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# Cost-Benefit Analysis

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A soft drink maker wants to expand into a neighboring country. They want the product bottled in that country to avoid political issues and to enhance the local image of the product. They have identified two options for the expansion. The first is to build a highly automated process. The economies of scale would allow them to produce a can of soda for \$0.04 and the distribution costs would be \$0.02 per can. This facility would cost \$1 million per year in fixed costs. The second option would be to build a semi-automated plant that would cost \$650,000 per year in fixed costs. However, the cost to produce a can would be \$0.07 and the distribution cost would be \$0.04 per can.

a) Over what range of product would each plant be preferred?

b) Suppose the company believes that the demand would be approximately 6,000,000 cans per year. Suppose all costs except the variable cost (sum of the production and distribution costs) for the highly automated process are certain and can not change. What would the variable cost (the sum of the production and distribution cost) for the highly automated process have to be so that the soft drinker maker is indifferent between the two types of plants?

c) Now suppose each alternative has a different capacity. The total estimated demand for the year is 5,000,000. However, only the highly automated process can produce and distribute this amount. If the semi-automated process is used, the company would only be able to produce and distribute 4,200,000 cans annually. If the company can sell each can for \$0.35, which process should it use? Why?

#### Solution Preview

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A soft drink maker wants to expand into a neighboring country. They want the product bottled in that country to avoid political issues and to enhance the local image of the product. They have identified two options for the expansion. The first is to build a highly automated process. The economies of scale would allow them to produce a can of soda for \$0.04 and the distribution costs would be \$0.02 per can. This facility would cost \$1 million per year in fixed costs. The second option would be to build a semi-automated plant that would cost \$650,000 per year in fixed costs. However, the cost to produce a can would be \$0.07 and the distribution cost would be \$0.04 per can.

For the first option, the fixed costs are 1000000, and each can costs 0.06.
For the second option, the fixed costs are 650000, and each can costs 0.11.

For y = the total costs, and x = the number of cans, you can set up equations for each option:

1. y1 = -0.06x - 1000000
2. y2 = -0.11x - 650000

a) Over what range of ...

#### Solution Summary

This problem set analyzes two options for the expansion of a soft drink company. It looks at which option would be more profitable over different production levels, different variable costs, and different production capacities.

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