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?

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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