Management Accounting · Decision Theory

Expected Value of Perfect Information (EVPI) Explained

Updated 10 October 2026 · Fact-checked

EVPI is the most you should pay for a perfect forecast of the future state of nature. EVPI = Expected profit with perfect information (EPPI) − best Expected Monetary Value (EMV) without it. It also equals the minimum Expected Opportunity Loss (EOL). Find the best payoff in each state, weight by probability, add, then subtract the best EMV.

Understand Expected Value of Perfect Information (EVPI)

In decision making under risk you choose an action before you know which state of nature will occur. Demand may be high or low, and you only know the probabilities. The best you can do is pick the action with the highest EMV (Expected Monetary Value).

Now imagine a forecaster who is never wrong. If this person says demand will be high, you pick the best action for high demand. If low, you pick the best action for low demand. You choose a different action in each state, always the best one. You do not know in advance which state will come, so you still weight each outcome by its probability.

The weighted total of those best payoffs is the Expected Profit with Perfect Information (EPPI). It is always at least as large as the best EMV. The gap between the two is the EVPI. It is the value of removing the uncertainty.

EVPI is a ceiling on what you should pay. If the information costs less than EVPI, it may be worth buying. If it costs more, it cannot pay off, even when perfect. Real forecasts are imperfect, so their worth is lower than EVPI.

The EOL (Expected Opportunity Loss) approach gives the same number. Opportunity loss is the payoff you give up by not choosing the best action in a state. The action with the minimum EOL is the same action as the maximum EMV, and that minimum EOL equals EVPI. This works as a built-in check on your answer.

Key rules to remember

Expected profit with perfect information: EPPI = Σ (best payoff in each state × probability of that state); Take the highest payoff in each column (state), not the payoff of one action.
EVPI (main formula): EVPI = EPPI − maximum EMV; Use the maximum EMV of the actions without information. For costs, use the lowest expected cost and EVPI = lowest EMV cost − expected cost with perfect information.
EVPI by opportunity loss: EVPI = minimum EOL; Opportunity loss = best payoff in the state − payoff of the action in that state. It holds when the payoffs are profits and the probabilities are known.
Expected monetary value of an action: EMV = Σ (payoff × probability); Probabilities of all states must add up to 1.

How to solve Expected Value of Perfect Information (EVPI) questions

Use this method for any EVPI question with a payoff table and probabilities.

1Write the payoff table with actions in rows and states of nature in columns. Check that the probabilities add up to 1.
2Compute the EMV of each action: multiply each payoff by its state probability and add across the row.
3Pick the maximum EMV (or minimum expected cost if the table shows costs). This is the best decision without information.
4Underline the best payoff in each column. For costs, underline the lowest.
5Compute EPPI: multiply each underlined payoff by its state probability and add.
6Compute EVPI = EPPI − maximum EMV.
7Check with the EOL table: minimum EOL should equal EVPI. If it does not, find the slip.
8State the conclusion: the maximum you should pay for perfect information is the EVPI. Compare it with the cost of information if given.

Quickest way: Column-best and EMV subtraction

When to use it: Use when the question asks only for EVPI and the table is small, and you have little time.

Find the best EMV row by row, and note it.
Pick the best value in each column and weight it by probability to get EPPI.
Subtract: EVPI = EPPI − best EMV.
If time allows, build the EOL table for only the best action's row. Its EOL should equal your EVPI.

Common mistakes in Expected Value of Perfect Information (EVPI)

Using the payoffs of one action to calculate EPPI.
Students confuse EPPI with the EMV of the best action.
Fix: EPPI uses the best payoff in each column, so different actions can appear in different states.
Subtracting the wrong EMV, such as the lowest or an average of EMVs.
Students rush through the EMV list.
Fix: Subtract only the maximum EMV (for profits) from EPPI.
Forgetting to weight best payoffs by probability.
Students simply add the column maximums.
Fix: Multiply every best payoff by its state probability before adding.
Getting a negative EVPI.
An arithmetic slip, or choosing the wrong column maximums.
Fix: EVPI cannot be negative. Recheck the EMVs and column maxima, and cross-check with minimum EOL.
Treating cost tables like profit tables.
Students apply 'highest' by habit.
Fix: For costs, take the lowest value in each column and the lowest EMV. EVPI = lowest EMV cost − expected cost with perfect information.
Paying more than EVPI for information, or ignoring the cost of information.
Students stop after the calculation.
Fix: Write a final sentence comparing EVPI with the information cost; buy only if the cost is below EVPI.

Worked examples

Example 1

A trader in Pune can stock 100, 200 or 300 units of a festival item. Profit (₹) by demand: Stock 100: low 10,000, medium 10,000, high 10,000. Stock 200: low 4,000, medium 20,000, high 20,000. Stock 300: low −2,000, medium 14,000, high 30,000. Probabilities of demand: low 0.2, medium 0.5, high 0.3. Find the EMV-best action and the EVPI.

Show the solution

EMV of 100 units = 10,000 × (0.2 + 0.5 + 0.3) = ₹10,000.
EMV of 200 units = 4,000 × 0.2 + 20,000 × 0.5 + 20,000 × 0.3 = 800 + 10,000 + 6,000 = ₹16,800.
EMV of 300 units = −2,000 × 0.2 + 14,000 × 0.5 + 30,000 × 0.3 = −400 + 7,000 + 9,000 = ₹15,600.
Best action without information: stock 200 units, EMV ₹16,800.
Best payoff per state: low 10,000 (stock 100), medium 20,000 (stock 200), high 30,000 (stock 300).
EPPI = 10,000 × 0.2 + 20,000 × 0.5 + 30,000 × 0.3 = 2,000 + 10,000 + 9,000 = ₹21,000.
EVPI = 21,000 − 16,800 = ₹4,200.
Check with EOL of 200 units: low 10,000 − 4,000 = 6,000; medium 0; high 30,000 − 20,000 = 10,000. EOL = 6,000 × 0.2 + 0 + 10,000 × 0.3 = 1,200 + 3,000 = ₹4,200. It matches.

Answer: Best action: stock 200 units with EMV ₹16,800. EPPI = ₹21,000. EVPI = ₹4,200, which is the maximum worth of perfect information.

Example 2

A firm in Chennai chooses between launching Product X or Product Y. Profit (₹ lakh): X: market weak 5, market strong 25. Y: market weak 12, market strong 18. P(weak) = 0.4, P(strong) = 0.6. A research agency offers a perfect forecast for ₹2 lakh. Should the firm buy it?

Show the solution

EMV of X = 5 × 0.4 + 25 × 0.6 = 2 + 15 = ₹17 lakh.
EMV of Y = 12 × 0.4 + 18 × 0.6 = 4.8 + 10.8 = ₹15.6 lakh.
Best without information: X, EMV ₹17 lakh.
Best payoff if weak: 12 (Y). Best payoff if strong: 25 (X).
EPPI = 12 × 0.4 + 25 × 0.6 = 4.8 + 15 = ₹19.8 lakh.
EVPI = 19.8 − 17 = ₹2.8 lakh.
Check: EOL of X = (12 − 5) × 0.4 + 0 = 2.8 lakh. It matches.
The fee of ₹2 lakh is below EVPI of ₹2.8 lakh.

Answer: EVPI = ₹2.8 lakh. Since the fee of ₹2 lakh is less than this, buying the forecast can add value, with a maximum net gain of ₹0.8 lakh if the forecast is truly perfect.

Exam tips

Always show the EMV table, the column-best values and the EPPI line separately. Step marks are given for each.
Add the EOL check in a short line. It shows the examiner you verified the answer.
In MCQs, remember EVPI = minimum EOL and EVPI = EPPI − max EMV; options often include the EPPI or the max EMV as traps.
End the written answer with a decision sentence comparing EVPI with the cost of information, if one is given.
Read the table carefully for cost or loss data. Then use the lowest, not the highest.

Practice questions from Decision Theory

Expected Value of Perfect Information (EVPI) in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Expected Value of Perfect Information (EVPI): frequently asked questions

Why does EVPI equal the minimum EOL?

EOL measures the expected payoff lost by not knowing the true state. EPPI is the best possible expected payoff, and the EMV of an action is EPPI minus its EOL. So the action with the highest EMV has the lowest EOL, and that EOL equals EPPI minus the best EMV, which is EVPI.

Can EVPI be negative or zero?

It cannot be negative. It is zero when one action is best in every state, as then information changes nothing. A negative answer means you made a calculation error.

Is EVPI the same as EPPI?

No. EPPI is the expected profit if you always knew the state beforehand. EVPI is EPPI minus the best EMV you can get without that knowledge.

What if the payoff table shows costs instead of profits?

Pick the lowest cost in each state to get the expected cost with perfect information. EVPI is the lowest EMV cost without information minus that expected cost.