Explain decision tree analysis

A decision tree is a diagram that lays out a sequence of decisions and chance events over time, with the cash flows and probabilities attached to each branch. It is used to choose the alternative with the best expected value when the future outcome is uncertain, especially when later decisions depend on earlier results.

Symbols

• Square (□) decision node: the decision maker chooses one branch.
• Circle (○) chance node: nature decides; each branch has a probability and the probabilities leaving a chance node sum to 1.
• End point: the cash flow or equivalent worth (PW, FW or AW) of that complete path.

Procedure

1. List the decisions, the possible outcomes of each uncertain event and their probabilities.
2. Draw the tree from left to right in time order.
3. Compute the PW (or AW/FW) of every end path at the MARR.
4. Work backwards (roll back): at a chance node take the expected value E = Σ p × value; at a decision node take the branch with the best (highest PW or lowest cost) value.
5. The value at the root is the expected value of the best strategy.

Example

A firm can launch a new product (investment Rs 10 lakh) or do nothing. If launched, demand is high with probability 0.6 (PW of net returns = Rs 18 lakh) or low with probability 0.4 (PW = Rs 6 lakh).

                      high (0.6)  PW = 18 − 10 = +8
          ┌─ launch ──○
  Decision□           └ low  (0.4)  PW =  6 − 10 = −4
          └─ do nothing ................ PW =  0

E(launch) = 0.6(8) + 0.4(−4) = +3.2 lakh
E(do nothing) = 0

The expected PW of launching (Rs 3.2 lakh) is greater than 0, so the firm should launch. The tree also shows the risk: there is a 40% chance of losing Rs 4 lakh.

Advantages and limits

• It gives a clear picture of the choices and their probabilities, and can handle multi-stage decisions.
• It depends on probability estimates that are often subjective, and the expected value alone does not show the spread of outcomes (risk attitude).