Expected Monetary Value (EMV) and Decision Trees

EMV and Decision Trees: Making Decisions Under Uncertainty

The PMP exam expects you to calculate Expected Monetary Value and analyze decision trees. These are quantitative risk analysis techniques that assign dollar values to uncertain outcomes, enabling project managers to make data-driven decisions rather than relying on intuition alone. EMV is the simpler concept; decision trees extend it to sequential decisions with multiple branches.

Expected Monetary Value (EMV) Fundamentals

EMV is the average outcome of a risk when you account for probability. The formula is:

EMV = Probability × Impact

For threats, the impact is negative (a cost). For opportunities, the impact is positive (a benefit). The total EMV of all identified risks on a project represents the overall risk exposure and often serves as the basis for contingency reserves.

EMV Calculation Example

A project has three identified risks:

• Risk A: 30% probability, −$50,000 impact. EMV = 0.30 × (−$50,000) = −$15,000
• Risk B: 20% probability, −$80,000 impact. EMV = 0.20 × (−$80,000) = −$16,000
• Risk C (opportunity): 40% probability, +$30,000 impact. EMV = 0.40 × $30,000 = +$12,000

Total project EMV = −$15,000 + (−$16,000) + $12,000 = −$19,000

This −$19,000 represents the expected risk cost and could justify a contingency reserve of at least that amount.

Decision Tree Analysis

A decision tree is a diagram that models a sequence of decisions and chance events. It uses two types of nodes:

• Decision nodes (squares): Points where the project manager chooses between options.
• Chance nodes (circles): Points where uncertain outcomes occur with associated probabilities.

The tree is built left to right (decisions, then outcomes) but solved right to left — you calculate EMV at the chance nodes, then compare the options at each decision node, choosing the one with the highest EMV (or least negative EMV for costs).

Decision Tree Worked Example

A project manager must decide between two approaches to a software module:

Option A: Build in-house (cost: $200,000)

• 60% chance of success: additional benefit of $400,000
• 40% chance of partial failure: additional cost of $100,000 to fix

EMV of Option A = $200,000 cost + (0.60 × $400,000) + (0.40 × −$100,000) = −$200,000 + $240,000 − $40,000 = $0 net

Option B: Purchase COTS solution (cost: $300,000)

• 80% chance it meets all needs: additional benefit of $350,000
• 20% chance of integration issues: additional cost of $150,000

EMV of Option B = −$300,000 + (0.80 × $350,000) + (0.20 × −$150,000) = −$300,000 + $280,000 − $30,000 = −$50,000 net

Option A has the higher EMV ($0 vs −$50,000), so the decision tree recommends building in-house.

PMP Exam Tips for EMV and Decision Trees

1. Always solve right to left. Calculate the EMV at each chance node before evaluating the decision node.
2. Include all costs. The cost of the decision itself (building, purchasing, insuring) must be factored in — not just the chance outcomes.
3. Probabilities at each chance node must sum to 100%. If they don't, the problem is missing a branch.
4. Higher EMV = better choice. Even if both options have negative EMVs, the less negative one is preferred.
5. EMV does not tell you what will happen. It tells you the statistically best choice over many similar decisions. A single project might have a different actual outcome.

Common Traps

• Forgetting to subtract the decision cost when comparing branches.
• Confusing threat EMV (negative) with opportunity EMV (positive) when summing.
• Trying to solve a decision tree left to right — you will get the wrong answer.

Practice EMV and decision tree problems with our dedicated quantitative risk analysis module. For step-by-step visual guides, see our PMP cheat sheets.