Performance Management · Dealing with risk and uncertainty in decision-making

How to Calculate the Value of Perfect and Imperfect Information

Updated 11 October 2026 · Fact-checked

The value of perfect information is the most you should pay for a forecast that is always right. It equals the expected value with perfect information minus the best expected value without it. Imperfect information, such as market research, is valued the same way, but using revised probabilities.

Understand Value of Perfect and Imperfect Information

A decision under risk has several possible outcomes, each with a probability. Normally you pick the option with the best expected value (EV). But you choose before you know which outcome will happen, so sometimes you pick the wrong option for the outcome that actually occurs.

Perfect information is a forecast that is always right. It tells you exactly which outcome will occur before you decide. With it, you would pick the best option for each outcome. The gain from doing that is the expected value of perfect information (EVPI). It is the most you should pay for the information, because paying more would leave you worse off than deciding without it.

Perfect information rarely exists. Imperfect information, such as market research or a pilot study, is usually right but sometimes wrong. Its reliability is given as probabilities, for example: if the market will be strong, the report says favourable 80% of the time. You use these to work out the probability of each outcome after seeing each report. Then you choose the best option after each report and calculate the EV.

The value of imperfect information is the EV with the research minus the best EV without it. It is never more than the EVPI. If the research costs less than its value, it is worth buying. The cost is not part of the value. Compare them at the end.

The method assumes the probabilities and payoffs are reliable, and EV is a long-run average. For a one-off decision, it may not match what you actually get. Say so in written parts.

Key rules to remember

Expected value: EV = Σ (probability × payoff); Calculate it for every option. Payoffs can be profit, contribution or cost, so check whether you want the highest or the lowest.
Expected value of perfect information: EVPI = EV with perfect information − EV without perfect information; EV with perfect information = Σ (probability of each outcome × best payoff for that outcome). EV without = the best EV from the original table.
Value of imperfect information: Value = EV with imperfect information − EV without information; EV with research = Σ (probability of each report × EV of the best option after that report).
Revised (posterior) probability: P(outcome | report) = P(outcome and report) ÷ P(report); P(outcome and report) = prior probability × probability of that report given the outcome.
Decision on buying information: Buy if value of information > cost of information; The most you would pay is the value of the information. Its cost must be below this.

How to solve Value of Perfect and Imperfect Information questions

Use this order for any perfect or imperfect information question. Keep the figures in a table.

1Draw the payoff table: options down the side, outcomes across the top, probabilities above each outcome.
2Calculate the EV of each option and pick the best. This is the EV without information.
3For perfect information, find the best option under each outcome and write down its payoff.
4Multiply each best payoff by the probability of its outcome and add them. This is the EV with perfect information.
5Subtract step 2 from step 4. This is the EVPI and the maximum price worth paying.
6For imperfect information, work out the probability of each report and the revised outcome probabilities after each report. Total joint probabilities to check they sum to 1.
7After each report, find the EV of each option, take the best, weight it by the report probability and add up. Subtract the EV without information to get its value.
8Compare the value with the cost, if given, and state whether to buy. Add a brief comment on the limits of EV.

Quickest way: Joint probability shortcut for imperfect information

When to use it: Use it when the research reliability is given and you have only two or three outcomes and reports. It saves you from dividing to get revised probabilities.

Multiply the prior probability of each outcome by the report probability given that outcome. These are joint probabilities.
For each report, use the joint probabilities directly as weights in the payoff calculation. Do not divide by P(report).
Choose the best option for each report. The sum of the weighted payoffs of the chosen options is the EV with research.
Subtract the EV without research. Check the answer is no more than the EVPI.

Common mistakes in Value of Perfect and Imperfect Information

Subtracting the cost of the information when finding its value.
Students think of the research as a cost that reduces profit.
Fix: Find the value first, without the cost. Then compare the value with the cost. The maximum price is the value.
Using the EV of the best option for each outcome in the without-information figure.
The two EV calculations look alike.
Fix: Without information you must pick one option and stick with it. Calculate EV for each option and take the best single one.
Picking the best option once for all outcomes in the with-perfect-information calculation.
Students forget that perfect information lets you change the option for each outcome.
Fix: Go outcome by outcome and choose the best payoff in each column. Then weight by the probabilities.
Using the prior probabilities after a research report.
The report changes the odds, but students keep the old figures.
Fix: Revise the probabilities using the reliability figures, or use joint probabilities, for each report.
Getting a value of imperfect information larger than the EVPI.
Arithmetic slips, or reports probabilities that do not sum to 1.
Fix: Treat EVPI as an upper limit. If your answer exceeds it, recheck the joint probabilities and the chosen option for each report.
Choosing the highest payoff when the figures are costs.
Students apply the rule automatically.
Fix: Read whether the payoffs are profits or costs. For costs, the best option is the lowest EV, and the gain is the reduction in expected cost.

Worked examples

Example 1

A firm chooses one of three products. Demand will be strong (probability 0.3), moderate (0.5) or weak (0.2). Profits are: X: $80,000, $50,000, -$20,000. Y: $60,000, $45,000, $10,000. Z: $30,000 in every case. Calculate the most the firm should pay for perfect information about demand.

Show the solution

EV of X = 0.3 × 80,000 + 0.5 × 50,000 + 0.2 × (-20,000) = 24,000 + 25,000 - 4,000 = $45,000.
EV of Y = 0.3 × 60,000 + 0.5 × 45,000 + 0.2 × 10,000 = 18,000 + 22,500 + 2,000 = $42,500.
EV of Z = $30,000. The best option without information is X, at $45,000.
With perfect information: strong demand, choose X for $80,000. Moderate demand, choose X for $50,000. Weak demand, choose Z for $30,000.
EV with perfect information = 0.3 × 80,000 + 0.5 × 50,000 + 0.2 × 30,000 = 24,000 + 25,000 + 6,000 = $55,000.
EVPI = 55,000 - 45,000 = $10,000.

Answer: The firm should pay no more than $10,000 for perfect information.

Example 2

A company can launch a product. If it succeeds (probability 0.4), profit is $100,000. If it fails (probability 0.6), the loss is $60,000. Not launching gives $0. Market research costs $5,000. If the product would succeed, the research reports favourable with probability 0.8. If it would fail, the research reports unfavourable with probability 0.7. Calculate the EVPI and the value of the research, and advise whether to buy it.

Show the solution

EV of launching without research = 0.4 × 100,000 - 0.6 × 60,000 = 40,000 - 36,000 = $4,000. Not launching is $0, so launch. EV without information = $4,000.
EVPI: with perfect information, launch only if it will succeed. EV = 0.4 × 100,000 + 0.6 × 0 = $40,000. EVPI = 40,000 - 4,000 = $36,000.
Joint probabilities: success and favourable = 0.4 × 0.8 = 0.32. Success and unfavourable = 0.4 × 0.2 = 0.08. Failure and favourable = 0.6 × 0.3 = 0.18. Failure and unfavourable = 0.6 × 0.7 = 0.42. These sum to 1.
P(favourable) = 0.32 + 0.18 = 0.50. P(unfavourable) = 0.08 + 0.42 = 0.50.
After a favourable report: P(success) = 0.32 ÷ 0.50 = 0.64 and P(failure) = 0.36. EV of launching = 0.64 × 100,000 - 0.36 × 60,000 = 64,000 - 21,600 = $42,400. Launch.
After an unfavourable report: P(success) = 0.08 ÷ 0.50 = 0.16 and P(failure) = 0.84. EV of launching = 16,000 - 50,400 = -$34,400. Do not launch, so the EV is $0.
EV with research = 0.5 × 42,400 + 0.5 × 0 = $21,200. Check with joint probabilities: 0.32 × 100,000 - 0.18 × 60,000 = 32,000 - 10,800 = $21,200.
Value of the research = 21,200 - 4,000 = $17,200. This is below the EVPI of $36,000. The cost is $5,000, so the net gain is $12,200.

Answer: EVPI is $36,000. The research is worth $17,200 against a cost of $5,000, so buy it. Launch if the report is favourable and do not launch if it is unfavourable.

Exam tips

In objective test questions, the answer is usually one figure. Do the EV without information first, then the EV with perfect information. Check the sign: EVPI cannot be negative.
Check whether payoffs are profits or costs before choosing the best option. For costs, take the lowest EV and the lowest cost in each column.
For imperfect information in the constructed response section, set out the joint probability table. Marks are given for method, so show each probability and each EV.
Always add a conclusion: compare value with cost and say whether to buy. Add one comment that EV is an average and may not suit a one-off decision, and that the probabilities are estimates.
If a question asks only for the maximum price, stop at the EVPI. Do not subtract any cost.

Practice questions from Dealing with risk and uncertainty in decision-making

Value of Perfect and Imperfect Information in other exams

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

Value of Perfect and Imperfect Information: frequently asked questions

How do I calculate the value of perfect information in ACCA PM?

Find the best EV from the payoff table without information. Then take the best payoff in each outcome, weight it by the outcome probability and add up. The difference is the EVPI.

What is the difference between perfect and imperfect information?

Perfect information is always right and tells you which outcome will happen. Imperfect information, like market research, can be wrong. Its value is lower than the EVPI because it only changes the odds.

Is the value of information the same as its cost?

No. The value is the gain in expected value from having the information. The cost is what you pay for it. You buy if the value exceeds the cost.

Can the value of imperfect information be more than the EVPI?

No. Perfect information is the best you can have, so the EVPI is an upper limit. If your answer is higher, check your calculations.