The local Ford dealer wants to determine whether to give all purchasers of new cars free oil changes. The Forddata.xlsx contains information on loyalty of car purchasers. A sample of this data is shown in Figure 21-8. For example, the data in row 7 indicates that customer number 113 bought a non-Ford on 8/15/1990.

Use this data to determine the current chance that a Ford purchaser will next buy a Ford and the current chance a purchaser of another type of car will next buy a Ford. You have the following information:
■ The length of time a person keeps a new car is equally likely to be between 700 and 2,000 days.
■ Ford makes $2,000 on the purchase of a new car.
■ Without free oil changes Ford earns $350 profi t per year from servicing a car.
■ Currently customers pay $100 per year for oil changes, which cost Ford $60 to perform. Assume all Ford purchasers always have their oil changed at the dealer.
■ All purchase and service profi ts are booked at the time the car is purchased, and profi ts are discounted at 10 percent per year.

■ If you give free oil changes, loyalty percentages and switch percentages will improve by an unknown amount, equally likely to be between 2 percent and 15 percent.
Suppose a customer has bought a car from a competitor today. Determine the 20-year value of this customer to Ford without the free oil changes. What is the chance that the free oil changes increase the value of this customer?