The Southern Textile Company is considering two alternatives: to expand its exis

Question

The Southern Textile Company is considering two alternatives: to expand its existing production operation to manufacture a new line of lightweight material, or to purchase land on which to construct a new facility in the future. Each of these decisions has outcomes based on product market growth in the future that result in another set of decisions (during a 10-year planning horizon), as shown in the figure of a sequential decision tree. In this figure, the square nodes represent decisions, and the circle nodes reflect different states of nature and their probabilities. The first decision facing the company is whether to expand or buy land. If the company expands, two states of nature are possible. Either the market will grow (with a probability of 0.60) or it will not grow (with a probability of 0.40). Either state of nature will result in a payoff. On the other hand, if the company chooses to purchase land, three years in the future another decision will have to be made regarding the development of the land. Using decision tree analysis, what is the best option?

Market Growth 0.6 $2,000,000.00 Purchase 0.4 Land -$800,000 No Market Growth 225,000.00 Market Growth $3,000,000.00 0.8 Expand$800,000. 6 0.2 No Market Growth $700,000.00 Market Growth 3 y Sell Land $450,000 Expand (no payoff) Land -$200,000 0.3 Market Growth $2,300,000.00 0.6 warehouse -$600,0 7 0.4 0.7 No Market Growth $1,000,000 No Market Growth fo 3 years, (no payoff) Sell Land $210,000

Explanation / Answer

For making a best option, first start with node1 and analysis is show. If the plant is purchase, two states of nature are possible at probability node 2: the market will grow, with a probability of 0.60, or it will not grow or will decline, with a probability of 0.4. If the market grows, the company will achieve a payoff of $2,000,000 over a 10-year period. However, if no growth occurs, a payoff on only $225,000 will result.

If the decision is to Expand, two states of nature are possible at node 3. These two states of nature are identical at node 2; however, the payoffs are different. If market growth occurs for a 3-year period, no payoff will occur, but the company will make another decision at node 4 regarding development of the land. At that point, either the plant will be expanded at a cost of $800,000 or the land will be sold, with a payoff of $450,000. The decision situation at node 4 can occur only if market growth occurs first. If no market growth occurs at node 3, there is no payoff, and another decision situation becomes necessary at node 5: A warehouse can be constructed at a cost of $600,000 or the land can be sold for $210,000.

If the decision at decision node 4 is to expand, two states of nature are possible: The market may grow, with a probability of 0.80, or it may not grow, with a probability of 0.20. The payoffs for these two states of nature at the end of the 10-year period are $3,000,000 and $700,000, respectively. If the company decides to build a warehouse at node 5, two states of nature can occur: Market growth can occur, with a probability of 0.30 and an eventual payoff of $2,300,000, or no growth can occur, with a probability of 0.70 and a payoff of $1,000,000.

The last option is the best of above nodes becuase it gives a greater payoff value among these but with some probability. THus, to purphase land is a best option.

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