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Performance Management · Dealing with risk and uncertainty in decision-making

Decision Trees and Simulation for ACCA PM

Updated 11 October 2026 · Fact-checked

A decision tree maps a sequence of choices and uncertain outcomes. You draw decision nodes (squares) and chance nodes (circles), then roll back from the right. At chance nodes you take expected values; at decision nodes you pick the best option. Simulation uses random numbers to model many possible outcomes of a risky situation.

Understand Decision Trees and Simulation

A decision tree is a diagram of a decision that happens in stages. Some points are choices you control. Others are events you do not control, each with a probability. The tree shows every path and its result.

There are two kinds of node. A decision node is drawn as a square. You choose one branch. A chance node is drawn as a circle. Nature chooses, and each branch carries a probability. The probabilities leaving a chance node must add up to 1.

You solve the tree by rolling back. Start at the far right with the final outcomes. At each chance node, calculate the expected value (EV) of the branches. At each decision node, choose the branch with the best value. Keep moving left until you reach the first decision. Then state the best strategy and its EV.

A tree beats a simple pay-off table when decisions come in sequence. A pay-off table shows one decision against one set of outcomes. A tree handles a later choice that depends on an earlier result, such as testing a market before launching.

Simulation is used when there are too many variables, or too many possible values, for a tree. You build a model, give each uncertain variable a probability distribution, and use random numbers to pick values. You repeat this many times. The results show the range of outcomes and how likely each is. When the model runs on a computer with many repetitions, it is often called Monte Carlo simulation.

Key rules to remember

Expected value
EV = Σ (probability × outcome)
Used at every chance node. Probabilities leaving a node must total 1.
Rollback at a decision node
Value of decision node = best of the values of its branches
Best means highest for profit or NPV, lowest for cost. Use the value after deducting any cost on that branch.
Net value of a branch
Net EV = EV of later outcomes − cost incurred on the branch
Deduct costs like a survey fee or investment at the point they are paid.
Random number allocation
Allocate random numbers in proportion to probability, e.g. P = 0.30 → numbers 00–29 from a 00–99 set
Each outcome gets a range of numbers matching its probability. Ranges must not overlap or leave gaps.

How to solve Decision Trees and Simulation questions

Use the same method for any decision tree question. Work neatly and label every node.

  1. 1Read the scenario and list the decisions, the uncertain events and the time order of both.
  2. 2Draw the tree from left to right. Use a square for each decision and a circle for each chance event. Write probabilities on chance branches and costs on the branches where they occur.
  3. 3Write the final outcome (profit, cash flow or NPV) at the end of each path.
  4. 4Check that the probabilities at each chance node total 1.
  5. 5Roll back from the right. Calculate the EV at each chance node and write it beside the circle.
  6. 6At each decision node, compare the branch values after deducting costs. Choose the best and cross out the rejected branches.
  7. 7State the best strategy in words, giving the EV. Add a comment on risk, because EV is an average and may never actually happen.

Quickest way: Right-to-left rollback on one sketch

When to use it: Use this in the three-hour exam when a tree has two or three stages and you have limited time.

  1. Sketch the tree in a few lines. Do not redraw it neatly twice.
  2. Put the end values on the right. Calculate the nearest chance node first.
  3. Write each EV in the circle straight away.
  4. At each square, subtract branch costs, compare, and note the winner.
  5. Finish with one sentence: the strategy, the EV, and one risk comment.

Common mistakes in Decision Trees and Simulation

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

    The tree is read from left to right, so it feels natural to calculate in that order.

    Fix: Always start at the far-right outcomes. Later decisions must be solved before earlier ones.

  • Forgetting to deduct the cost of a branch, such as a survey or test fee.

    Costs sit on the branch and are easily missed when focusing on outcomes.

    Fix: Mark every cost on its branch when drawing. Deduct it when you compare options at the decision node.

  • Using probabilities that do not add to 1 at a chance node.

    Students copy figures from the question without checking, or miss a branch.

    Fix: Add the probabilities at each circle before calculating. Find the missing branch if the total is wrong.

  • Taking an EV at a decision node.

    Students treat all nodes the same way.

    Fix: Remember: circle means weighted average, square means choose the best.

  • Presenting EV as the result that will happen.

    The calculation gives a single figure, which looks certain.

    Fix: Say the EV is a long-run average for a one-off decision. Point out the range of outcomes and the decision maker's attitude to risk.

  • Overlapping or incomplete random number ranges in simulation.

    Students allocate numbers from probabilities without checking the total range.

    Fix: Use cumulative probabilities. Check that the ranges cover every number once, such as 00–99.

Worked examples

Example 1

A company can launch a product now or pay ₹2,00,000 for market research first. Launching now gives a profit of ₹10,00,000 if demand is high (probability 0.4) or a loss of ₹3,00,000 if demand is low (probability 0.6). The research predicts high demand with probability 0.4 and low demand with probability 0.6, and it is perfectly reliable. If research shows low demand, the company will not launch and makes no profit or loss (apart from the research cost). Advise the company.

Show the solution
  1. Launch now, no research: EV = (0.4 × ₹10,00,000) + (0.6 × −₹3,00,000) = ₹4,00,000 − ₹1,80,000 = ₹2,20,000.
  2. Research first: if the research says high demand (probability 0.4), launch and earn ₹10,00,000. If it says low demand (probability 0.6), do not launch and earn ₹0.
  3. EV before the research cost = (0.4 × ₹10,00,000) + (0.6 × 0) = ₹4,00,000.
  4. Deduct the research cost: ₹4,00,000 − ₹2,00,000 = ₹2,00,000.
  5. Compare: launch now ₹2,20,000 against research first ₹2,00,000.

Answer: Launch now without research. Its EV of ₹2,20,000 is ₹20,000 higher than the EV of ₹2,00,000 with research. The research costs ₹2,00,000, which is more than the value of the perfect information, ₹1,80,000.

Example 2

A simulation models daily demand for a product. Demand is 100 units with probability 0.2, 200 units with probability 0.5 and 300 units with probability 0.3. Allocate two-digit random numbers (00–99). Then use the random numbers 47, 82 and 15 to find the three simulated days' demand and the average.

Show the solution
  1. Allocate numbers in proportion to probability: 100 units has 20% of the numbers, so 00–19.
  2. 200 units has 50%, so 20–69.
  3. 300 units has 30%, so 70–99. Check: 20 + 50 + 30 = 100 numbers, with no overlap.
  4. Random number 47 falls in 20–69, so demand is 200.
  5. Random number 82 falls in 70–99, so demand is 300.
  6. Random number 15 falls in 00–19, so demand is 100.
  7. Average = (200 + 300 + 100) ÷ 3 = 200 units.

Answer: Simulated demands are 200, 300 and 100 units. The average is 200 units. Three trials are too few to be reliable, so a real simulation would run many more.

Exam tips

  • In a tree question, mark every cost on its branch as you draw. Missing a cost is the most common way to lose marks.
  • Show the EV beside each chance node and cross out rejected branches. This earns method marks even if one figure is wrong.
  • In Section C, finish with a clear recommendation and a comment that EV ignores risk and is a long-run average.
  • For simulation discussion, give both sides. Advantages: it handles many variables and shows the range of outcomes. Disadvantages: it is costly, needs good probability estimates and does not itself give the answer.
  • In objective test questions, check whether the question asks for the best strategy or its value. These are different answers.

Practice questions from Dealing with risk and uncertainty in decision-making

Decision Trees and Simulation in other exams

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

Decision Trees and Simulation: frequently asked questions

How do I draw a decision tree in ACCA PM?

Draw from left to right. Use squares for decisions and circles for chance events. Put probabilities on the chance branches and costs on the branches where they are paid. Write the final outcomes at the right-hand end of each path.

What is the difference between a decision tree and a pay-off table?

A pay-off table handles one decision against a set of possible outcomes. A decision tree handles a sequence of decisions and events, where later choices depend on earlier results. Both can use expected values.

What are the advantages of Monte Carlo simulation?

It can model many uncertain variables together and shows the whole range of possible outcomes with their likelihood. It is useful when a tree would be too large. Its limits are cost, reliance on estimated distributions and the need for expertise.

Why does the tree use expected values if the decision happens only once?

EV gives a consistent way to compare options using probabilities. For a one-off decision the actual result will differ from the EV. So you should also comment on the range of outcomes and the risk attitude of the decision maker.