Decision tree

A decision tree is a branching diagram mapping decisions and uncertain outcomes, evaluated by rolling expected values back from the end branches to find the best choice.

ByHoang TruongUpdated July 11, 2026

See it move

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A firm weighs launching a product against doing nothing. Launching has a 60% chance of €200,000 profit and a 40% chance of a €50,000 loss: 0.6 × €200,000 + 0.4 × (−€50,000) = €120,000 − €20,000 = €100,000 expected value. Doing nothing is worth €0, so the decision tree recommends launching.

Where it fits

SubjectCost AccountingCoreTopicRelevant Costs & Decision-MakingCore

The formula

LaTeX

EV = \sum_{i} p_i \times X_i

Variables

$E V$: Expected value (€)
$p_{i}$: Probability of outcome i (probability (0–1))
$X_{i}$: Payoff of outcome i (€)

Combines every chance outcome at a node into the single expected value used to compare branches.

Check yourself

PracticeCORE

A firm is choosing between investing in new equipment and not investing. Investing has a 70% chance of a €150,000 profit and a 30% chance of a €30,000 loss. Not investing has a certain profit of €0. Based on expected value, which option should the firm choose, and what is its expected value?

Select an answer to check your understanding.