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Decision tree for plant improvement alternatives
Short answer
Decision tree with three alternatives (A, B, C) and success probabilities evaluated using future worth at 15% for 6 years. Expected FW: A = Rs 860,607, B = Rs 669,292, C = Rs 234,646. Alternative A has the highest expected FW and should be chosen despite a 10% chance of a Rs 12.1 lakh loss.
For the improvement of a manufacturing plant, the following three alternatives are being considered. The estimated investments and the corresponding increment in income are given below. Draw decision tree diagram of the situation and decide on the best alternative using FW formulation. MARR = 15%. Life of the project is 6 years.
| Alternative | Investment Cost | Sales | Probability | Annual Income |
|---|---|---|---|---|
| A | 1000000 | High Success | 0.4 | 500000 |
| A | 1000000 | Medium Success | 0.5 | 300000 |
| A | 1000000 | Low Success | 0.1 | 125500 |
| B | 600000 | High Success | 0.2 | 400000 |
| B | 600000 | Medium Success | 0.5 | 250000 |
| B | 600000 | Low Success | 0.3 | 100000 |
| C | 400000 | High Success | 0.5 | 200000 |
| C | 400000 | Medium Success | 0.1 | 125000 |
| C | 400000 | Low Success | 0.4 | 50000 |
FW at the end of year 6 for each branch = −I(F/P,15%,6) + A(F/A,15%,6), where (F/P,15%,6) = 2.3131 and (F/A,15%,6) = 8.7537. The best alternative is the one with the highest expected FW.
Decision tree
┌ High 0.4 A = 5,00,000
┌ Alt A (10,00,000) ─○ Medium 0.5 A = 3,00,000
│ └ Low 0.1 A = 1,25,500
│ ┌ High 0.2 A = 4,00,000
□───┼ Alt B (6,00,000) ──○ Medium 0.5 A = 2,50,000
│ └ Low 0.3 A = 1,00,000
│ ┌ High 0.5 A = 2,00,000
└ Alt C (4,00,000) ──○ Medium 0.1 A = 1,25,000
└ Low 0.4 A = 50,000
□ = decision, ○ = chance (probability on the branch)
Expected FW of each alternative
Alternative A (investment 1,000,000; FW of investment = 1,000,000 × 2.3131 = 2,313,061)
| Sales | Probability | Annual income | FW = −I(F/P) + A(F/A) | p × FW |
|---|---|---|---|---|
| High | 0.4 | 500,000 | 2,063,808 | 825,523 |
| Medium | 0.5 | 300,000 | 313,061 | 156,530 |
| Low | 0.1 | 125,500 | -1,214,467 | -121,447 |
E[FW(A)] = 860,607
Alternative B (investment 600,000; FW of investment = 600,000 × 2.3131 = 1,387,836)
| Sales | Probability | Annual income | FW = −I(F/P) + A(F/A) | p × FW |
|---|---|---|---|---|
| High | 0.2 | 400,000 | 2,113,659 | 422,732 |
| Medium | 0.5 | 250,000 | 800,598 | 400,299 |
| Low | 0.3 | 100,000 | -512,463 | -153,739 |
E[FW(B)] = 669,292
Alternative C (investment 400,000; FW of investment = 400,000 × 2.3131 = 925,224)
| Sales | Probability | Annual income | FW = −I(F/P) + A(F/A) | p × FW |
|---|---|---|---|---|
| High | 0.5 | 200,000 | 825,523 | 412,762 |
| Medium | 0.1 | 125,000 | 168,993 | 16,899 |
| Low | 0.4 | 50,000 | -487,537 | -195,015 |
E[FW(C)] = 234,646
Roll back at the decision node
| Alternative | Expected FW (Rs) |
|---|---|
| A | 860,607 |
| B | 669,292 |
| C | 234,646 |
Answer: Choose alternative A. It has the highest expected FW (Rs 860,607, equal to PW ≈ Rs 372,064), although it also has the largest downside: a low-success outcome gives FW ≈ −Rs 12.1 lakh with probability 0.1.
✓ Answer checked by Claude Opus 5.5 (high effort)
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