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13 June, 13:06

A company is considering the expansion of its current facility to meet increasing demand. A major expansion would cost $500,000, while a minor expansion would cost $200,000. If demand is high in the future, the major expansion would result in an additional profit of $800,000, but if demand is low, then there would be a loss of $500,000. If demand is high, the minor expansion will result in an increase in profits of $200,000, but if demand is low, then there is a loss of $100,000. The company has the option of not expanding. For what probability of a high demand will the company be indifferent between the two expansion alternatives?

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  1. 13 June, 14:15
    0
    0.7

    Explanation:

    States of Nature

    Alternatives Demand is High Demand is Low

    Major Expansion $800, 000 - $500,000 - $500,000 - $500,000

    Minor Expansion $200, 000 - $200,000 - $100, 000 - $200,000

    Doing Nothing $0 $0

    States of Nature

    Alternatives Demand is High Demand is Low

    Major Expansion $300,000 - $1,000,000

    Minor Expansion $0 - $300,000

    Doing Nothing $0 $0

    Let D to be the probability of the high demand;

    Then:

    300,000 * D - 1,000,000 * (1 - D) = 0 * D - 300,000 * (1 - D)

    300,000D - 1,000,000 - 1,000,000D = - 300,000 + 300, 000D

    -700,000 D - 1,000,000 = - 300,000 + 300,000 D

    -1,000,000 + 300,000 = 700,000 D + 300,000 D

    700,000 = 1,000, 000 D

    D = 700,000/1,000,000

    D = 0.7

    ∴ the probability of a high demand that the company will be indifferent between the two expansion alternatives = 0.7
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