PMP RISK WALKTHROUGH
The Kraken Wasn't in the Budget: Expected Monetary Value and a Live EMV Calculator
The treasure is real. So is the kraken. Work through expected monetary value, choose a route, then change the odds in a live calculator.
“Probably fine” is not a budget forecast
An expedition is recovering a treasure chest from a sunken city. The team can take the direct channel or pay extra for a protected passage. Both get the same job done. One costs more upfront; the other leaves more equipment exposed to a very curious kraken.
Expected monetary value (EMV) gives the team a way to compare those uncertain costs. Before you move the sliders, make the decision with the original numbers. The creature may have eight arms. You only need one formula.
Here for the numbers? Open the standalone EMV calculator. No question required.
Expected monetary value and decision trees
A treasure-recovery project has a $20,000 base cost under either route. Route A, the direct channel, has a 25% chance of equipment damage that adds $40,000 to the cost. Route B, the protected passage, requires a guaranteed $6,000 premium and reduces the chance of that same $40,000 extra loss to 5%. There are no other monetary outcomes. Both routes meet the same safety, legal, schedule, and delivery requirements. The sponsor asks for the route with the lowest expected total monetary cost. What should the project manager recommend?
Choose a response to continue.
The strongest response is B
Compare like-for-like expected total costs: base cost + guaranteed extra spending + probability × extra loss. Choose the lower result when the stated criterion is a risk-neutral cost comparison.
A. Upfront cost leaves out the risk
Route A begins at $20,000, but a 25% chance of a $40,000 extra loss adds $10,000 to its expected cost. Its expected total is $30,000, not $20,000.
B. Strongest response
A costs $20,000 + 0.25 × $40,000 = $30,000 in expectation. B costs $20,000 + $6,000 + 0.05 × $40,000 = $28,000. B has the lower expected cost by $2,000 under the sponsor's stated criterion.
C. Protection is not elimination
The protected passage reduces the probability, but a 5% chance of damage remains. That residual risk contributes $2,000, bringing B's expected total to $28,000.
D. A different decision criterion
These are the correct worst-case totals, and affordability of those outcomes matters in a real decision. But the sponsor explicitly asked for the lowest expected cost, which weights both damage and no-damage outcomes by their probabilities.
A low starting price is not necessarily a low expected cost. Conversely, paying for protection does not make the remaining risk disappear. Include both the guaranteed premium and the residual risk.
The protected passage wins this comparison
Route A's expected equipment loss is $10,000. Route B's is $2,000. Paying a $6,000 premium removes $8,000 of expected loss, so B has a $2,000 expected-cost advantage.
That is a comparison, not a promise. The actual total for A is either $20,000 or $60,000; for B, either $26,000 or $66,000. Neither route's expected total is an actual outcome in this simplified example.
Four checks before you choose
Use this short routine when the scenario asks for a monetary decision under uncertainty:
- Identify the decision criterion. Minimize expected costs or maximize expected net payoffs; do not mix the two conventions.
- Separate costs paid for certain from additional costs that occur only if a risk happens.
- Include residual risk after the response. Check that the chance outcomes for each option add up to 100%.
- Compare the totals, then check whether mandatory constraints or risk tolerance change the decision.
What expected monetary value actually means
Expected monetary value, or EMV, weights each possible monetary outcome by its probability. For a single risk, multiply the probability by its monetary impact. For a choice with several possible outcomes, add those weighted values.
EMV = sum of (probability × monetary outcome)
A 25% chance of a $40,000 extra cost contributes $10,000 to expected cost. That does not mean the expedition will receive a $10,000 bill: in this example, the extra bill is either $0 or $40,000. The weighted average helps compare the choices.
Cost or payoff? Choose one sign convention
When threats are recorded as negative monetary impacts, this risk's EMV is −$10,000. Here we show expenses as positive costs and choose the lower expected total. When comparing net payoffs instead, choose the higher EMV. Both conventions work if you use one consistently.
Opportunities can have positive EMV. A 20% chance of receiving a $5,000 bonus gives +$1,000 of expected benefit. Keep benefits and expenses distinct before combining them into a net payoff.
Follow the decision tree
The first branch is your choice of route. Each route then splits into two chance outcomes: the extra loss occurs or it does not. Work backward from those outcomes, multiplying each total cost by its probability.
| Route | No equipment damage | Equipment damage |
|---|---|---|
| A · Direct channel | 75% × $20,000 | 25% × $60,000 |
| B · Protected passage | 95% × $26,000 | 5% × $66,000 |
A: 0.75 × $20,000 + 0.25 × $60,000 = $30,000
B: 0.95 × $26,000 + 0.05 × $66,000 = $28,000
The $6,000 premium appears in both outcomes for B because it is paid upfront. Its remaining 5% risk still counts. Do not add the premium a second time after using these complete outcome costs.
How much is protection worth?
The passage reduces the expected extra loss from $10,000 to $2,000. That $8,000 reduction is the break-even premium in this model. At a $6,000 premium, B saves $2,000 in expected cost. At $8,000, the routes tie. Above $8,000, A has the lower expected cost.
Move the numbers below. The question and its explanation stay fixed to the original expedition; the calculator is your separate experiment.
Move the odds. Follow the cost.
Put the kraken on the spreadsheet
Change the inputs to compare expected costs. Option B pays an extra upfront premium. Both options share the same base cost and extra loss amount.
Amounts are in USD. Choose a scenario or enter your own values.
Compare the expected costs
Option A · No premium
Expected total cost
base + expected extra loss
Two possible outcomes
- · No extra loss
Total cost: - · Extra loss occurs
Total cost:
Option B · Pay a premium
Expected total cost
base + premium + expected extra loss
Two possible outcomes
- · No extra loss
Total cost: - · Extra loss occurs
Total cost:
Break-even premium for Option B
Show the formulas
Expected extra loss = probability / 100 × loss amount.
A = base cost + expected extra loss under A.
B = base cost + upfront premium + expected extra loss under B.
Break-even premium = (A probability − B probability) / 100 × loss amount.
Decision tree check: multiply each outcome's total cost by its probability, then add the two branches. Each route's probabilities add to 100%.
This is a cost comparison, so lower is better. Costs are shown as positive amounts. Each option has one modeled extra-loss event and two mutually exclusive outcomes. Benefits and other costs are assumed equal; costs share one time basis with no discounting. EMV describes an average, not a guaranteed bill or a safety decision.
What the number cannot decide for you
EMV uses a risk-neutral financial comparison: it treats the weighted average as the decision criterion. A team unable to absorb the worst possible loss may choose differently. Safety requirements, legal obligations, schedule commitments, and risk tolerance still apply. In our fictional question, those requirements are already satisfied and the sponsor explicitly asks for the lowest expected monetary cost.
Good estimates matter too. If the probabilities or cost impacts are uncertain, test a range rather than treating one precise answer as certain. The kraken does not sign your assumptions.
EMV is different from earned value management (EVM): EMV compares uncertain monetary outcomes; EVM compares project work, spending, and the plan. For that topic, try the earned value calculator.
Sources: PMI: Decision tree analysis; PMI: Decision trees and risk tolerance. The expedition and question are original educational examples.
Put the reasoning to work
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