Explanation:
The correct answer is C ($1.90). The expected dividend per share under the favorable scenario is calculated as follows:
Conditional Expectation: The expected value of the dividend given the favorable scenario is computed by weighting each possible dividend by its conditional probability:
$2.00 × 0.80 = $1.60$1.50 × 0.20 = $0.30$1.60 + $0.30 = $1.90Incorrect Answers:
$1.14): Incorrectly multiplies the conditional expectation ($1.90) by the probability of the favorable scenario (0.60).$1.37): Represents the unconditional expected dividend per share, which combines both favorable and unfavorable scenarios.This question tests the understanding of conditional expectations and their application in investment analysis, particularly in scenarios modeled using probability trees.
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A tree diagram provides the following data regarding the dividend per share for a company under two scenarios:
$2.00 (80% probability) or $1.50 (20% probability).$0.75 (30% probability) or $0.50 (70% probability).
The expected dividend per share under the favorable scenario is closest to:A
$1.14.
B
$1.37.
C
$1.90.
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