Build decision trees with probability-weighted outcomes, expected monetary value, and sensitivity analysis for business decisions.
Enter each decision alternative, its chance branches, branch probabilities, and monetary outcomes. The calculator multiplies each terminal outcome by its path probability, rolls those weighted values up the tree, and compares alternatives by expected monetary value. Its sensitivity analysis tests how changes to an assumption can change that ranking. The common surprise is that EMV is not the payoff most likely to occur in a single decision; it is a probability-weighted average based on the entered scenarios.
A concrete input and expected output from the current implementation.
Input
Decision: Launch Success | probability 0.60 | outcome $50,000 Failure | probability 0.40 | outcome -$20,000 Decision: Hold Certain | probability 1.00 | outcome $5,000
Expected output
Launch EMV: $22,000 Hold EMV: $5,000
Launch has an EMV of (0.60 x $50,000) + (0.40 x -$20,000) = $22,000. Hold has an EMV of 1.00 x $5,000 = $5,000, so Launch leads by $17,000 under these assumptions.
For each terminal branch, multiply its monetary outcome by the probability of reaching it. In a nested tree, the path probability is the product of the chance probabilities encountered along that path. Add terminal contributions beneath a chance node, then compare the resulting EMVs at the decision node. Costs already included in terminal outcomes should not be added again.
Sensitivity analysis changes an uncertain probability or payoff and recalculates the competing alternatives. The useful result is the break-even value where their EMVs are equal; on either side, the preferred alternative can switch. This analysis does not establish whether the tested range is credible. It only shows how strongly the ranking depends on assumptions supplied by the user.
Yes, for mutually exclusive and collectively exhaustive outcomes leaving the same chance node. Probabilities from different nodes do not need to total 100% together. In a nested tree, the probability of a terminal outcome is the product along its path. If outcomes overlap, reorganize the branches before interpreting the EMV.
No. It identifies the largest probability-weighted monetary result under the values entered. A one-time decision with severe downside, binding cash constraints, nonfinancial objectives, or poorly supported probabilities may justify another choice. Treat the ranking as one decision criterion, and inspect downside cases and sensitivity before using it as a recommendation.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
Calculate gross, operating, and net profit margins from cost and revenue with breakeven analysis.
Convert between annual salary and hourly rate with adjustments for work hours, overtime, and benefits.
Calculate sales tax amounts, tax-inclusive and tax-exclusive prices for any tax rate or jurisdiction.
Calculate return on investment from initial cost and final value with annualized ROI and comparison tables.
Convert between markup and margin percentages, calculate selling price, and compare pricing strategies.
Convert numeric amounts to written words for invoices, checks, and legal documents in multiple currencies.