You have decided to obtain a delivery van for your business. You will need the van for one year. You can lease a van with a full warranty at a cost of $4,000 for the year. A business acquaintance has also offered to sell you a used van for $12,800. You expect to be able to sell this van for $10,000 a year from now, so its net cost for the year would be $2,800.

Your acquaintances used van appears to be in good working order, with the possible exception of its transmission and brakes. You estimate there is a 40% chance the transmission will fail, in which case you must repair it at a cost of $1,600. There is a 70% chance, independent of the condition of the transmission, that the brakes will need servicing, which costs $600.

Before deciding which van to obtain, you have the option of having the used van inspected by your mechanic, at a cost of $100, which covers a full examination of the entire vehicle. The mechanic will then be able to tell you for certain whether the brakes will need servicing or not. He will also pronounce the transmission as either looking good or looking bad. In the past, in cases where transmissions have ended up working throughout the following year, he has First Midterm Review Questions 3 Business Decision Analytics under Uncertainty pronounced them as looking good 2/3 of the time. Similarly, in cases where transmissions have ended up failing within a year, he has pronounced them as looking bad 75% of the time. Overall, there are four possible outcomes of the mechanics inspection, namely transmission looking good, brakes OK, transmission looking bad, brakes OK, transmission looking good, brakes will need service, and transmission looking bad, brakes will need service.

(a) Determine the course of action that will give you the lowest expected cost. State the best policy and its expected cost.

(b) What is the expected value of sample information (EVSI) provided by the mechanics inspection?