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AST Ltd. has early-completion bonuses on a ₹25 cr contract: 15% bonus at 25% likelihood, 10% at 40%, 5% at 15%, none at 20%. Using the EXPECTED VALUE method, the variable-consideration estimate for the early-completion bonus is approximately:
A₹3.75 crore — the bonus at the highest-bonus (15%) outcome
B₹6.25 crore — the average of the four possible bonus amounts (15+10+5+0)/4 × ₹25 cr
C₹2.13 crore — probability-weighted sum (0.25 × 3.75 + 0.40 × 2.50 + 0.15 × 1.25 + 0.20 × 0)
D₹2.50 crore — the bonus at the highest-likelihood (40%) outcome
Answer & Solution
Correct answer: C. ₹2.13 crore — probability-weighted sum (0.25 × 3.75 + 0.40 × 2.50 + 0.15 × 1.25 + 0.20 × 0)
Expected value = Σ(probability × bonus amount). 0.25 × 15% × ₹25 cr = ₹0.9375 cr; 0.40 × 10% × ₹25 cr = ₹1.00 cr; 0.15 × 5% × ₹25 cr = ₹0.1875 cr; 0.20 × nil = 0. Sum = ₹2.125 cr ≈ ₹2.13 cr. The most-likely-amount method (the 40%-likely 10% bonus) would give ₹2.50 cr — different method, different result.
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