Study guide
14.1 Expected Monetary Value (EMV) & Decision Tree Analysis
AACE Certified Cost Professional CCP
Track your progress as you read
Finished sections get a check mark.
1 Chapter 1: Introduction & Total Cost Management (TCM) Framework
1.1 AACE CCP Exam Structure, Eligibility & the In-Exam Memo 1.2 The Total Cost Management (TCM) Framework & PDCA Cycle 1.3 Strategic Asset Management vs. Project Control Processes
2 Chapter 2: Cost Estimating Fundamentals & Classification
2.1 AACE Recommended Practice 18R-97 Estimate Classification System 2.2 Direct vs. Indirect Costs and Cost Element Breakdown 2.3 Quantity Takeoff, Standard Cost Databases & Pricing Sources
3 Chapter 3: Conceptual & Parametric Estimating Techniques
3.1 Capacity Factoring & the Six-Tenths Rule 3.2 Parametric Estimating, Lang Factors & Hand Factors 3.3 Cost Indices, Location Adjustments & Escalation Modeling
4 Chapter 4: Cost Engineering Economics & Time Value of Money
4.1 Simple & Compound Interest, Equivalence & Cash Flow Diagrams 4.2 Discrete Compounding Formulas & Uniform Series Factors 4.3 Nominal vs. Effective Interest Rates & Continuous Compounding
5 Chapter 5: Project Profitability & Capital Investment Decision-Making
5.1 Net Present Value (NPV) & Present Worth Analysis 5.2 Internal Rate of Return (IRR) & Incremental IRR Analysis 5.3 Payback Period, Benefit-Cost Ratio (BCR) & Breakeven Analysis
6 Chapter 6: Depreciation Methods, Taxes & Asset Valuation
6.1 Classical Depreciation Methods (Straight-Line, DDB, Sum-of-Years-Digits) 6.2 Modified Accelerated Cost Recovery System (MACRS) & Tax Shield 6.3 After-Tax Cash Flow Analysis & Asset Replacement Economics
7 Chapter 7: Project Scope, Work Breakdown Structure (WBS) & Baselines
7.1 Work Breakdown Structure (WBS) Principles & the 100% Rule 7.2 Organizational Breakdown Structure (OBS) & Control Accounts 7.3 Establishing the Performance Measurement Baseline (PMB)
8 Chapter 8: Critical Path Method (CPM) Planning & Scheduling Logic
8.1 Precedence Diagramming Method (PDM) & Dependency Relationships 8.2 Forward Pass, Backward Pass & Float Calculations (Total vs. Free Float) 8.3 Schedule Baseline Development, Calendar Constraints & Milestones
9 Chapter 9: Schedule Optimization, Compression & Probabilistic PERT
9.1 Schedule Crashing & Least-Cost Slope Optimization 9.2 Fast-Tracking Risks, Overlap Analysis & Execution Strategies 9.3 PERT Three-Point Estimating & Probabilistic Duration Variance
10 Chapter 10: Resource Management, Productivity & Learning Curves
10.1 Resource Loading, Leveling vs. Resource Smoothing 10.2 Labor Productivity Factors, Work Sampling & Efficiency Loss 10.3 Learning Curve Theory (Wright Cumulative vs. Crawford Unit Models)
11 Chapter 11: Earned Value Management (EVM) Core Principles & Metrics
11.1 ANSI/EIA-748 EVM Framework & Core Metrics (PV, EV, AC) 11.2 EVM Variances & Performance Indices (CV, SV, CPI, SPI) 11.3 Work Progress Measurement Techniques (0/100, 50/50, Milestone Weighting)
12 Chapter 12: EVM Forecasting, Indices & Baseline Change Control
12.1 Estimate at Completion (EAC) & Estimate to Complete (ETC) Formulas 12.2 To-Complete Performance Index (TCPI) & Variance at Completion (VAC) 12.3 Integrated Change Control, Baseline Revisions & Trend Management
13 Chapter 13: Risk Management Planning & Qualitative Risk Analysis
13.1 Risk Management Framework & Risk Breakdown Structure (RBS) 13.2 Qualitative Risk Assessment & Probability-Impact (P-I) Matrix 13.3 Risk Response Strategies & Threat/Opportunity Management
14 Chapter 14: Quantitative Risk Analysis, Monte Carlo & Contingency Estimating
14.1 Expected Monetary Value (EMV) & Decision Tree Analysis 14.2 Monte Carlo Simulation & Probability Distributions in Cost/Schedule 14.3 Contingency Estimating & AACE Recommended Practice 40R-08
15 Chapter 15: Contract Types, Procurement Strategy & Commercial Terms
15.1 Contract Types & Risk Allocation (Firm Fixed Price, Cost-Plus, T&M) 15.2 Project Delivery Systems & Procurement Lifecycle (DBB, DB, EPC, CMAR) 15.3 Commercial Terms, Bonds, Retainage & Claims Management
16 Chapter 16: Quality Management, Value Engineering & Technical Communication
16.1 Quality Management & Cost of Quality (CoQ) 16.2 Value Engineering, Function Analysis System Technique (FAST) & Life Cycle Costing 16.3 The CCP Memo, Cost Report Writing, Data Presentation & AACE Ethics 16.4 AACE CCP Capstone Review & High-Yield Exam Strategies
17 Chapter 17: Cost Accounting, Budget Administration & Cost System Governance
17.1 Historical Cost Databases, Data Organization & Benchmarking 17.2 Committed Costs, Accruals, Work-in-Place & Invoice Validation 17.3 Budget Creation, Operating Budgets & Funding Requirement Forecasting 17.4 Cost System Governance, the Code of Accounts & Preserving Project Controls Data
18 Chapter 18: Estimate Preparation, Review & Cost Driver Analysis
18.1 ROM, Summary-Level and Detailed Estimates: Preparing and Reviewing 18.2 Verifying the Basis of Estimate & Analyzing Estimates 18.3 Cost Drivers, Change Order Impact & Resource Utilization Analysis
19 Chapter 19: Interfacing with Other Disciplines & Stakeholders
19.1 Coordinating with Internal Disciplines & Supporting Project Leadership 19.2 Communicating Cost Estimates and Cost/Schedule Key Performance Indicators 19.3 Supporting Tenders, Procurement, Audits, Field Verification & Recovery
20 Chapter 20: Cost Reporting, Dashboards & Profitability Analysis
20.1 Cost Reports, Performance Dashboards & the Reporting Cycle 20.2 Variance Reports & Explaining Project Financial Health 20.3 Profit Margin Analysis & Profitability Enhancement
21 Chapter 21: Cost Support to Scheduling & the CCP Exam Memo
21.1 Cost and Resource Loading Summaries from the Project Schedule 21.2 Translating Schedule Change into Cost Impact 21.3 Writing the CCP Exam Memo: A Worked Domain 7 Walkthrough
14.1 Expected Monetary Value (EMV) & Decision Tree Analysis
Key Takeaways Explain This Topic AI
Expected Monetary Value ( E M V = ∑ P i × I m p a c t i EMV = \sum P_i \times Impact_i EM V = ∑ P i × I m p a c t i ) quantifies the statistical average financial outcome of uncertain scenarios under risk neutrality, weighting discrete gains (positive) and losses (negative) by their respective probabilities.
Decision Tree Analysis models sequential decision alternatives (represented by square decision nodes) and probabilistic state-of-nature uncertainties (represented by circular chance nodes), evaluated chronologically from left to right and solved mathematically via backward induction (folding back) from right to left.
The Expected Value of Perfect Information (EVPI = |EMV_with_perfect_info - EMV_without_info|) establishes the absolute economic ceiling an organization should expend to eliminate uncertainty (e.g., through geotechnical investigations or pilot plants) prior to committing capital.
Risk neutrality evaluates alternatives strictly by maximizing EMV or minimizing expected cost, whereas risk aversion incorporates non-linear concave utility functions where the Certainty Equivalent is less than the EMV, reflecting a positive Risk Premium to avoid catastrophic losses.
Real options valuation treats capital investment flexibility (options to expand, defer, abandon, or switch) as financial call/put options, capturing strategic value that standard discounted cash flow (DCF) models systematically ignore under high volatility.
Last updated: August 2026
14.1 Expected Monetary Value (EMV) & Decision Tree Analysis
In capital project decision-making and cost engineering, project leaders constantly face strategic choices characterized by significant uncertainty, irreversible capital commitments, and variable future outcomes. Under the AACE International Total Cost Management (TCM) Framework (specifically Section 7.6, Risk Management ), cost professionals must move beyond intuitive guesswork to apply rigorous, mathematically defensible decision analysis tools.
Two foundational quantitative tools in the cost engineer's toolkit are Expected Monetary Value (EMV) and Decision Tree Analysis (DTA) . Together with Expected Value of Perfect Information (EVPI) , Utility Theory , and Real Options Valuation , these techniques provide an analytical framework for evaluating complex, sequential decisions under conditions of risk and uncertainty.
1. Expected Monetary Value (EMV) Fundamentals
Expected Monetary Value (EMV) is a statistical technique that calculates the average outcome when the future includes scenarios that may or may not happen. It converts a range of probabilistic future outcomes into a single, weighted expected monetary figure. +-----------------------------------------------------------------------------+
- | EXPECTED MONETARY VALUE (EMV) FORMULA |
- | |
- | EMV = \sum_{i=1}^{n} (P_i \times \text{Impact}_i) |
- | |
- | Where: |
- | - P_i = Probability of occurrence for scenario i |
- | - Impact_i = Monetary value (payoff or cost) of scenario i |
- | - \sum P_i = 1.00 (Mutually exclusive & collectively exhaustive events) |
- | |
- | CONVENTIONS: |
- | - Gains / Revenues / Cost Savings --> Positive Values (+) |
- | - Losses / Expenditures / Overruns --> Negative Values (-) |
- +-----------------------------------------------------------------------------+
- Operational Principles of EMV
Linear Expectation: EMV assumes that the decision-maker is risk-neutral —meaning that an outcome with an EMV of + $ 1 , 000 , 000 +\text{\textdollar}1,000,000 + $ 1 , 000 , 000 derived from a 100 % 100\% 100% certain event is evaluated identically to a 50 % 50\% 50% chance of + $ 2 , 000 , 000 +\text{\textdollar}2,000,000 + $ 2 , 000 , 000 and a 50 % 50\% 50% chance of $ 0 \text{\textdollar}0 $ 0 .
Long-Run Statistical Average: EMV represents the mean outcome if the exact same decision scenario were repeated an infinite number of times. On a single, non-repeatable capital project, the actual realized outcome will almost never equal the EMV; it will equal one of the discrete realized scenario outcomes.
Decision Criteria:
When evaluating revenue/profit opportunities , select the alternative that maximizes EMV .
When evaluating project cost/expenditure risks , select the alternative that minimizes Expected Cost .
2. Decision Tree Architecture & The Mechanics of "Folding Back"
A Decision Tree is a visual and mathematical model that maps out the chronological sequence of choices, uncertain events, and final financial payoffs. It allows cost engineers to structure multi-stage capital decisions where subsequent choices depend on earlier probabilistic outcomes. +-----------------------------------------------------------------------------+
- | DECISION TREE NODE TAXONOMY |
- | |
- | 1. DECISION NODE (Square: [ ]): |
- | - Represents an active choice under the decision-maker's direct control|
- | - Costs of choosing a branch are deducted at this point |
- | - Evaluation Rule: Select the branch with the optimal EMV (Max/Min) |
- | |
- | 2. CHANCE / PROBABILITY NODE (Circle: ( )): |
- | - Represents an uncertain "state of nature" beyond direct control |
- | - Radiating branches must have probabilities summing to 1.00 |
- | - Evaluation Rule: Calculate weighted EMV: \sum (P_i \times Payoff_i) |
- | |
- | 3. TERMINAL / END NODE (Triangle: < > or End Value): |
- | - Represents the final milestone payoff or net cost of a scenario path |
- +-----------------------------------------------------------------------------+
- The Backward Induction ("Folding Back") Algorithm
Decision trees are constructed chronologically from left to right (past to future), but they are mathematically solved and evaluated in reverse order from right to left (future to present). This process is known as backward induction or folding back the tree . +-----------------------------------------------------------------------------+
- | BACKWARD INDUCTION (FOLDING BACK) STEPS |
- | |
- | Step 1: Calculate Net Terminal Payoffs at each end branch: |
- | Net Payoff = Gross Revenue - Direct Costs - Branch Capex |
- | |
- | Step 2: Fold back Chance Nodes (Circles) from right to left: |
- | EMV(Node) = \sum [ P(Branch_i) \times Value(End_i) ] |
- | |
- | Step 3: Fold back Decision Nodes (Squares) from right to left: |
- | Select MAX(EMV) for revenue, or MIN(Expected Cost) for costs. |
- | Prune (cross out with //) the rejected inferior branches. |
- | |
- | Step 4: Continue folding back until the root decision node is resolved. |
- +-----------------------------------------------------------------------------+
- 3. Expected Value of Perfect Information (EVPI)
In capital projects, management often has the opportunity to purchase additional information before committing to a major expenditure—such as conducting geotechnical exploratory boreholes, performing a front-end engineering design (FEED) study, running 3D seismic testing, or executing pilot plant test runs.
The Expected Value of Perfect Information (EVPI) quantifies the absolute upper limit on what a rational project owner should spend to acquire perfect foresight that completely eliminates uncertainty. +-----------------------------------------------------------------------------+
- | EXPECTED VALUE OF PERFECT INFORMATION (EVPI) |
- | |
- | EVPI = | EMV_{with perfect information} - EMV_{without information} | |
- | |
- | Where: |
- | - EMV_{without info} = EMV of the best decision made under current |
- | uncertainty (standard decision tree outcome). |
- | - EMV_{with perfect info}= Weighted expected payoff when the decision- |
- | maker always selects the optimal strategy for |
- | whichever state of nature actually occurs. |
- | |
- | MANAGEMENT RULE: |
- | Cost of Information Gathering <= EVPI |
- | (Paying more than EVPI for studies is economically irrational). |
- +-----------------------------------------------------------------------------+
- Expected Value of Imperfect (Sample) Information (EVSI)
In reality, engineering studies and market tests rarely provide 100% perfect clarity; they provide imperfect sample information. The Expected Value of Sample Information (EVSI) is calculated using Bayesian revision of prior probabilities to posterior probabilities based on test reliability. EVSI is strictly bounded by: 0 ≤ E V S I ≤ E V P I 0 \le EVSI \le EVPI 0 ≤ E V S I ≤ E V P I .
4. Risk Attitudes and Utility Theory
While EMV assumes risk neutrality, corporate entities and project sponsors often exhibit distinct risk preferences, especially when single project decisions carry the threat of catastrophic financial ruin or bankruptcy. Von Neumann-Morgenstern Utility Theory models these risk attitudes. +-----------------------------------------------------------------------------+
- | RISK ATTITUDE & UTILITY SPECTRUM |
- | |
- | 1. RISK-NEUTRAL: |
- | - Linear utility function: U(W) = aW + b |
- | - Evaluates alternatives purely on EMV. |
- | - Certainty Equivalent (CE) = EMV; Risk Premium (RP) = $0. |
- | |
- | 2. RISK-AVERSE (Standard Corporate / Engineering Behavior): |
- | - Concave utility function: U''(W) < 0 (Diminishing marginal utility) |
- | - Strongly penalizes large negative outcomes. |
- | - Prefers a guaranteed certain payoff over a risky gamble with the |
- | same EMV. |
- | - Certainty Equivalent (CE) < EMV; Risk Premium (RP = EMV - CE) > $0. |
- | |
- | 3. RISK-SEEKING / RISK-PRONE: |
- | - Convex utility function: U''(W) > 0 |
- | - Willing to accept negative EMV gambles for the chance of high reward.|
- | - Certainty Equivalent (CE) > EMV; Risk Premium (RP) < $0. |
- +-----------------------------------------------------------------------------+
- Attribute Risk Averse Risk Neutral Risk Seeking
- Utility Curve Shape Concave (curves downward) Linear (straight line) Convex (curves upward)
- Marginal Utility of Wealth Diminishing Constant Increasing
Certainty Equivalent vs. EMV CE < EMV \text{CE} < \text{EMV} CE < EMV CE = EMV \text{CE} = \text{EMV} CE = EMV CE > EMV \text{CE} > \text{EMV} CE > EMV
Risk Premium ( R P = E M V − C E RP = EMV - CE RP = EM V − CE ) Positive ( R P > 0 RP > 0 RP > 0 ) Zero ( R P = 0 RP = 0 RP = 0 ) Negative ( R P < 0 RP < 0 RP < 0 )
Typical Project Context High-capex mega-projects, nuclear/chemical process safety Diversified portfolio of standard repeatable sub-projects Speculative exploration, start-ups, venture projects
Note
Certainty Equivalent (CE): The exact guaranteed, risk-free cash amount that a decision-maker views as having equal utility to a risky probabilistic venture. Risk Premium ( R P RP RP ): The amount of expected monetary return an organization is willing to forfeit to eliminate risk: R P = E M V − C E RP = EMV - CE RP = EM V − CE .
5. Real Options Valuation in Capital Projects
Traditional Discounted Cash Flow (DCF) and Net Present Value (NPV) techniques suffer from a major theoretical flaw: they assume that once an investment decision is made, management follows a fixed, inflexible execution plan regardless of how market conditions, technology, or commodity prices evolve.
Real Options Analysis (ROA) applies financial options theory (e.g., Black-Scholes and Binomial Lattice models) to tangible capital assets, valuing managerial flexibility to respond to future uncertainties. +-----------------------------------------------------------------------------+
- | TYPES OF REAL OPTIONS IN PROJECTS |
- | |
- | 1. OPTION TO DEFER / WAIT (Call Option): |
- | - Right to delay capital expenditure until market conditions clarify. |
- | |
- | 2. OPTION TO EXPAND / PHASE (Growth Option / Call Option): |
- | - Staged investment (e.g., Phase 1 pilot, followed by Phase 2 full- |
- | scale rollout only if Phase 1 yields high returns). |
- | |
- | 3. OPTION TO ABANDON / TERMINATE (Put Option): |
- | - Right to exit a project early and recover salvage value, truncating |
- | downside losses. |
- | |
- | 4. OPTION TO SWITCH (Flexibility Option): |
- | - Ability to switch inputs (e.g., dual-fuel gas/oil power plant) or |
- | outputs based on market price differentials. |
- +-----------------------------------------------------------------------------+
Strategic NPV Formula Expanded (Strategic) NPV = Traditional Static NPV + Real Option Value \text{Expanded (Strategic) NPV} = \text{Traditional Static NPV} + \text{Real Option Value} Expanded (Strategic) NPV = Traditional Static NPV + Real Option Value
Because real options provide rights without obligations, their value is always non-negative ( Option Value ≥ 0 \text{Option Value} \ge 0 Option Value ≥ 0 ).
In highly volatile environments, projects with negative static NPV may be commercially justified when the embedded real options provide significant upside or downside protection.
6. Comprehensive Worked Step-by-Step Engineering Case Study
Petrochemical Facility Off-Gas Processing Case Data: An industrial owner must choose an execution strategy for an off-gas processing unit with a planned 10-year operating life. Two primary technical alternatives are available at Decision Node 1 ( D 1 D_1 D 1 ):
Alternative A: Modular Pre-Fabrication (Off-site modular assembly in a yard):
Initial Capital Cost ( C a p e x Capex C a p e x ): $ 12 , 000 , 000 \text{\textdollar}12,000,000 $ 12 , 000 , 000
Transport & Logistics Outcomes (Chance Node C A C_A C A ):
Favorable Transport & Fit-up ( P = 0.70 P = 0.70 P = 0.70 ): Total 10-year Net Operating Profit = + $ 30 , 000 , 000 +\text{\textdollar}30,000,000 + $ 30 , 000 , 000
Heavy-Lift Crane Failure & Marine Transport Delay ( P = 0.30 P = 0.30 P = 0.30 ): Total 10-year Net Operating Profit = + $ 15 , 000 , 000 +\text{\textdollar}15,000,000 + $ 15 , 000 , 000
Alternative B: Stick-Built On-Site Construction:
Initial Capital Cost ( C a p e x Capex C a p e x ): $ 9 , 000 , 000 \text{\textdollar}9,000,000 $ 9 , 000 , 000
Site Weather & Labor Productivity Outcomes (Chance Node C B C_B C B ):
Mild Weather & Normal Labor Productivity ( P = 0.60 P = 0.60 P = 0.60 ): Total 10-year Net Operating Profit = + $ 32 , 000 , 000 +\text{\textdollar}32,000,000 + $ 32 , 000 , 000
Severe Winter & Severe Craft Shortage ( P = 0.40 P = 0.40 P = 0.40 ): Total 10-year Net Operating Profit = + $ 10 , 000 , 000 +\text{\textdollar}10,000,000 + $ 10 , 000 , 000
Geotechnical / Meteorological Early Survey Option:
A specialized consulting firm offers a proprietary advance site testing and simulation study that provides perfect information regarding site weather and transport logistics conditions.
Step 1: Calculate Net Payoffs for Each Terminal Branch Net Terminal Payoff = Gross Operating Profit − Initial Capex \text{Net Terminal Payoff} = \text{Gross Operating Profit} - \text{Initial Capex} Net Terminal Payoff = Gross Operating Profit − Initial Capex
Alternative A (Modular):
Branch A1 (Favorable, P = 0.70 P=0.70 P = 0.70 ): $ 30 , 000 , 000 − $ 12 , 000 , 000 = + $ 18 , 000 , 000 \text{\textdollar}30,000,000 - \text{\textdollar}12,000,000 = \mathbf{+\text{\textdollar}18,000,000} $ 30 , 000 , 000 − $ 12 , 000 , 000 = + $ 18 , 000 , 000
Branch A2 (Delays, P = 0.30 P=0.30 P = 0.30 ): $ 15 , 000 , 000 − $ 12 , 000 , 000 = + $ 3 , 000 , 000 \text{\textdollar}15,000,000 - \text{\textdollar}12,000,000 = \mathbf{+\text{\textdollar}3,000,000} $ 15 , 000 , 000 − $ 12 , 000 , 000 = + $ 3 , 000 , 000
Alternative B (Stick-Built):
Branch B1 (Mild/Normal, P = 0.60 P=0.60 P = 0.60 ): $ 32 , 000 , 000 − $ 9 , 000 , 000 = + $ 23 , 000 , 000 \text{\textdollar}32,000,000 - \text{\textdollar}9,000,000 = \mathbf{+\text{\textdollar}23,000,000} $ 32 , 000 , 000 − $ 9 , 000 , 000 = + $ 23 , 000 , 000
Branch B2 (Severe Weather/Shortage, P = 0.40 P=0.40 P = 0.40 ): $ 10 , 000 , 000 − $ 9 , 000 , 000 = + $ 1 , 000 , 000 \text{\textdollar}10,000,000 - \text{\textdollar}9,000,000 = \mathbf{+\text{\textdollar}1,000,000} $ 10 , 000 , 000 − $ 9 , 000 , 000 = + $ 1 , 000 , 000
Step 2: Backward Induction (Folding Back Chance Nodes)
EMV of Chance Node C A C_A C A (Modular): E M V ( C A ) = ( 0.70 × $ 18 , 000 , 000 ) + ( 0.30 × $ 3 , 000 , 000 ) = $ 12 , 600 , 000 + $ 900 , 000 = + $ 13 , 500 , 000 EMV(C_A) = (0.70 \times \$18,000,000) + (0.30 \times \$3,000,000) = \$12,600,000 + \$900,000 = \mathbf{+\$13,500,000} EM V ( C A ) = ( 0.70 × $18 , 000 , 000 ) + ( 0.30 × $3 , 000 , 000 ) = $12 , 600 , 000 + $900 , 000 = + $13 , 500 , 000
EMV of Chance Node C B C_B C B (Stick-Built): E M V ( C B ) = ( 0.60 × $ 23 , 000 , 000 ) + ( 0.40 × $ 1 , 000 , 000 ) = $ 13 , 800 , 000 + $ 400 , 000 = + $ 14 , 200 , 000 EMV(C_B) = (0.60 \times \$23,000,000) + (0.40 \times \$1,000,000) = \$13,800,000 + \$400,000 = \mathbf{+\$14,200,000} EM V ( C B ) = ( 0.60 × $23 , 000 , 000 ) + ( 0.40 × $1 , 000 , 000 ) = $13 , 800 , 000 + $400 , 000 = + $14 , 200 , 000
Step 3: Backward Induction (Evaluating Decision Node D 1 D_1 D 1 Without Study) Optimal Decision = max [ E M V ( C A ) , E M V ( C B ) ] = max [ $ 13 , 500 , 000 , $ 14 , 200 , 000 ] = + $ 14 , 200 , 000 \text{Optimal Decision} = \max [ EMV(C_A), EMV(C_B) ] = \max [ \$13,500,000,\; \$14,200,000 ] = \mathbf{+\$14,200,000} Optimal Decision = max [ EM V ( C A ) , EM V ( C B )] = max [ $13 , 500 , 000 , $14 , 200 , 000 ] = + $14 , 200 , 000
Strategic Selection: Under risk neutrality, the owner selects Alternative B (Stick-Built) , yielding an E M V = $ 14 , 200 , 000 EMV = \text{\textdollar}14,200,000 EM V = $ 14 , 200 , 000 .
Step 4: Calculate Expected Value of Perfect Information (EVPI)
Assume general environmental state probabilities are 60 % 60\% 60% Favorable/Mild and 40 % 40\% 40% Severe/Unfavorable:
If the study reveals Favorable/Mild Conditions ( P = 0.60 P = 0.60 P = 0.60 ):
- Modular Net Payoff = $ 18 , 000 , 000 \text{\textdollar}18,000,000 $ 18 , 000 , 000
- Stick-Built Net Payoff = $ 23 , 000 , 000 \text{\textdollar}23,000,000 $ 23 , 000 , 000
Optimal Choice: Select Stick-Built ( P a y o f f = $ 23 , 000 , 000 Payoff = \text{\textdollar}23,000,000 P a yo ff = $ 23 , 000 , 000 ).
If the study reveals Severe/Unfavorable Conditions ( P = 0.40 P = 0.40 P = 0.40 ):
- Modular Net Payoff = $ 3 , 000 , 000 \text{\textdollar}3,000,000 $ 3 , 000 , 000
- Stick-Built Net Payoff = $ 1 , 000 , 000 \text{\textdollar}1,000,000 $ 1 , 000 , 000
Optimal Choice: Select Modular ( P a y o f f = $ 3 , 000 , 000 Payoff = \text{\textdollar}3,000,000 P a yo ff = $ 3 , 000 , 000 ).
EMV with Perfect Information: E M V perfect = ( 0.60 × $ 23 , 000 , 000 ) + ( 0.40 × $ 3 , 000 , 000 ) = $ 13 , 800 , 000 + $ 1 , 200 , 000 = + $ 15 , 000 , 000 EMV_{\text{perfect}} = (0.60 \times \$23,000,000) + (0.40 \times \$3,000,000) = \$13,800,000 + \$1,200,000 = \mathbf{+\$15,000,000} EM V perfect = ( 0.60 × $23 , 000 , 000 ) + ( 0.40 × $3 , 000 , 000 ) = $13 , 800 , 000 + $1 , 200 , 000 = + $15 , 000 , 000
Expected Value of Perfect Information (EVPI): E V P I = E M V perfect − E M V without info = $ 15 , 000 , 000 − $ 14 , 200 , 000 = $ 800 , 000 EVPI = EMV_{\text{perfect}} - EMV_{\text{without info}} = \$15,000,000 - \$14,200,000 = \mathbf{\$800,000} E V P I = EM V perfect − EM V without info = $15 , 000 , 000 − $14 , 200 , 000 = $800 , 000
Important
Decision Rule: The project owner should pay no more than $ 800 , 000 \text{\textdollar}800,000 $ 800 , 000 for the advance site testing study. If the consulting firm quotes $ 950 , 000 \text{\textdollar}950,000 $ 950 , 000 , the study must be rejected on economic grounds.
7. Key Exam Alerts & Problem-Solving Strategies
Sign Conventions: Always maintain strict arithmetic consistency. For cost trees where all numbers are expenditures, either treat all values as positive costs (and minimize expected cost at decision nodes) or treat them as negative numbers (and maximize EMV). Mixing conventions causes catastrophic calculation errors.
Probability Summation: Verify that the branches radiating from every chance node sum to exactly 1.00 1.00 1.00 ( 100 % 100\% 100% ).
Folding Back Direction: Build the tree left-to-right; solve and prune the tree strictly right-to-left .
Risk Aversion on the Exam: If an exam scenario describes an executive rejecting a higher-EMV option because a potential loss would 'exceed corporate debt covenants' or 'force project cancellation,' recognize this immediately as risk-averse utility theory , where C E < E M V CE < EMV CE < EM V .