William Jaeger, partner and owner of Freemark Abbey Winery, has a crop of Riesling grapes that are close to ripening with a possible rainstorm approaching. Freemark produces 1,000 cases per year of Riesling wine, which equates to 12,000 bottles. Mr. Jaeger has to decide on whether to harvest the grapes right now or let the grapes get caught in the rainstorm. Each decision comes with a certain level of risk. If he harvests the grapes now, he will avoid the rainstorm altogether, and have a respectable type of grape that would get him a good return on his decision. However, if he allows the grapes to remain in the storm, he has the opportunity to more than triple his return if the rainstorm produces a certain type of mold that allows the grapes to retain more sugar, thereby producing a much higher quality wine. On the other hand, if the mold is not present in the storm, then he runs the risk of oversaturating the grapes which would result in a thin, lower quality wine.
In addition, if he does not harvest the grapes and the storm does not come, Mr. Jaeger has 3 more possibilities open to him, all based on luck. There is the chance that the grapes will retain 25% of their sugar content and produce a high quality wine. There is also a chance of those grapes retaining 20% of their sugar content and produce a lighter wine than the first, but still above what he would have if he harvested the grapes early. Third, there is a small chance that the grapes will retain less than 19% of their sugar content, which would result in a thinner wine that would produce less of a return than if he had harvested the grapes early. With so many options, how does Mr. Jaeger come to a decision? It will be helpful to utilize the flowchart diagram attached to the end of the analysis.
Begin with the option with the least amount of risk, and that is the option to harvest. This is the least risky of the options because he knows what he can get if he harvested the grapes right now. If he harvested the grapes immediately in their current state, he would be able to sell the wine at $2.85 per bottle. $2.85/bottle * 12,000 bottles = $34,200
The result is that Mr. Jaeger would make $34,200 profit by picking the grapes immediately. There are no other alternatives, so the EMV of harvesting immediately is the same as the profit ($34,200).
Do Not Harvest, No Storm
Now to observe the options available to Mr. Jaeger if he decides to not harvest the grapes. There is a 50-50 chance that the storm will actually appear. So for now, let us see what the decisions are available if the storm does not actually happen. With the storm not coming, this still allows Mr. Jaeger to leave the grapes on the vine to mature longer, thereby giving them a better quality to make better wine. The percentage chance that the grapes retain 25% of their sugar content is 40%, and the same percentage holds for the grapes retaining 20%. The chance that they retain 19% or less, therefore, is 20%. The prices at which the wine would sell at each sugar content level is as follows: 25% : $3.50/bottle
20% : $3.00/bottle
Look now at the options available to Mr. Jaeger if he decides not to harvest and the storm does come down on his vineyard. The chances that the rainstorm contains the mold that he needs is 40%, whereas the likelihood that it does not contain the mold is 60%. Addressing the possibilities available to Mr. Jaeger if the storm does not contain the mold, the juice from the grapes would increase by 7.5% but would thin out the wine. So, he can either sell the thinned wine for $2.00/bottle or sell the grapes in bulk and make about half of what he would make if he sold the wine. Each selection is no more likely than the other (50-50), so the two possibilities are as follows: Sell Wine : $2.00 * 12,000 * 1.075 = $25,800
Sell Grapes in Bulk = $25,800 * .5 = $12,900
Neither option is very enticing compared to the other options so far, but that is part of the risk. Let us look at the EMV of this particular group of decisions: EMV (Not Harvesting, Storm with No Mold) : ($25,800 * .5) + ($12,900 * .5) = $19350
Do Not Harvest, Storm Comes, Mold Present
Now, look at the scenario if the storm does come and it does carry the mold with it. This is the most optimistic scenario, as it leads to the greatest profit. The wholesale price for the wine that contains this mold would be $8.00 per bottle, but with the caveat that production would actually be 30% less because of a reduction in overall juice in the grapes. So the profit margin for the grapes containing the mold is as follows: Grapes with Mold : $8.00 * .7 * 12,000 = $67,200
As you can see, this holds the greatest opportunity for profit. Now that all the potential profits have been found for the storm actually happening, it is important to find the overall EMV of this scenario. Remember that the chances of the storm containing the mold was 40%, while the chances of it not having the mold was 60%. The result is as follows: EMV (Do Not Harvest, Storm Comes) : ($67,200 * .4) + ($19,350 * .6) = $38,490
EMV of Not Harvesting
Lastly, now that we have accounted for all potential scenarios of the decision to not harvest, the overall EMV of this decision needs to be made to see which option is ultimately the wiser decision. Recall that the chances that the storm would hit were 50-50, so that is what should be used to figure the total EMV of the decision to not harvest. The two figures that are used come from the EMV’s of the storm happening ($38,490), and the storm not happening ($37,200). The result is as follows: EMV (Do not Harvest) : ($38,490 * .5) + (38,720 * .5) = $38,745
In conclusion, one can see that it is a better decision to take the risk of waiting to harvest to see if the storm comes and brings the mold, as the EMV of that is $3,645 higher than the EMV of harvesting immediately. The decision does come with higher risk, but the odds are in Mr. Jaeger’s favor that if he waits to harvest, then he will make a higher profit, or break even on what he would have made by harvesting immediately. It is therefore, my recommendation that he wait to harvest his grapes to see if the storm comes, and what comes of the grapes at that time.
Bodily, S. F., Carraway, R. L., Frey Jr., S. C., and Pfeifer, P.E. (1998). Quantitative Business Analysis: Text and Cases. New York, NY: McGraw-Hill Publishing.