects are how asset investment decisions are
put into effect.
Ultimately, at the end of a project, a usable or operational asset is returned to the
enterprise’s asset portfolio. Project Control is focused on delivering an asset that
meets all of the business objectives identified by the strategic asset planning
process; it is about “doing the project right”

The lifecycle of a strategic asset can be summarized by the following five (5)
stages:
Creation
Ideation
Determine an
opportunity for
a new asset;
research,
evaluate,
Create or
Operation
Modification
evaluate,
define and
develop
potential
solutions;
select the
optimal
solution
Create or
implement
the asset
solution
Modify,
improve or
otherwise
change the
asset
Deploy the
new asset
into service
or operation
Termination
Decommission, retire,
demolish or otherwise
terminate the asset from
the enterprise portfolio

The lifecycle of a project can be summarized by the following four (4) phases:
Planning
Ideation
Establish the
project
requirements
and project
Develop plans to
Execution
Closing
Continuous improvement
and project
goals
Develop plans to
achieve project
requirements and
goals
Review, test,
validate
Implement the
project plans and
execute the
project to meet
requirements and
project goals

THE INTERNATIONAL SYSTEM OF UNITS (SI)THE INTERNATIONAL SYSTEM OF UNITS (SI)
The Système International d'Unites (The international system of units), also known
as (SI), was adopted in 1960 to facilitate the world market outreach.
The SI uses seven base units accompanied by twenty two derived units
When working on multi-national projects and contracts, familiarity of SI is essential
to improve project controls and communication.
SI The international system of units
SI The international system of units
Metric
conversion
Changeover from the U.S. customary measuring system to the SI
Soft
conversion
Calculated equivalent of the customary measuring expressions in metric
terms
Hard
conversion
A complete immersion into the new “language” and applications of the SI
without reference to the old system and the opportunity to review old
standards
Significant
digits
When conversion calculations are performed, accuracy of the original data
should be taken into account

Base Units and Derived Units with Special Names

Prefixes for Multiples and Submultiples of SI Units

Multiplication Table to Convert to SI

France defined the sizes of official
documents requiring stamp duty.
The original size A0 =1 m2,
halved four times, leads to the
size A4.
Following this method for cutting
paper, results in no paper
International Paper Sizes
paper, results in no paper
trimming waste.

PLEASE CHECK THE 24
RULES FOR SI STYLE AND
USAGE
USAGE

THANK YOU

CCP_SEC6_Economic Analysis Statistics and Probability and Risk

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