--- title: "Explain decision tree analysis" subject: "Engineering Economics" chapter: 6 key: "semester_6/engineering_economics:explain-decision-tree" source: https://www.bctengineer.com/q/semester_6/engineering_economics/explain-decision-tree site: BCT Engineering --- # Explain decision tree analysis Engineering Economics · Chapter 6: Risk Analysis - Asked in: 2076 Shrawan, 2 marks; 2070 Magh, 4 marks; 2068 Jestha, 6 marks; 2067 Mangsir, 4 marks; 2066 Magh, 4 marks (asked 5 times) - Video: [Unit:7 | Risk Analysis | Engineering Economics | Decision Tree | Prashant YT | BE Civil | TU,PU,PoU](https://www.youtube.com/watch?v=Mt26LVmHyvo) — Prashant YT - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/explain-decision-tree - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6 ## Question Explain decision tree analysis with a suitable example. ## Short answer A decision tree maps sequential decisions and chance events with probabilities and cash flows, using expected value rollback to choose the best alternative. Example: invest Rs 10 lakh to launch a product; high demand (0.6) yields PW +8 lakh, low demand (0.4) yields PW -4 lakh. Expected PW = +3.2 lakh > 0, so launch. ## Answer 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). ```text 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). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A decision tree analysis is mainly used to: A. Compute depreciation of assets B. Find the IRR of a single cash flow C. Choose the best alternative by expected value when outcomes are uncertain and later decisions depend on earlier results D. Draw the cash flow diagram of a loan Answer: C. It lays out sequential decisions and chance events with probabilities to select the alternative with the best expected value. (Key point: Purpose of decision tree) 2. In a decision tree, what do a square node and a circle node represent? A. Square: chance event; circle: decision B. Square: decision made by decision maker; circle: chance event decided by nature C. Both are decisions D. Square: end point; circle: start point Answer: B. Squares are decision nodes where a branch is chosen; circles are chance nodes with probabilities summing to 1. (Key point: Node types) 3. During roll back, what is done at chance nodes and decision nodes? A. Chance: take the best branch; decision: take the expected value B. Chance: add the probabilities; decision: multiply them C. Both: take the average of branches D. Chance: take expected value (sum of p x value); decision: take the best branch Answer: D. Work backwards from the end, using expected value at chance nodes and the best branch at decision nodes. (Key point: Roll back rule) 4. Launch: high demand 0.6 (net PW +8 lakh), low 0.4 (net PW -4 lakh). What is E(launch) and the decision? A. +3.2 lakh; launch B. +4.0 lakh; do nothing C. +8.0 lakh; launch D. -1.6 lakh; do nothing Answer: A. E = 0.6(8) + 0.4(-4) = 3.2 lakh, which exceeds 0 for doing nothing, so launch. 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