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CCP_SEC6_Economic Analysis Statistics and Probability and Risk

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A CCP is an experienced practitioner with advanced knowledge and technical expertise to apply the broad principles and best practices of Total Cost Management (TCM) in the planning, execution and management of any organizational project or program. CCPs also demonstrate the ability to research and communicate aspects of TCM principles and practices to all levels of project or program stakeholders, both internally and externally.

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CCP_SEC6_Economic Analysis Statistics and Probability and Risk

  1. 1. EECONOMICCONOMIC AANALYSIS,NALYSIS, SSTATISTICS,TATISTICS, PPROBABILITY ANDROBABILITY AND RRISKISK Hisham Haridy, PMP, PMI-RMP, PMI-SP CCP_Section VI
  2. 2. 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
  3. 3. 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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 )( + =
  4. 4. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  5. 5. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS $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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  6. 6. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  7. 7. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  8. 8. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS BANK Loans Share capital Methods of Financing Debt Financing Equity Financing ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  9. 9. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Cost of Equity Opportunity cost associated with using shareholders’ capital creditors Costofcapital
  10. 10. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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% ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  11. 11. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Interest rate i The number of discounting or compounding periods n.
  12. 12. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  13. 13. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS Discount Factors for Discrete Compounding ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  14. 14. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 55%% ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 66%%
  15. 15. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 0 $20,000 1 $5,000 $500 2 $5,000 $600 3 $5,000 $700 4 $5,000 $800 5 $5,000 $900
  16. 16. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS $5,000 0 1 2 3 $5,000 $5,000 $5,000 $5,000 4 5 Cash Flow Diagram ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK $500 $600 $700 $800 $900$20,000 Cash Flow Conventions
  17. 17. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS Cash Flow Notation ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  18. 18. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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., ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  19. 19. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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? ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  20. 20. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  21. 21. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  22. 22. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  23. 23. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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) . ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  24. 24. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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: ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  25. 25. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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: ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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”
  26. 26. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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” ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  27. 27. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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%: ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK What is the net present value of this cash flow?
  28. 28. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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? ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  29. 29. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  30. 30. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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: ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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????
  31. 31. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  32. 32. FINANCIAL AND CASH FLOW ANALYSISFINANCIAL AND CASH FLOW ANALYSIS 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  33. 33. 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: ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  34. 34. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  35. 35. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE Forms of Business Organizations 1. Proprietorship 2. Partnership 3. Corporation 20% 9% ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 71% Proprietorship Partnership Corporation
  36. 36. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE Corporate Organization ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  37. 37. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE Goals of the Corporation Primary Goal MAXIMIZE Stockholder Wealth = MAXIMIZE Stock Price Managerial Incentives Controlled by competitive forces ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Controlled by competitive forces Social Responsibility Must be mandated initially to reduce disadvantages Stock Price Maximization and Social Welfare Maximizing stock = benefiting society
  38. 38. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Benchmark studies show benefits of up to 30% reduced cost and shorter project execution times when FEED studies are performed.
  39. 39. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  40. 40. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  41. 41. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  42. 42. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Capital Cost variance
  43. 43. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  44. 44. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE Project Drivers Capital Revenue Expense Schedule Project Drivers ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  45. 45. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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). ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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).
  46. 46. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  47. 47. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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)
  48. 48. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  49. 49. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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] ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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]
  50. 50. PRACTICAL CORPORATE INVESTMENT DECISION-MAKING GUIDE 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK The variance on annual revenue generated
  51. 51. 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK data generalization about the population based on the data from a sample. ‫معلومات‬ ‫جمع‬ ‫و‬ ‫تنظيمھا‬ ‫عرضھا‬ ‫إستخراج‬ ‫و‬ ‫تحليلھا‬ ‫منھا‬ ‫مقاييس‬
  52. 52. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Data Information Raw facts about physical phenomena Data that has been converted into meaningful and useful context.
  53. 53. Quantitative Discrete Continuous STATISTICS & PROBABILITYSTATISTICS & PROBABILITY Describing Data Qualitative Data Quantitative data Graphic methods Numerical methods ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  54. 54. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY Graphic Methods Frequency Distribution Stem and Leaf Plots Histogram The stem-and-leaf plot It shows data arranged by place value. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  55. 55. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  56. 56. 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. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  57. 57. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  58. 58. The sum of measurements divided by the number of measurements STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  59. 59. For symmetric data set, the mean = the median If the median < the mean, the data set is skewed to the right STATISTICS & PROBABILITYSTATISTICS & PROBABILITY If the median > the mean, the data set is skewed to the left. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  60. 60. The difference between the largest and the smallest STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK from the mean The population standard deviation is denoted by σ The sample standard deviation is denoted by s The sample standard deviation s =
  61. 61. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  62. 62. 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. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY Percentile of 50????? Number of observation less than/total number of observations X 100 Percentile of observation 50 =32/50= 64% 50 under P64% ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  63. 63. 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 STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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%. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  64. 64. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  65. 65. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY Probability Distributions Discrete Continuous The probability that the random variable X will equal is P(x) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Binomial Poisson Normal Distribution Standard Normal Distribution ‫ذو‬‫الحدين‬
  66. 66. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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: ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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).
  67. 67. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY Population variance It is calculated similarly. It is the weighted average of the squared deviations from the mean. Standard deviation ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK The standard deviation is the same as before:
  68. 68. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY Example Probability distributions can be estimated from relative frequencies. Consider the discrete (countable) number of televisions per household from US survey data. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  69. 69. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Variance: Standard Deviation = (0 – 2.084)2(.012) + (1 – 2.084)2(.319)+…+(5 – 2.084)2(.028)= 1.107
  70. 70. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  71. 71. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY Example Say 40% of the class is female. Mean Variance Standard Deviation 2 np npq npq µ σ σ = = = ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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)!
  72. 72. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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)
  73. 73. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK b) The total area under the curve between a and b is 1.0 xba area=1 ‫الكليه‬ ‫االحتماالت‬ ‫مجموع‬
  74. 74. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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: ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  75. 75. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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. 95.46% of the values will fall within 2σ from the mean. 99.73% of the values will fall within 3σ from the mean. 99.99966% of the values will fall within 6σ from the mean. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  76. 76. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY Standard Normal Distribution It is a normal distribution whose mean is zero and standard deviation is one. 0 1 1 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Any normal distribution can be converted to a standard normal distribution
  77. 77. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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− =< ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 0228. 4772.5. )2Z0(P5. )2Z(P 5 P)0X(P = −= <<−= −<=     < σ =<
  78. 78. Regression Analysis Regression analysis is a statistical process for estimating the relationships among STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  79. 79. 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 STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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] ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  80. 80. Linear Regression Last year, five randomly selected students took a math aptitude test before they STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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? ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  81. 81. STATISTICS & PROBABILITYSTATISTICS & PROBABILITY 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Sum 390 385 730 630 470 Mean 78 77
  82. 82. Correlation (r) STATISTICS & PROBABILITYSTATISTICS & PROBABILITY Correlation Pearson’s Correlation Coefficient Spearman’s Rank Correlation Coefficient Pearson’s Correlation Coefficient ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  83. 83. 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 2. Monte Carlo Simulation 3. Sensitivity Analysis
  84. 84. OPTIMIZATIONOPTIMIZATION 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) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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!!!!
  85. 85. OPTIMIZATIONOPTIMIZATION 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  86. 86. OPTIMIZATIONOPTIMIZATION 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) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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)
  87. 87. OPTIMIZATIONOPTIMIZATION 300x + 200y ≤ 2,400 x + y = 10 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK X , y 40x + 30y = Z (8, 0) 320 (0, 10) 300 (4, 6) 340
  88. 88. OPTIMIZATIONOPTIMIZATION 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) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK There are numerous commercial computer software programs available to perform Monte Carlo Simulations such Crystal Ball, @Risk, Risk Solver, Arena, and GoldSim.
  89. 89. OPTIMIZATIONOPTIMIZATION 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK The purpose is to determine which variables and constants have the most influence upon the solution.
  90. 90. 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  91. 91. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  92. 92. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  93. 93. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS Project Risk Management Processes To establish Risk Management objectives. By monitoring, communicating and enhancing Risk Management To identify and analyze risk. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Management effectiveness. analyze risk. By planning and implementing risk responses.
  94. 94. 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  95. 95. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  96. 96. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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, ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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).
  97. 97. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  98. 98. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS Identification tools 2) Interviewing ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 1) Brainstorming 3) Delphi Technique 2) Interviewing 4) Root Cause Analysis
  99. 99. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  100. 100. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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, ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  101. 101. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  102. 102. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  103. 103. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND 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.
  104. 104. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  105. 105. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  106. 106. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  107. 107. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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, ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  108. 108. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  109. 109. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  110. 110. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK @Risk for Project, Palisade Corp. Primavera, Oracle Corp.
  111. 111. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS 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: ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  112. 112. RISK MANAGEMENT PRACTICAL GUIDERISK MANAGEMENT PRACTICAL GUIDE 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 ): ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  113. 113. RISK MANAGEMENT PRACTICAL GUIDERISK MANAGEMENT PRACTICAL GUIDE ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK
  114. 114. RISK MANAGEMENT PRACTICAL GUIDERISK MANAGEMENT PRACTICAL GUIDE 4. Risk Control Risk control is a vital step in the risk management process cycle. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  115. 115. RISK MANAGEMENT PRACTICAL GUIDERISK MANAGEMENT PRACTICAL GUIDE 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  116. 116. RISK MANAGEMENT PRACTICAL GUIDERISK MANAGEMENT PRACTICAL GUIDE 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  117. 117. RISK MANAGEMENT PRACTICAL GUIDERISK MANAGEMENT PRACTICAL GUIDE 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  118. 118. RISK MANAGEMENT FUNDAMENTALSRISK MANAGEMENT FUNDAMENTALS Integrate with Project management Open and Honest Communication Organizational Commitment Risk Effort Scaled to Project ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Risk Management Success Value Risk Management management Project Responsibility
  119. 119. 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. ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  120. 120. TOTAL COST MANAGEMENT OVERVIEWTOTAL COST MANAGEMENT OVERVIEW 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  121. 121. TOTAL COST MANAGEMENT OVERVIEWTOTAL COST MANAGEMENT OVERVIEW 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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.
  122. 122. TOTAL COST MANAGEMENT OVERVIEWTOTAL COST MANAGEMENT OVERVIEW 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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”
  123. 123. TOTAL COST MANAGEMENT OVERVIEWTOTAL COST MANAGEMENT OVERVIEW 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  124. 124. TOTAL COST MANAGEMENT OVERVIEWTOTAL COST MANAGEMENT OVERVIEW 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  125. 125. 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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK 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
  126. 126. THE INTERNATIONAL SYSTEM OF UNITS (SI)THE INTERNATIONAL SYSTEM OF UNITS (SI) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Base Units and Derived Units with Special Names
  127. 127. THE INTERNATIONAL SYSTEM OF UNITS (SI)THE INTERNATIONAL SYSTEM OF UNITS (SI) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Prefixes for Multiples and Submultiples of SI Units
  128. 128. THE INTERNATIONAL SYSTEM OF UNITS (SI)THE INTERNATIONAL SYSTEM OF UNITS (SI) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Multiplication Table to Convert to SI
  129. 129. THE INTERNATIONAL SYSTEM OF UNITS (SI)THE INTERNATIONAL SYSTEM OF UNITS (SI) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Multiplication Table to Convert to SI
  130. 130. THE INTERNATIONAL SYSTEM OF UNITS (SI)THE INTERNATIONAL SYSTEM OF UNITS (SI) ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK Multiplication Table to Convert to SI
  131. 131. THE INTERNATIONAL SYSTEM OF UNITS (SI)THE INTERNATIONAL SYSTEM OF UNITS (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 ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK International Paper Sizes paper, results in no paper trimming waste.
  132. 132. THE INTERNATIONAL SYSTEM OF UNITS (SI)THE INTERNATIONAL SYSTEM OF UNITS (SI) PLEASE CHECK THE 24 RULES FOR SI STYLE AND USAGE ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK USAGE
  133. 133. THANK YOU ECONOMIC ANALYSIS, STATISTICS, PROBABILITY AND RISK

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