Question

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?

Answer 1

0.7

Step-by-step 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