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Management Accounting · Decision Theory

Decision Tree Analysis: Nodes and Rollback Method

Updated 10 October 2026 · Fact-checked

A decision tree maps a sequence of decisions and uncertain outcomes as branches. Decision nodes are choices; chance nodes carry probabilities. Solve it by folding back from the right: compute the expected monetary value at each chance node, choose the best option at each decision node, and deduct costs along the path.

Understand Decision Tree Analysis

A decision tree is a diagram of a problem in which you must choose among actions, and each action leads to outcomes you cannot control. It is drawn left to right, in the order events happen. It helps most when one decision leads to another, such as testing a product before deciding to launch it.

There are two kinds of node. A decision node (usually a square) is where you choose. A chance node (usually a circle) is where nature decides, and each branch from it carries a probability. The probabilities on the branches of one chance node must add up to 1.

You solve a tree by rollback (folding back). Start at the far right, at the final payoffs. At each chance node, work out the expected monetary value (EMV): multiply each payoff by its probability and add. At each decision node, pick the branch with the best value (highest profit, or lowest cost) and cross out the other branches. Keep moving left until you reach the first decision.

The logic is simple. A later decision depends on what has already happened, so you must know the best later choice before you can value an earlier one. That is why you work backwards, not forwards.

The result is a strategy, not just a number: for example, test the market, launch if the result is favourable, drop the product if it is not. Always state the full strategy and its expected value.

Key rules to remember

EMV at a chance node
EMV = Σ (probability × payoff of each branch)
Probabilities of all branches from one chance node must total 1.
Value at a decision node
Value = highest EMV among the branches (for profit); lowest for cost
Reject the other branches; do not average them.
Net EMV of a path with a cost
Net EMV = EMV of outcomes − cost incurred on that path
Deduct costs such as test or investment cost on the branch where they arise. Do not deduct them twice.
Payoff of an outcome
Payoff = total inflow or profit on the path − all costs on the path
Use one consistent basis: either all payoffs net of costs, or gross payoffs with costs deducted at the end.

How to solve Decision Tree Analysis questions

Use this method for any decision tree question, whether it has one decision or several.

  1. 1List the decisions, the uncertain events, their probabilities and every cost and payoff given in the question.
  2. 2Draw the tree from left to right in time order. Use a square for each decision and a circle for each uncertain event. Label every branch.
  3. 3Write probabilities on chance branches and check that each set adds to 1. Write costs on the branches where they are incurred.
  4. 4Compute the payoff at the end of every path. Add up all costs and inflows along that path.
  5. 5Fold back from the right. At each chance node, calculate EMV. At each decision node, choose the best branch and strike out the rest.
  6. 6Continue left until you reach the first decision node. Deduct any cost on the path, such as a test cost, if not already included.
  7. 7State the recommended strategy in words and give its expected value. Compare it with the alternatives you rejected.

Quickest way: Right-to-left EMV with strike-outs

When to use it: Use when the tree is already given or is small enough to sketch in under two minutes, which is typical for a 14-mark question.

  1. Sketch a rough tree. Do not spend time on neat shapes; clear labels matter more.
  2. Write the net payoff at each tip first.
  3. Calculate every chance node EMV directly beside its circle.
  4. At each square, write the higher value and put a double stroke on the rejected branch.
  5. Compare the first-stage options in one line and write the strategy as a sentence.

Common mistakes in Decision Tree Analysis

  • Working left to right instead of folding back from the right.

    The tree is read in time order, so students value it in time order.

    Fix: Always start at the final payoffs. Later decisions must be solved before earlier ones.

  • Averaging the branches at a decision node.

    Students apply the EMV habit from chance nodes everywhere.

    Fix: Use probabilities only at chance nodes. At a decision node, choose the best branch and ignore the others.

  • Forgetting to deduct a cost, or deducting it twice.

    Costs sit on branches, and some payoffs are already stated net of cost.

    Fix: Decide first whether each payoff is gross or net. Deduct each cost once, on the path where it is incurred.

  • Using probabilities that do not add to 1, or using the wrong set after a test result.

    Questions give several probability sets, and students mix them up.

    Fix: Check every chance node totals 1. After a test result, use the probabilities given for that result.

  • Giving only a number and no recommended strategy.

    Students stop once the EMV is computed.

    Fix: Write the full strategy, such as which option to choose and what to do after each outcome, with its EMV.

Worked examples

Example 1

Sundaram Foods Ltd can launch a new snack by investing ₹10,00,000. If demand is high (probability 0.6), the inflow is ₹25,00,000. If demand is low (probability 0.4), the inflow is ₹8,00,000. If it does not launch, there is no gain or loss. Use a decision tree to advise the company.

Show the solution
  1. Draw a decision node with two branches: Launch and Do not launch. On Launch, draw a chance node with High (0.6) and Low (0.4).
  2. Net payoff, High = ₹25,00,000 − ₹10,00,000 = ₹15,00,000.
  3. Net payoff, Low = ₹8,00,000 − ₹10,00,000 = −₹2,00,000.
  4. EMV at the chance node = (0.6 × 15,00,000) + (0.4 × −2,00,000) = 9,00,000 − 80,000 = ₹8,20,000.
  5. Do not launch has a value of ₹0.
  6. At the decision node, compare ₹8,20,000 with ₹0. Launch is higher, so reject Do not launch.

Answer: Launch the snack. The expected monetary value is ₹8,20,000, against ₹0 for not launching.

Example 2

Kaveri Textiles can launch a new fabric directly, or first run a test market costing ₹2,00,000. Direct launch: high sales (probability 0.5) gives a net profit of ₹30,00,000; low sales (probability 0.5) gives a loss of ₹12,00,000. Test market: the result is favourable with probability 0.6 and unfavourable with probability 0.4. After a favourable result, high sales has probability 0.7 and low sales 0.3. After an unfavourable result, high sales has probability 0.2 and low sales 0.8. After the test, the company may launch or drop the fabric (drop gives ₹0). The profit and loss figures are before the test cost. Advise the company.

Show the solution
  1. Direct launch EMV = (0.5 × 30,00,000) + (0.5 × −12,00,000) = 15,00,000 − 6,00,000 = ₹9,00,000. Not launching directly gives ₹0, so the direct-launch value is ₹9,00,000.
  2. After a favourable result, launch EMV = (0.7 × 30,00,000) + (0.3 × −12,00,000) = 21,00,000 − 3,60,000 = ₹17,40,000. Dropping gives ₹0. Choose Launch: ₹17,40,000.
  3. After an unfavourable result, launch EMV = (0.2 × 30,00,000) + (0.8 × −12,00,000) = 6,00,000 − 9,60,000 = −₹3,60,000. Dropping gives ₹0. Choose Drop: ₹0.
  4. EMV at the test-result chance node = (0.6 × 17,40,000) + (0.4 × 0) = ₹10,44,000.
  5. Deduct the test cost: 10,44,000 − 2,00,000 = ₹8,44,000.
  6. Compare at the first decision node: direct launch ₹9,00,000 against test market ₹8,44,000. Direct launch is higher by ₹56,000.

Answer: Launch the fabric directly without the test. Expected value is ₹9,00,000, against ₹8,44,000 for testing first. The test costs more than the value of the information it gives.

Exam tips

  • Draw the tree even if the question does not ask for it. The diagram earns step marks and keeps your rollback organised.
  • Write each EMV calculation in full beside its node, so a small slip still earns method marks.
  • Read carefully whether payoffs are stated before or after costs, and say which basis you use.
  • Close with a one-line recommendation naming the strategy and its expected value. For MCQs, solve only the last decision first, since it often settles the answer.

Practice questions from Decision Theory

Decision Tree Analysis in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Decision Tree Analysis: frequently asked questions

What is the difference between a decision node and a chance node?

A decision node is a point where you choose between actions, drawn as a square. A chance node is a point where an uncertain outcome occurs, drawn as a circle, with probabilities on its branches. You pick the best branch at a decision node and take a weighted average at a chance node.

Why do we solve a decision tree from right to left?

Later decisions depend on earlier events, so you must know the best later choice and its value first. Only then can you value the earlier choice correctly. Rollback does exactly this.

Where do I deduct the cost of a test or survey?

Deduct it on the branch where you incur it, once only. In a usual layout, you deduct it from the EMV of the test branch before comparing it with the no-test option.

Is the highest EMV always the right choice?

For exam questions, yes, unless the question asks for another criterion. EMV ignores how much risk the decision maker can bear, which is why utility theory is studied separately.