Chance Path Value: Decision Tree Analysis for Expected Monetary Value

PMBOK v8 Definition

Chance Path Value is the computed net value along a decision tree branch, calculated as payoffs minus costs for each possible outcome path. It represents the monetary result of a specific scenario when a chance event occurs, feeding into the overall Expected Monetary Value (EMV) calculation. The chance node receives inputs of scenario probability and reward if it occurs, producing the net path value that contributes to the decision node's EMV output.

Why It Matters for the Exam

This concept appears in approximately 3-5 questions on the PMI exam, typically within quantitative risk analysis and decision-making scenarios. Questions test your ability to calculate net path values correctly, distinguish between decision nodes and chance nodes, and select the optimal decision based on comparative EMV calculations. Expect these questions in the Planning and Executing performance domains.

Key Points to Remember (for the exam)

• Chance Node Inputs: Scenario probability + Reward if it occurs → Net Path Value = Payoffs minus Costs along path
• Decision Node Output: Expected Monetary Value (EMV) = Sum of all probability-weighted net path values for that decision branch
• Decision Rule: Select the decision branch with the HIGHEST EMV (not necessarily the highest potential payoff)
• Risk Consideration: The optimal EMV choice often represents the lowest risk option, avoiding worst-case outcomes
• Cost Accounting: ALWAYS subtract investment costs from gross payoffs to get net path values before calculating EMV
• Probability Sum: All scenario probabilities at a chance node must sum to 100%
• Common Confusion: Net Path Value is the branch-specific result; EMV is the probability-weighted aggregate across all branches for one decision option

Typical PMI Exam Example

A project team evaluates building a new plant (invest $120M) versus upgrading an existing plant (invest $80M). For the build option: 60% probability of strong demand ($200M revenue) and 40% weak demand ($90M revenue). For the upgrade option: 60% strong demand ($160M revenue) and 40% weak demand ($100M revenue). Calculate the net path values: Build strong demand = $200M-$120M = $80M; Build weak demand = $90M-$120M = -$30M. EMV for build = 0.60($80M) + 0.40(-$30M) = $36M. The upgrade option yields EMV = $46M, making it the better decision.

PMI Exam Traps

• Trap: Using gross revenue instead of net path value (forgetting to subtract investment costs)

  • Reality: Always compute Net Path Value = Payoffs minus Costs before calculating EMV

• Trap: Selecting the branch with the highest single payoff ($200M) rather than the highest EMV ($46M)

  • Reality: EMV accounts for probability-weighted outcomes; the highest payoff may carry unacceptable risk

• Trap: Confusing Decision Node with Chance Node

  • Reality: Decision nodes represent choices you control; chance nodes represent uncertain events with probabilities

• Trap: Adding probabilities across different decision branches instead of within a single chance node

  • Reality: Probabilities only sum to 100% within one chance node, not across alternative decisions

Important PMI Connections

Quick Review Questions

1. A decision tree shows two chance nodes. One has three branches with probabilities 50%, 30%, and 20%. The other has two branches with probabilities 70% and 30%. What is the probability sum required for each chance node?

2. Calculate the Net Path Value for a branch where the investment cost is $50,000 and the expected payoff is $120,000.

3. If Decision A has EMV of $75,000 and Decision B has EMV of $82,000, which decision should be selected according to PMBOK guidance?

4. What is the difference between a Decision Node and a Chance Node in terms of what the project team controls?

5. A project has two decision options. Option 1 has EMV of $46M but a worst-case loss of $30M. Option 2 has EMV of $36M with no loss scenario. Which option represents lower risk?

PMBOK v8 Reference

Section 5.5 - Decision Making and Decision Tree Analysis (Page 163-164)