Decision theory: deciding before the uncertainty resolves
Four interactive investment decisions: invest now or wait (real options and the hurdle above NPV), build vs buy under fat-tailed cost overruns, pilot-first with the expected value of information, and the sunk-cost kill decision.
Every model on this site produces a distribution; decision theory is the step that turns a distribution into an action: commit, wait, pay to learn, or walk away. It often disagrees with the answer you get from comparing averages, because flexibility and information both have value that a single expected number ignores.
The four scenarios are corporate-finance staples. Invest-or-wait shows why a positive NPV is not yet a green light: at the defaults a project worth $100M that costs $80M (NPV $20M) is worth about $25.9M if you wait a year and invest only if the news is good, so the rational trigger sits at about $116M, 46% above break-even, and climbs with uncertainty. Build-vs-buy compares a fat-tailed build cost (median $10M) with a certain $18M price: building wins on the average ($11.3M) but loses at the 90th percentile ($19.0M). Pilot-first prices information with Bayes' rule: a test is worth running only if its result could change the decision, and at the defaults the pilot's value of information ($6.1M) comfortably exceeds its $2M cost.
Kill-or-continue closes the set with the sunk-cost principle: only the remaining cost and the expected payoff matter, and the money already spent appears nowhere in the rational rule. At the defaults, spending $8M more for a 20% chance of $30M is a kill (expected value −$2M), and moving the sunk-cost slider leaves that verdict unchanged. Each scenario has an interactive chart, a live verdict and the governing formula.
Investment trigger with the option to delay
V* = I · (½ + r) / (½ + r − ½σ)
Two-state model: in a year the project's value V moves up or down by a fraction σ with equal probability (±35% by default); I is the investment cost and r the discount rate. The formula applies when the down state is not worth investing in, V(1 − σ) < I, and the trigger V* exceeds break-even I whenever σ > 0.
Frequently asked questions
Why wait on a project whose NPV is already positive?
Because investing now gives up the option to avoid the bad outcome. Waiting lets you commit only in the good state, and that flexibility is worth more than the head start whenever uncertainty is high relative to the project's margin, so the rational hurdle sits strictly above NPV = 0.
What is the expected value of sample information (EVSI)?
The increase in expected payoff from making the decision after seeing a test result rather than before: the expected value over possible results of max(EV at the updated probability, 0), minus max(EV at the prior, 0). A pilot, survey or due-diligence exercise is worth buying only when its EVSI exceeds its cost.
Why should sunk costs be ignored?
Money already spent is the same under every action still available, so it cancels out of every comparison; only costs and payoffs still ahead can differ between continuing and stopping. Honouring sunk costs leads to escalation of commitment: funding projects past their kill point because of what they have already consumed.
Interactive explorer
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