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Strategic Financial Management · Evaluation of Risky Proposals for Investment Decisions

Decision Tree Analysis for Investment Decisions

Updated 11 October 2026 · Fact-checked

Decision tree analysis maps a sequence of investment decisions and uncertain outcomes as a tree. You solve it by rollback: start at the far right, compute expected values at chance nodes, pick the best option at decision nodes, discount back to today, and subtract the initial outlay to get the expected NPV of the best strategy.

Understand Decision Tree Analysis

A project rarely ends with one decision. You invest, see how demand turns out, and then decide whether to expand, continue or abandon. A decision tree draws this sequence so you can value each choice in light of what may happen later.

The tree has two kinds of nodes. A decision node (usually a square) is where you choose between alternatives. A chance node (usually a circle) is where nature decides, and each branch carries a probability. The probabilities on the branches leaving a chance node must add up to 1.

You solve the tree backwards. This is the rollback method (or backward induction). At the last chance nodes you take the probability-weighted average of the payoffs. At the last decision nodes you pick the branch with the highest value and discard the rest. You repeat this moving left until you reach the first decision.

The reason for working backwards is simple. The best choice today depends on what you would do later. A later choice cannot be judged until you know the best value of what follows it.

Because cash flows fall in different years, discount them to the same point in time at the given rate. The result is the expected NPV of each strategy. It lets you see the value of flexibility, such as an option to expand or abandon, which a single-stage expected NPV ignores.

Key rules to remember

Expected value at a chance node
EV = Σ (probability × value of branch)
Probabilities on the branches leaving the node must sum to 1. Use PV of the branch values at the same date.
Value at a decision node
Value = highest of (value of each alternative after its own outlay or proceeds)
Choose the maximum for NPV or profit. Cross out (prune) the rejected branches.
Present value of a later value
PV = Value at time t ÷ (1 + r)^t
Discount the rolled-back value to time 0 before deducting the initial outlay.
Expected NPV of a strategy
Expected NPV = PV of expected inflows (with best later decisions) − initial outlay
Accept if it is positive. Between mutually exclusive strategies, pick the higher expected NPV.
Joint probability of a path
P(path) = product of the branch probabilities along the path
Use it when the question asks for the probability of a particular outcome or for NPV along each path.

How to solve Decision Tree Analysis questions

Use the same routine for any decision tree question. Draw first, then roll back. Do not compute anything until the tree is on paper.

  1. 1Read the question and list the decisions, the uncertain events, their probabilities, the outlays, the cash flows and the discount rate.
  2. 2Draw the tree from left to right in time order. Use a square for each decision and a circle for each chance event. Write the probability on each chance branch and the cash flow or outlay on each branch.
  3. 3Check that the probabilities leaving each chance node add up to 1. Where the probabilities are conditional on an earlier outcome, use the right set for each branch.
  4. 4Start at the far right. At each chance node compute the expected value of the PVs at that date. At each decision node, deduct the outlay on each alternative and choose the highest net value. Strike out the rejected branches.
  5. 5Move one step left and repeat. Add any cash flow received at that date to the node value. Discount rolled-back values to the date of the next node using the given rate.
  6. 6Discount the final expected value to time 0 and deduct the initial outlay to get the expected NPV of the best strategy.
  7. 7Compare with the alternatives, including doing nothing (NPV 0). State the recommended strategy as a sequence: what to do now, and what to do after each outcome.
  8. 8Add a short note on risk if useful, for example the worst-case NPV, since expected value alone hides the downside.

Quickest way: Right-to-left rollback with a node table

When to use it: Use it when the tree has two or more stages and you have limited time. It avoids path-by-path calculation.

  1. Sketch a skeleton tree with only node labels (A, B, C...) and the data on branches.
  2. Write a small table with one row per node: its type, the working, and the rolled-back value.
  3. Fill the rows from the last node to the first. For decision nodes, write the chosen branch next to the value.
  4. Convert the first-stage value to present value once, at the end.
  5. Write the final line as a recommendation: strategy, expected NPV, and the later actions.

Common mistakes in Decision Tree Analysis

  • Working left to right and choosing the best branch at the first decision without looking ahead.

    It feels natural to read the question in time order.

    Fix: Always roll back from the right. A first-stage choice is judged by the best value of everything after it.

  • Forgetting to deduct the outlay on an alternative before comparing it with others at a decision node.

    Students compare gross inflows because the outlay is mentioned in a different line of the question.

    Fix: At each decision node, write net value = expected inflows − outlay for every alternative, then compare.

  • Adding cash flows from different dates without discounting.

    Rolled-back values look like ordinary numbers, so the date is forgotten.

    Fix: Note the date beside each node value. Discount to a common date before adding or comparing.

  • Using the unconditional probability on a branch that depends on an earlier outcome.

    The question gives several probability sets and students use the first one.

    Fix: Label each chance node with the probabilities that apply to it. Check that each set sums to 1.

  • Leaving out the cash flow earned at the node date, such as the year 1 inflow, when adding up a branch's value.

    Students focus on the later PV figures and treat the year 1 cash flow as already counted.

    Fix: At each node, add the cash flow received at that date to the rolled-back value of what follows.

  • Stopping at expected NPV and not giving a recommendation, or not comparing with doing nothing.

    The calculation feels like the end of the answer.

    Fix: Finish with an accept or reject call, the best strategy at each stage, and a brief comment on risk.

Worked examples

Example 1

A Surat textile firm can launch a new fabric line in one of two ways. A large plant costs ₹40 lakh. A small plant costs ₹20 lakh. Demand will be High (probability 0.6) or Low (probability 0.4). For the large plant, the present value of inflows is ₹70 lakh if demand is High and ₹30 lakh if Low. For the small plant, it is ₹38 lakh if High and ₹22 lakh if Low. Doing nothing gives NPV zero. Which option should the firm choose?

Show the solution
  1. Draw one decision node with three branches: large plant, small plant, do nothing. Each plant branch leads to a chance node with High (0.6) and Low (0.4).
  2. Large plant: expected PV of inflows = 0.6 × 70 + 0.4 × 30 = 42 + 12 = ₹54 lakh.
  3. Large plant: expected NPV = 54 − 40 = ₹14 lakh.
  4. Small plant: expected PV of inflows = 0.6 × 38 + 0.4 × 22 = 22.8 + 8.8 = ₹31.6 lakh.
  5. Small plant: expected NPV = 31.6 − 20 = ₹11.6 lakh.
  6. Do nothing: NPV = ₹0. The highest expected NPV is the large plant.
  7. Risk check: if demand is Low, the large plant gives 30 − 40 = −₹10 lakh, while the small plant gives 22 − 20 = +₹2 lakh.

Answer: Choose the large plant, with an expected NPV of ₹14 lakh against ₹11.6 lakh for the small plant. Note that the large plant loses ₹10 lakh if demand is Low, so a risk-averse management might still consider the small plant.

Example 2

A company can invest ₹50 lakh now (time 0) in a plant. At the end of year 1, demand turns out High (probability 0.6) or Low (probability 0.4). The cost of capital is 10%. If demand is High, the year 1 cash flow is ₹20 lakh. The firm can then either continue, with the PV at year 1 of later inflows being ₹60 lakh, or expand by spending ₹30 lakh at year 1. After expansion, the PV at year 1 of later inflows is ₹120 lakh with probability 0.5 or ₹70 lakh with probability 0.5. If demand is Low, the year 1 cash flow is ₹5 lakh. The firm can then either continue, with the PV at year 1 of later inflows being ₹25 lakh, or abandon and sell the plant for ₹35 lakh at year 1. Find the best strategy and the expected NPV.

Show the solution
  1. Roll back the High branch. Continue: net later value = ₹60 lakh. Expand: expected PV of later inflows = 0.5 × 120 + 0.5 × 70 = 60 + 35 = ₹95 lakh. Net of the ₹30 lakh outlay, this is ₹65 lakh.
  2. Expand (65) beats continue (60). Value of the High node at year 1 = 20 + 65 = ₹85 lakh.
  3. Roll back the Low branch. Continue: 5 + 25 = ₹30 lakh. Abandon: 5 + 35 = ₹40 lakh. Abandon is better. Value of the Low node at year 1 = ₹40 lakh.
  4. Expected value at year 1 = 0.6 × 85 + 0.4 × 40 = 51 + 16 = ₹67 lakh.
  5. Discount to time 0: 67 ÷ 1.10 = ₹60.91 lakh (approximately).
  6. Expected NPV = 60.91 − 50 = ₹10.91 lakh. This is positive, so invest.
  7. Value of flexibility: if the firm always continued, the year 1 values would be 20 + 60 = 80 and 5 + 25 = 30, giving 0.6 × 80 + 0.4 × 30 = ₹60 lakh at year 1. Its PV is 54.55 and NPV is 4.55. The options add about 10.91 − 4.55 = ₹6.36 lakh.

Answer: Invest ₹50 lakh now. If demand is High at year 1, expand. If it is Low, abandon and sell the plant for ₹35 lakh. The expected NPV is about ₹10.91 lakh, compared with about ₹4.55 lakh if the firm simply continued in both cases.

Exam tips

  • Draw the tree even if the question does not ask for it. Marks are often given for a correct structure and for showing the rollback at each node.
  • Write the date next to every node value and say which rate you used to discount. Examiners look for correct time treatment.
  • Show rejected branches clearly (strike them out) and name the chosen action at each decision node.
  • End with a recommendation in words, covering the first decision and the follow-up action for each outcome. Where useful, comment on the worst-case result.
  • In MCQs, check whether the question asks for the expected NPV of the best strategy, the expected value at a particular node, or the value of an option. Each needs a different stopping point in the rollback.

Practice questions from Evaluation of Risky Proposals for Investment Decisions

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 where you choose an action, so you pick the branch with the best value. A chance node is where an uncertain event happens, so you take the probability-weighted average of its branches. Mixing these up is the most common structural error.

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

The value of an early decision depends on what you will do later. You only know the best later action once you have valued the last stage. Rolling back gives each node the best value of everything that follows.

Do I always need to discount in a decision tree problem?

Discount whenever cash flows fall on different dates and a rate is given. If all values are already present values at the same date, as in a one-stage problem, no extra discounting is needed. Check the dates before you add anything.

How is a decision tree different from expected NPV with a probability distribution?

Expected NPV with a probability distribution treats the project as a single decision with fixed later actions. A decision tree lets you choose different actions after seeing outcomes, such as expand or abandon. That flexibility often raises the project's value.