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Strategic Cost Management · Decision Making using Probability

Expected Value of Perfect Information: EVPI and EVSI Explained

Updated 11 October 2026 · Fact-checked

Expected Value of Perfect Information (EVPI) is the most you should pay for a forecast that removes all uncertainty. Find the best expected payoff without information, then the expected payoff if you always chose the best action for each state. EVPI is the difference. Any information costing more than EVPI is not worth buying.

Understand Expected Value of Perfect Information

Most decisions are made before you know what will happen. You pick an action, then the demand, price or cost turns out to be high, medium or low. Using probabilities, you choose the action with the best expected monetary value (EMV). That is your decision without extra information.

Now imagine a forecaster who can tell you in advance, without error, which state will occur. You would then pick the best action for that state every time. You do not know in advance which state the forecaster will announce, so you weight each best payoff by the probability of that state. This gives the expected value with perfect information (EVwPI).

EVPI is the gain from having that forecaster: EVwPI minus the best EMV you can get today. It is a ceiling. Perfect information is rarely available, so no real study can be worth more than EVPI. If a market survey costs more than EVPI, reject it without further work.

Real information is usually imperfect, such as a pilot run or a sample survey. The expected value of sample information (EVSI) is the gain from that imperfect information: the expected value with the sample information minus the best EMV without it. EVSI is always less than or equal to EVPI. You buy the information only if EVSI is greater than its cost.

EVPI also equals the lowest expected opportunity loss (EOL). Opportunity loss is the payoff you give up by not choosing the best action in a state. This gives you a quick cross-check in the exam.

Key rules to remember

Expected monetary value of an action
EMV = Σ (probability of state × payoff of the action in that state)
Take the highest EMV for profits and the lowest expected cost for costs. This is your decision without information.
Expected value with perfect information
EVwPI = Σ (probability of state × best payoff in that state)
Use the largest payoff in each state for profit, and the smallest cost in each state for cost problems.
EVPI for profit problems
EVPI = EVwPI − best EMV without information
Never negative. It is the maximum price worth paying for perfect information.
EVPI for cost problems
EVPI = lowest expected cost without information − expected cost with perfect information
The direction flips because lower cost is better.
Opportunity loss check
EVPI = minimum EOL, where opportunity loss = best payoff in the state − payoff of the action
The action with the best EMV also has the lowest EOL. Use this to verify your answer.
EVSI and net gain
EVSI = EV with sample information − EV without information; net gain = EVSI − cost of the information
EVSI ≤ EVPI. Buy the information only if the net gain is positive.

How to solve Expected Value of Perfect Information questions

Use this method for any question that asks whether to buy information, or how much to pay for it.

  1. 1Draw the payoff table with actions in rows and states in columns. Check that the probabilities add up to 1.
  2. 2Note whether the payoffs are profits (maximise) or costs (minimise). This decides which value you pick in every later step.
  3. 3Calculate the EMV of each action and choose the best one. This is the best EMV without information.
  4. 4For each state, pick the best payoff across all actions. Multiply by the state's probability and add up to get EVwPI.
  5. 5Subtract to get EVPI: EVwPI − best EMV for profits, or best expected cost − EVwPI for costs.
  6. 6Cross-check with opportunity losses. The minimum EOL should equal EVPI.
  7. 7If the question gives imperfect information, compute its expected value and subtract the best EMV without information to get EVSI. Then deduct the fee.
  8. 8State the decision in a sentence: buy or do not buy, with the maximum price you would pay.

Quickest way: Best-in-column shortcut

When to use it: Use it when the payoff table is small and the question asks only for EVPI, with no imperfect information.

  1. Circle the best payoff in each column (highest for profit, lowest for cost).
  2. Multiply each circled value by its probability and add. That is EVwPI.
  3. Find the best EMV of the current options.
  4. Take the difference. That is EVPI.
  5. Verify with the EOL of the chosen action only. It should give the same figure.

Common mistakes in Expected Value of Perfect Information

  • Picking the best payoff across the whole table instead of the best in each state.

    Students look for one big number instead of thinking state by state.

    Fix: Work column by column. Perfect information means you choose the best action after knowing the state.

  • Taking the highest value in a cost problem.

    The habit of maximising from profit problems carries over.

    Fix: Underline at the start whether you minimise or maximise. For costs use the lowest cost per state, and reverse the subtraction.

  • Subtracting in the wrong order and getting a negative EVPI.

    Students forget that perfect information can only help.

    Fix: EVPI is never negative. If you get a negative, recheck the best EMV and the column maxima.

  • Not using probabilities when computing EVwPI, or using the wrong ones.

    Students add the best payoffs directly because the table looks simple.

    Fix: Always weight each best payoff by the prior probability of that state.

  • Deducting the cost of information before calculating EVPI.

    The fee is mixed into the payoffs.

    Fix: Compute EVPI on payoffs before any fee. Compare the fee with EVPI afterwards.

  • Treating EVSI as larger than EVPI, or confusing the two.

    Both terms sound alike and both are 'value of information'.

    Fix: EVPI is for perfect information and is the upper limit. EVSI is for imperfect information and is at most EVPI.

Worked examples

Example 1

A company can launch a product on a large scale, on a small scale, or not at all. Demand may be High (probability 0.3), Medium (0.5) or Low (0.2). Profits in ₹ lakh are: Large scale: 80, 40, −30. Small scale: 50, 35, 10. No launch: 0, 0, 0. Find the best action without information, the EVPI, and say whether a perfectly reliable study costing ₹5 lakh is worth buying.

Show the solution
  1. EMV of Large = 0.3 × 80 + 0.5 × 40 + 0.2 × (−30) = 24 + 20 − 6 = ₹38 lakh.
  2. EMV of Small = 0.3 × 50 + 0.5 × 35 + 0.2 × 10 = 15 + 17.5 + 2 = ₹34.5 lakh.
  3. EMV of No launch = ₹0. The best action is Large scale with EMV ₹38 lakh.
  4. Best payoff per state: High 80 (Large), Medium 40 (Large), Low 10 (Small).
  5. EVwPI = 0.3 × 80 + 0.5 × 40 + 0.2 × 10 = 24 + 20 + 2 = ₹46 lakh.
  6. EVPI = 46 − 38 = ₹8 lakh.
  7. Check: opportunity loss of Large is 0, 0 and 40 in the three states. EOL = 0.2 × 40 = ₹8 lakh, which matches.

Answer: Launch on a large scale (EMV ₹38 lakh). EVPI = ₹8 lakh. A perfectly reliable study costing ₹5 lakh is worth buying, since its cost is below EVPI and it would add a net ₹3 lakh.

Example 2

A firm must choose Machine X or Machine Y. Expected annual volume is Low (probability 0.6) or High (0.4). Annual cost in ₹ thousand: Machine X: 50 (Low), 90 (High). Machine Y: 70 (Low), 80 (High). (a) Find the best choice and EVPI. (b) A consultant offers a sample-based forecast for ₹3 thousand. With it, the expected cost would be ₹64 thousand. Should the firm buy it?

Show the solution
  1. Expected cost of X = 0.6 × 50 + 0.4 × 90 = 30 + 36 = ₹66 thousand.
  2. Expected cost of Y = 0.6 × 70 + 0.4 × 80 = 42 + 32 = ₹74 thousand.
  3. Without information, choose X at ₹66 thousand, the lower cost.
  4. With perfect information, choose the lowest cost in each state: Low 50 (X), High 80 (Y).
  5. Expected cost with perfect information = 0.6 × 50 + 0.4 × 80 = 30 + 32 = ₹62 thousand.
  6. EVPI = 66 − 62 = ₹4 thousand.
  7. For (b), EVSI = 66 − 64 = ₹2 thousand. This is below EVPI, as it should be.
  8. Net gain = EVSI − fee = 2 − 3 = −₹1 thousand.

Answer: (a) Choose Machine X at an expected cost of ₹66 thousand. EVPI = ₹4 thousand. (b) EVSI is ₹2 thousand, below the fee of ₹3 thousand, so the firm should not buy the forecast. It would lose ₹1 thousand on net.

Exam tips

  • Write down 'maximise' or 'minimise' next to the table before you start. Cost-based questions are where marks are lost.
  • Show the EMV of every action even if only EVPI is asked. Marks are given for the working.
  • Always end with a recommendation that names the maximum price worth paying and compares it with the fee offered.
  • In MCQs, remember EVPI = minimum EOL. It can save you the full EVwPI calculation.
  • If a question gives imperfect information, check that your EVSI is not above EVPI. If it is, there is an error somewhere.

Practice questions from Decision Making using Probability

Expected Value of Perfect Information 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: frequently asked questions

How do you calculate EVPI in CMA Final?

Find the best EMV without information. Then pick the best payoff in each state, weight by the state probabilities and add to get EVwPI. EVPI is EVwPI minus the best EMV, or the reverse for cost problems.

What is the difference between EVPI and EVSI?

EVPI is the value of information that tells you the state with certainty. EVSI is the value of imperfect information such as a sample or pilot. EVSI is never more than EVPI.

Can EVPI be negative?

No. Perfect information can never make your expected result worse. If you get a negative figure, you have made an error in the best EMV or in the best payoff per state.

How much should I pay for information?

Never more than its expected value. For perfect information that limit is EVPI. For imperfect information it is EVSI. Pay only if EVSI is greater than the fee.