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The Westhouser Paper Company in the state of Washington currently has an option to

purchase a piece of land with good timber forest on it$.$ It is now May first and the

current price of the land is $$2\mathrm{.}2$ million. Westhouser does not actually need the timber

from this land until the beginning of July, but its top executives fear that another

company might buy the land between now and the beginning of Julv. They assess that

there is a $5\%$ chance that a competitor will buy the land during May. If this does not

gccur, they assess that there is a $10\%$ chance that the competitor will buy the land

during June. If Westhouser does not take advantage of its current option it can attempt

to buy the land at the beginning of June or the beginning of July, provided that it is still

available.

Westhourser's incentive for delaying the purchase is that its financial experts believe

there is a good chance that the price of the land will fall significantly on one or both of

the next two months. They assess the possible price decreases and their probabilities as

displayed in the Exhibits below. For example, Exhibit $3$ indicates that if the price

decrease in May is $$60,000,$ then the possible price decreases in June are $$0,$$$30,000,$

and $$60,0000$ with respective probabilities $0\mathrm{.}6,0\mathrm{.}2$ and $0\mathrm{.}2.$

If Westhouser purchases the land, it believes that it can gross $$3$ million. $($This does not

count the cost of purchasing the land.$)$ But if it does not purchase the land, Westhouser

believes that it can make $$650,000$ from alternative investments. Use decision tree to

analyze Westhouser's optimal strategy.

Exhibit $1$: Distribution of Price Decrease in May

Exhibit $2$: Distribution of Price Decrease in June, if there was no Price Decrease in May

Exhibit $3$: Distribution of Price Decrease in June, if there was a $$60,000$ Price Decrease

in May

Exhibit $4$: Distribution of Price Decrease in June, if there was a $$120,000$ Price

Decrease in May

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