Expected Monetary Value

One probability-weighted number per option

Business Risk AnalysisExpected Value & Decision TreesFree preview

⏱️ About 16 min

Northwind Trading weighs launching now versus delaying. Launch now carries a 60% chance of a $500,000 gain and a 40% chance of a $200,000 loss, for an EMV of 0.60 x 500,000 + 0.40 x (-200,000) = $220,000. Delaying is safer at a 90% chance of a $150,000 gain and 10% of $0, EMV $135,000. On a single probability-weighted number, launch now wins.

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The big idea: Expected Monetary Value (EMV) collapses a risky option into one number: the sum of each outcome payoff $x_i$ times its probability $p_i$, EMV = sum of p_i x x_i. Compare options by their EMV and pick the higher one.

🎯 By the end, you'll be able to

Compute EMV as the probability-weighted sum of outcome payoffs.
Compare two risky options on a single EMV number.
Choose the option with the higher EMV.

📎 Helpful to know first

Completion of Module 3: Qualitative vs. Quantitative Risk.

One number per option

When a choice leads to several outcomes, you need a way to compare it against rival choices on common ground. Expected Monetary Value (EMV) does this by weighting each outcome's payoff by its probability. For each outcome multiply its probability (as a decimal) by its payoff, then add those products; the option with the higher EMV is the better bet, on average. The probabilities for one option must add up to 1 (100%).

\[ EMV = \sum p_i \times x_i \]

Reading the formula

For "Launch now" the outcomes are a 60% chance of +$500,000 and a 40% chance of -$200,000, so EMV = 0.60 x 500,000 + 0.40 x (-200,000) = 300,000 - 80,000 = $220,000. For "Delay" the outcomes are a 90% chance of +$150,000 and a 10% chance of $0, so EMV = 0.90 x 150,000 + 0.10 x 0 = $135,000. Because 220,000 is greater than 135,000, Launch now has the higher EMV and is the better choice.

✨ Average over many runs

EMV is the average payoff if you could repeat the same decision many times under the same odds. A single run may still land on the bad outcome, so EMV compares options on expected terms, not as a promise of any single result.

🎮 EMV Calculator LIVE

Predict first: Predict first: 60% of +$500,000 and 40% of -$200,000 -- what is the EMV?

Slide the outcome-1 probability (outcome 2 takes the rest) and both payoffs to watch each outcome's contribution and the EMV update.

📝 Worked example: Northwind considers "Launch now": 60% chance of +$500,000 and 40% chance of -$200,000. Find the EMV.

1. EMV = sum of probability x payoff.
2. = 0.60 x 500,000 + 0.40 x (-200,000) = 300,000 - 80,000.
3. = $220,000.

✓ EMV = $220,000

✏️ Practice: An option has a 70% chance of +$300,000 and a 30% chance of -$100,000. What is its EMV?

💡 Hint

EMV is the sum of each probability (as a decimal) times its payoff.

Solution

1. EMV = 0.70 x 300,000 + 0.30 x (-100,000).
2. = 210,000 - 30,000 = $180,000.

Check your understanding

1. Launch now: 60% of +$500,000 and 40% of -$200,000. What is the EMV?

EMV = 0.60 x 500,000 + 0.40 x (-200,000) = 300,000 - 80,000 = $220,000.

2. What does EMV let you do?

EMV reduces each option to a single probability-weighted number so you can compare risky choices directly.

✅ Key takeaways

EMV = sum of probability x payoff across an option's outcomes.
Probabilities for one option are entered as percents that sum to 100.
Pick the option with the higher EMV.

➡️ EMV compares options one at a time. Next we draw a decision tree that folds many chance nodes into a single recommendation.

Ready for the next step? Back to the course outline →