Decision Tree Analysis in 7 Minutes
Decision tree analysis maps out choices and uncertain outcomes as branches, so you can compare options when the future is not certain. Each outcome gets a probability and a payoff. You multiply, add up the expected value at each chance point, and pick the decision with the best expected result.
Decision tree analysis explained simply
A decision tree lays out choices and uncertain outcomes as branches. Multiply each outcome by its probability, add them up at each chance node, and pick the option with the best expected value. In the example, launching has an expected NPV of $70,000 versus $0 for not launching, so launch.
What this decision tree lesson covers
- What decision and chance nodes are
- How to label probabilities and payoffs on each branch
- How to calculate expected value at a chance node
- How to roll back the tree to find the best decision
- Where decision trees fit in capital budgeting
Decision tree formulas, explained
- pᵢ
- probability of outcome i (probabilities add up to 1)
- Payoffᵢ
- value of outcome i
- EV of outcomes
- probability-weighted present value of payoffs
How to solve a decision tree step by step (worked example)
Launching a product costs $100,000. There is a 60% chance it succeeds and is worth $250,000 (present value) and a 40% chance it flops and is worth $50,000. The alternative is not launching ($0). What should you do?
- Draw a decision node: Launch or Don't launch
- Under Launch, draw a chance node: Success 60%, Failure 40%
- Expected value: 0.6 × 250,000 + 0.4 × 50,000 = 170,000
- Expected NPV of launching: 170,000 − 100,000 = 70,000
- Compare with Don't launch: 70,000 > 0
Answer: Launch. The expected NPV is $70,000, which beats doing nothing.
The two branches of the launch
| Success | Flop | |
|---|---|---|
| Probability | 60% | 40% |
| Value (present value) | $250,000 | $50,000 |
| NPV after the $100,000 cost | +$150,000 | −$50,000 |
| Weighted | +$90,000 | −$20,000 |
Is a positive expected value always a safe bet? David's take
Expected NPV is +$70,000, so the rule says launch. But look at the branches: a 60% chance of +$150,000 and a 40% chance of −$50,000. If losing $50,000 would sink the company, the average doesn't help you. The road to success has infinite tiny mistakes, some big mistakes and zero vital mistakes. So before you trust the expected value, check whether any branch is a vital mistake.
From David's concept: Choose Your Mistakes. This is David's opinion, alongside the standard textbook answer above.
Harder decision tree questions
How low can the success probability go before launching stops making sense?
Expected NPV = p × 150,000 − (1 − p) × 50,000 = 0 gives p = 25%. Above a 25% chance of success, launching has a positive expected value.
What would perfect information be worth?
If you knew the outcome in advance, you'd launch only on success: 0.6 × 150,000 = $90,000. That's $20,000 more than $70,000, so a perfect forecast is worth up to $20,000.
Common decision tree questions
How do you calculate expected value in a decision tree?
At each chance node, multiply every outcome's payoff by its probability and add the results. Then subtract any costs on the path. At a decision node, you simply choose the branch with the highest expected value.
What is the difference between a decision node and a chance node?
A decision node, usually drawn as a square, is where you choose what to do. A chance node, usually a circle, is where the outcome is uncertain and each branch has a probability. Trees alternate between the two.
How are decision trees used in capital budgeting?
They help value projects with uncertain outcomes or future choices, such as testing a market before a full launch or abandoning a project if it goes badly. You compute expected NPV along each path and choose the strategy with the highest value.
What does rolling back a decision tree mean?
Rolling back means solving the tree from right to left. You start at the final outcomes, calculate expected values at chance nodes, pick the best option at decision nodes, and work back to the first decision.