5.2 Expected Monetary Value & Decision Trees

Expected Monetary Value

Expected Monetary Value (EMV) is the average outcome of a risk weighted by its probability:

EMV = Probability × Impact

Impact is in money. Threats take a negative sign (they cost you); opportunities take a positive sign (they save or earn). EMV is the cornerstone calculation of quantitative analysis and appears constantly on the PMI-RMP exam.

The sign convention is not cosmetic — it lets you add threats and opportunities on the same ledger. A project with several threats and a couple of opportunities produces one net EMV, the expected change to project cost. Keeping signs straight is the single most common arithmetic mistake candidates make under exam time pressure, so always write the minus sign on a threat impact before multiplying.

Worked EMV Examples

A threat: there is a 30% chance a vendor delay forces $50,000 of overtime.

• EMV = 0.30 × (−$50,000) = −$15,000

An opportunity: there is a 40% chance an early-finish bonus pays $20,000.

• EMV = 0.40 × (+$20,000) = +$8,000

A second threat: 10% chance of a $200,000 rework.

• EMV = 0.10 × (−$200,000) = −$20,000

EMV is not what will happen on this one project; it is the long-run average if the situation recurred many times. That is exactly why it is the right basis for sizing a reserve across a portfolio of risks.

Notice that no single risk pays out at its EMV. The vendor delay either costs the full $50,000 or nothing — never exactly $15,000. EMV only becomes meaningful when summed across many risks, where the highs and lows average out. A question that asks "what will this risk cost?" is testing whether you confuse the EMV with the actual impact; the EMV is the weighted expectation, not the realized cost.

Summing EMV Across Risks

Individual EMVs add together. Combining the three risks above:

The −$27,000 total is a defensible starting point for the contingency reserve: it captures both downside threats and the offsetting upside. Note how the low-probability, high-impact rework (−$20,000) dominates — EMV correctly rewards attention to tail risks, not just likely ones.

This is where EMV connects to reserve setting. A sponsor who asks "how much buffer do we need for these risks?" can be answered with the summed EMV, scaled up if the organization wants protection beyond the expected value. Opportunities reduce the reserve because their positive EMV offsets threats — a point candidates often miss when they treat reserve as a threats-only number. Always net the opportunity EMVs in.

Decision Trees

A decision tree evaluates competing choices when each leads to uncertain outcomes. Squares are decision nodes (you choose); circles are chance nodes (probability decides). You compute the EMV of each chance node, add the up-front cost of each decision branch, then pick the branch with the better EMV.

The rule: choose the branch with the most favorable EMV — the lowest expected cost for a threat-dominated tree, or the highest expected value when payoffs are positive. The cheapest up-front option is not automatically best once weighted outcomes are added.

The method, called rolling back the tree, works from the leaves to the root: compute the EMV at each chance node, fold it into the decision branch above it, then compare branches at the decision node. Decision trees shine when a choice today (build vs buy, accelerate vs not, single vs dual supplier) leads to uncertain downstream costs — they make the risk-adjusted economics of each option explicit rather than relying on gut feel.

Worked Decision Tree

A team chooses between building a custom tool or buying one.

Branch A — Build (up-front cost $100,000):

• 60% it works cleanly → additional $0
• 40% it needs rework → additional −$150,000
• Chance-node EMV = (0.60 × $0) + (0.40 × −$150,000) = −$60,000
• Total path = −$100,000 + (−$60,000) = −$160,000

Branch B — Buy (up-front cost $130,000):

• 80% it integrates fine → additional $0
• 20% it needs customization → additional −$50,000
• Chance-node EMV = (0.80 × $0) + (0.20 × −$50,000) = −$10,000
• Total path = −$130,000 + (−$10,000) = −$140,000

Decision: Buy. Its total EMV of −$140,000 is less costly than Build's −$160,000, even though Buy's up-front price is higher. The exam reliably tests this counterintuitive result.

The lesson generalizes: a low sticker price can hide a high expected cost once the probability and size of downstream problems are weighted in. Build looked $30,000 cheaper up front ($100K vs $130K) but its 40% chance of a $150,000 rework swamped that advantage. When a question gives two or more options with up-front costs and probabilistic outcomes, resist the instinct to pick the cheapest entry price — roll back each tree and compare the totals. Decision trees also handle opportunities (positive payoffs); there you choose the highest EMV branch.