Question

A manufacturing company has a production facility in Miami, FL. This facility can generate a regular profit of $10 million annually. The threat of hurricane is always an issue for this facility. It is estimated that a strong hurricane (category 3 or higher) can cause a damage of around $20 million. The company has the option of buying an insurance policy that covers 80% of this potential damage. The cost of this type of policy is $3.5 million. This policy should be bought at least 6 months before the hurricane season. The average probability of occurrence of a strong hurricane in that region is estimated to be 50%.

The company also has the option of waiting until the beginning of the hurricane season to buy the insurance policy with a higher price of $4 million. At the beginning of the season, the weather forecast indicates that either this is a high risk season or a low risk season. A high risk season happens with a probability of 50% and during such a high risk season, a strong hurricane happens with a probability of 90%. A low risk season which happens with a probability of 50% and during such a low risk season a strong hurricane happens with a probability of 10%.

Note: the company generates its $10 million profit regardless of happening of a hurricane.

Draw a decision tree and specify:

The best decision course;
whether to make a decision 6 months before the hurricane season or to wait for the beginning of the hurricane season

Answer 1

The best decision course is to buy the insurance policy 6 months before the hurricane season.

Step-by-step explanation:

To make the best decision on whether to buy the insurance policy 6 months before the hurricane season or wait until the beginning of the season, we can create a decision tree. Here's how:

1. If the company buys the insurance policy 6 months before the hurricane season, they will pay $3.5 million. If a strong hurricane occurs, the company receives an 80% coverage, which amounts to $16 million. The expected value of this decision is calculated by multiplying the probability of a strong hurricane (50%) by the potential damage ($16 million) and subtracting the cost of the insurance policy. The expected value is $4 million ($16 million x 0.5 - $3.5 million).
2. If the company waits until the beginning of the season and the weather forecast indicates a high-risk season, the company will pay $4 million for the insurance policy. In this case, the company has a 90% chance of a strong hurricane occurring, which would result in a potential damage of $20 million. The expected value of this decision is calculated by multiplying the probability of a high-risk season (50%) by the probability of a strong hurricane (90%) by the potential damage ($20 million) and subtracting the cost of the insurance policy. The expected value is $9 million ($20 million x 0.5 x 0.9 - $4 million).
3. If the weather forecast indicates a low-risk season, the company will also pay $4 million for the insurance policy. However, there is only a 10% chance of a strong hurricane occurring, resulting in a potential damage of $20 million. The expected value of this decision is calculated by multiplying the probability of a low-risk season (50%) by the probability of a strong hurricane (10%) by the potential damage ($20 million) and subtracting the cost of the insurance policy. The expected value is $1 million ($20 million x 0.5 x 0.1 - $4 million).

Based on these calculations, the best decision course is to buy the insurance policy 6 months before the hurricane season, as it has the highest expected value of $4 million. This decision minimizes the company's potential losses and maximizes their overall profit.