Why Put a Value on Perfect Information?
A development team may have to decide whether to fund the next stage before knowing whether the program’s true prospects are favorable. Under current evidence, the team chooses the action with the highest expected payoff. If it could instead learn the relevant state with certainty before deciding, it could choose differently in different states. The expected improvement from having that complete information is the expected value of perfect information, or EVPI.
EVPI is not a forecast of program value, nor is it the expected payoff from continuing development. It is the amount by which the decision’s expected payoff would improve if the specified uncertainty were completely resolved before the decision, assuming the information does not change payoffs or incur a cost. This makes EVPI useful for judging the importance of uncertainty and for setting an upper bound on what it could be worth to resolve it.
Definition and Assumptions
Represent the relevant uncertain condition by a finite set of mutually exclusive and collectively exhaustive states \(s_1,\ldots,s_J\). Let \(q_j\) be the probability of state \(s_j\) given the information currently available, so \(q_j\geq 0\) and \(\sum_{j=1}^{J}q_j=1\). Let \(a\) be a feasible decision from a set of actions \(\mathcal{A}\), and let \(V(a,s_j)\) be its payoff if state \(s_j\) occurs. Payoffs should be on a common scale, such as incremental net present value in millions of dollars.
The first term allows the chosen action to vary by state: after learning \(s_j\), the decision-maker selects the action with the largest payoff in that state. The second term requires one action to be selected using current information, before the state is known. The probabilities and payoffs must reflect the same decision point and the same evidence. In particular, probabilities should describe uncertainty that remains after using the current evidence, not ignore it.
The calculation assumes that the state definition captures all uncertainty relevant to the decision, that the listed states cover the possibilities, and that each payoff is correctly specified for each action-state combination. It also assumes perfect information arrives before the action, can be used without changing the action set or the payoffs, and is free. Thus, the result is a gross value: the value of information before subtracting any cost or accounting for delay.
Worked Example: A Go/No-Go Decision Under Two States
A hypothetical development team is deciding whether to fund a program. Under its current evidence, the state is favorable with probability 0.30 and unfavorable with probability 0.70. If the team goes, the incremental payoff is $120 million in the favorable state and \(-$40\) million in the unfavorable state. A no-go decision has payoff $0 in either state. Assume these are comparable payoffs at the same decision date, and that perfect information would reveal which state applies before the team decides.
Best action with current information. The expected payoff from going is $$ 0.30(\$120\text{ million})+0.70(-\$40\text{ million}) =\$36\text{ million}-\$28\text{ million} =\$8\text{ million}. $$ No-go has expected payoff $0, so the current decision is go, with an expected payoff of $8 million.
Expected payoff with perfect information. In the favorable state, the team would go and receive $120 million. In the unfavorable state, it would choose no-go and receive $0 rather than \(-$40\) million: $$ 0.30(\$120\text{ million})+0.70(\$0) =\$36\text{ million}. $$
Therefore, $$ \mathrm{EVPI}=\$36\text{ million}-\$8\text{ million}=\$28\text{ million}. $$ Under these assumptions, perfect knowledge before the go/no-go decision would improve expected payoff by $28 million. This is not a claim that the program will generate $28 million, or that information costing $28 million is automatically worthwhile.
Why EVPI Cannot Be Negative
Perfect information gives the decision-maker the option to choose the best action separately in each state. The decision-maker can always ignore the information and use the action that was best under current uncertainty. Consequently, perfect information cannot reduce the maximum expected payoff when it is free and does not alter the decision setting.
For a direct justification, fix any action \(a\). In every state \(s_j\), its payoff cannot exceed the largest available payoff in that state:
Multiply each inequality by \(q_j\geq 0\) and sum across states. Then take the maximum over actions \(a\) on the left. The result is
The right side is the expected payoff with perfect information, and the left side is the best expected payoff using current information. Their difference, EVPI, is therefore nonnegative. It is zero when knowing the state would not change the optimal action in any state with positive probability, or would not improve the payoff relative to the current best action.
Worked Example: Checking a Go/No-Go Threshold
Suppose going has payoff \(R=\$200\) million if development succeeds and \(-C=-\$60\) million if it fails; no-go yields $0. The current probability of success is \(p=0.20\). Assume these are the only two states and the stated probabilities and payoffs apply at the decision point.
The expected payoff from going is $$ pR-(1-p)C =0.20(\$200\text{ million})-0.80(\$60\text{ million}) =\$40\text{ million}-\$48\text{ million} =-\$8\text{ million}. $$ Since no-go yields $0, the best current decision is no-go.
With perfect information, the team would go in the success state and stop in the failure state. Its expected payoff would be $$ 0.20(\$200\text{ million})+0.80(\$0)=\$40\text{ million}. $$ Thus, $$ \mathrm{EVPI}=\$40\text{ million}-\$0=\$40\text{ million}. $$
The corresponding break-even success probability for going under current information solves \(pR-(1-p)C=0\). Rearranging gives \(p(R+C)=C\), so $$ p=\frac{C}{R+C} =\frac{\$60\text{ million}}{\$200\text{ million}+\$60\text{ million}} =0.2308. $$ The current probability, 0.20, is below this threshold, consistent with no-go. The threshold identifies the current-information decision; EVPI separately compares its expected payoff with the state-informed decision.
More Than One Development Option
The same calculation applies when the choice is not limited to a single program versus no-go. For each state, identify the best available action after perfect information; for the current decision, calculate each action’s probability-weighted payoff and select the action with the greatest result. The action that is best under current uncertainty need not be best in every state.
Worked Example: Choosing Between Development Strategies
A hypothetical sponsor is considering two development strategies, A and B, or stopping. Current evidence assigns probabilities 0.40, 0.35, and 0.25 to high, moderate, and low prospects, respectively. The payoff table gives incremental net present values in millions of dollars. Assume the three states are exhaustive, probabilities sum to 1, and all payoffs include the relevant future costs consistently.
| Action | High prospects | Moderate prospects | Low prospects |
|---|---|---|---|
| Strategy A | $100 million | $20 million | -$60 million |
| Strategy B | $55 million | $40 million | -$10 million |
| Stop | $0 | $0 | $0 |
The expected payoff for A is $$ 0.40(\$100\text{ million})+0.35(\$20\text{ million})+0.25(-\$60\text{ million}) =\$40\text{ million}+\$7\text{ million}-\$15\text{ million} =\$32\text{ million}. $$ For B it is $$ 0.40(\$55\text{ million})+0.35(\$40\text{ million})+0.25(-\$10\text{ million}) =\$22\text{ million}+\$14\text{ million}-\$2.5\text{ million} =\$33.5\text{ million}. $$ Stopping yields $0, so B is the best current action, with expected payoff $33.5 million.
With perfect information, choose A in the high-prospects state, B in the moderate-prospects state, and stop in the low-prospects state. The expected payoff is $$ 0.40(\$100\text{ million})+0.35(\$40\text{ million})+0.25(\$0) =\$40\text{ million}+\$14\text{ million} =\$54\text{ million}. $$ Therefore, EVPI is \(\$54\text{ million}-\$33.5\text{ million}=\$20.5\) million. The calculation reflects the benefit of being able to tailor the choice to the state, not a guarantee that a real information-gathering activity can reveal that state perfectly.
Interpretation, Diagnostics, and Alternatives
EVPI is expressed in the same units as the payoff, such as millions of dollars of expected incremental net present value at the specified decision point. It is the maximum expected improvement from resolving the defined uncertainty completely before acting. If an information activity costs more than EVPI, it cannot be justified on the basis of this decision and these payoffs alone. A cost below EVPI does not, by itself, show that the activity is worthwhile: the activity may provide less than perfect information, have costs or delays, or fail to affect the decision.
Before interpreting a result, check the decision model. Confirm that state probabilities are nonnegative and sum to 1; that states are mutually exclusive and cover the relevant possibilities; and that every action has a payoff in every state. Verify that payoffs use a consistent perspective, time basis, and currency. Costs already incurred should not be counted again as future consequences if they cannot be changed by the decision. Conversely, future costs that depend on the action should be represented in the relevant payoff.
A useful numerical diagnostic is the nonnegativity result: a negative EVPI signals an error in the calculation or inconsistent assumptions. Also verify that the state-informed payoff was maximized separately within each state, while the current-information payoff uses one action across states. Maximizing in the wrong order removes the distinction that EVPI measures. If the same action is optimal in every possible state, EVPI should be zero.
The current-information alternative is to choose the action with the largest expected payoff under the existing probabilities. Decision thresholds can help explain when that action changes as probabilities or payoffs vary. EVPI answers a different question: how much the expected payoff could improve if the relevant state were known with certainty. In practice, an information source may only update beliefs or provide a noisy signal; its value therefore need not equal EVPI. Perfect information is a benchmark, not a description of an ordinary development study.
The estimate is only as relevant as its state definitions and payoff model. If important uncertainty is omitted, probabilities are poorly grounded, or the payoffs fail to include consequential costs, the computed EVPI may give a misleading benchmark. It also concerns one decision model and one decision point: it does not automatically value information for other programs, later decisions, or broader portfolio choices. When information arrives after the decision, or changes timing and payoffs, the assumptions here do not apply without modifying the model.
Check Your Understanding
Answer each question using the definitions and decision rules above. Solutions follow the questions.
- A program has a 0.25 probability of a favorable state and 0.75 probability of an unfavorable state. Go yields $100 million if favorable and \(-$30 million if unfavorable; no-go yields $0 in either state. Calculate the best current expected payoff and EVPI.
- Going yields $150 million on success and \(-$50 million on failure; no-go yields $0. What success probability makes go and no-go have equal expected payoff under current information?
- Why is it incorrect to calculate the payoff with perfect information by selecting whichever action has the highest expected payoff before considering the state?
- A proposed payoff model assigns probabilities 0.60 and 0.50 to its only two states. What should be checked before calculating EVPI?
- If a model gives an EVPI of $18 million, what does that say about an information activity costing $20 million, assuming the same decision setting and no other benefits?
Solutions. (1) Going has expected payoff \(0.25(\$100\text{ million})+0.75(-\$30\text{ million})=\$25\text{ million}-\$22.5\text{ million}=\$2.5\text{ million}\), so go is preferred to no-go. With perfect information, go only in the favorable state, giving \(0.25(\$100\text{ million})+0.75(\$0)=\$25\text{ million}\). EVPI is \(\$25\text{ million}-\$2.5\text{ million}=\$22.5\) million. (2) Set \(p(\$150\text{ million})-(1-p)(\$50\text{ million})=0\). Then \(200p=50\), so the break-even probability is \(p=0.25\). (3) That calculation would allow only one action regardless of the state. Perfect information permits a separate best action in each state, which is the source of its potential value. (4) The probabilities sum to 1.10, not 1. The state definitions or probability assignments must be corrected so the states are mutually exclusive and collectively exhaustive with valid probabilities before EVPI is computed. (5) Under the model’s assumptions, $18 million is the gross maximum expected improvement from perfect information at that decision. A $20 million information cost exceeds that ceiling, so the activity is not justified by this decision’s value alone.