Mr. Maloy has just bought a new $30,000 sport utility vehicle. As a reasonably safe driver, he believes that there is only about a 5% chance of being in an accident in the coming year. If he is involved in an accident, the damage to his new vehicle depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are given in the file P06_67.xlsx.
Mr. Maloy is trying to decide whether he is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, he pays the first $300 in damages if he causes an accident and the insurance company pays the remainder.
a. Create a cost table that specifies the cost (in dollars) associated with each possible decision and type of accident.
b. Use PrecisionTree to identify the strategy that minimizes Mr. Maloy’s annual expected cost.
c. Perform a sensitivity analysis on the optimal decision with respect to the probability of an accident, the premium, and the deductible amount, and summarize your findings. (You can choose the ranges to test.) In response to which of these three inputs is the expected cost most sensitive?