A chemical plant produces one product whose current yearly demand is 10,000 KG. The product sells for $50/KG and has a variable cost of production of $20/KG, and the plant has a fixed cost of $40,000/year. The plant is currently set up with a yearly capacity of 10,000 KG, or just enough to meet demand, so the manager is considering expanding the capacity to deal with demand variability. Demand is expected to remain flat at an average of 10,000 KG for each of the next 2 years, but each year it is forecasted to either increase by 10% with a 25% probability, decrease by 10% with a 25% probability, or stay the same with a 50% probability. There is an option to increase the plant's yearly capacity to 12,000 KG, which will incur a one-time up front cost of $10,000 (which must be paid now), but won't change the plant's current fixed or variable costs. The company uses a discount rate of 10%. Assume that the product loses patent protection in two years, so the company's planning horizon consists of the current year and the next two years. Assuming an objective of maximizing expected discounted profits, should the manager invest in the additional capacity? What is the maximum amount the manager should be willing to pay up front for this additional capacity?

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