Westhouser Paper Decision Tree

Westhouser Paper Decision Tree Example (Adapted from Winston and Albright, Example 2.5)

The Westhouser Paper Company is contemplating purchasing a piece of land with a good timber forest on it. It is now May 1 and the current price of the land is $2,200,000. Westhouser does not need the timber from this land until the beginning of July, but management fears that another company might buy the land between now and then. They believe that there is 1 chance in 20 that a competitor will buy the land in May. If this does not occur, they think there is a 1 chance in 10 that the competitor will buy the land in June. If Westhouser does not purchase the land now, they can attempt to buy the land at the beginning of June or the beginning of July, if it is still available. Westhouser’s incentive for delaying the purchase is that they believe that the price of the land might decrease in one or both of the next two months. The possible price decreases and their probabilities are shown below. Table 1 shows the probability of a price decrease in May. Table 2 shows the conditional probabilities of the possible price decreases in June, given the price decrease in May. For example, if the price decrease in May is $100,000, then the possible price decreases in June are $0 and $50,000 with probabilities .6 and .4, respectively.

Table 1: Distribution of Price Decrease in May

Price Decrease Probability

$0 .8

$100,000 .2

Table 2: Distribution of Price Decrease in June

Price Decrease in May

$0 $100,000 June Decrease Probability June Decrease Probability

$0 .3 $0 .6

$100,000 .7 $50,000 .4

If Westhouser purchases the land, they will gross $3 million. (This does not count the cost of purchasing the land.) But if they do not purchase the land, they believe that they can make $650,000 from alternative investments. What should Westhouser do?

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