Bill owns a winery in a Caribbean Island. In a typical year, Bills winery yields 120,000 bottles

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Question:

Bill owns a winery in a Caribbean Island. In a typical year, Bill’s winery yields 120,000 bottles in a single harvest, with plenty of bottling capacity to spare. This year was expected to be another typical year, until a storm was spotted heading towards the island.

The Weather Channel thinks there is a 50-50 chance that the storm will hit the Island. Bill is trying to decide whether to harvest early and not risk the storm. If he harvests immediately, the grapes will not have as complex a taste (they have not yet fully matured), and he would only be able to sell the bottles at $5.70 each.

If the storm directly hits the island, it will drop one of two kinds of rain depending on the formation of the storm: a cold heavy rain or a warm light rain.

A cold, heavy rain would increase the yield by 10%. At the same time though, it would result in some dilution in the taste of the grapes. Bill thinks he can sell all of the diluted wine for around $4 a bottle, approximately 70% of the early harvest price. An additional consideration is the small risk of hurting the brand Bill faces by selling a diluted wine. As such, he may choose to instead sell the grapes directly (instead of making wine), generating about only half of the revenue of the thinned-out wine, but protecting the brand.

A light warm rain (which Bill gives a 40 percent chance of occurring if the storm hits), on the other hand, will actually benefit the wine through the creation of a beneficial mold, giving the wine a more complex taste and lead to a more desirable wine. Based on experience, Bill knows that, when the mold develops he could probably sell the wine for about $16 a bottle instead. Unfortunately, the mold also leads to some wastage in the grapes, decreasing the yield by 30 percent.

Finally, if the storm misses the Island entirely, Bill would most likely wait for the grapes to ripen. Then, there is a 20 percent chance that he will end up with a low acidity wine that he can sell for $5 each, and a 40 percent chance that he will end up with an average wine that will bring about $6 each. There is also the chance that he will end up with a good wine, which will bring about $7 each. All prices are wholesale.

You can assume that bottling and labeling costs will not play a significant factor in choosing between the possible options.

Assignment Questions:

1. What should Bill’s decision be early harvesting information Build a decision tree to show his options.

2. How much should Bill be willing to pay, to learn in advance, whether the storm will hit , decide whether to harvest early? Assume that the information would be perfect, i.e., it will tell with 100% certainty whether the storm will hit or miss the island.

3. How much should Bill be willing to pay, to learn in advance, about whether the conditions of the storm are conducive to the formation of the mold? Again, assume the information would be perfect. He will not know in advance if the storm will hit or miss the island, but he will know whether the storm brings with it a light warm rain or a heavy cold rain.