Incentive program by car dealer to offer a 'tires for life'

A commercial on TV last night in which a local car dealer was trying to attract customers by offering them a "Tires for Life" program. The way it works is if you buy a car from the dealership, they agree to replace the tires whenever needed at no charge for as long as you own the car.

When I saw the commercial I was instantly reminded of how many, many of the problems that finance people deal with every day out in the real world are simply present value problems like we studied last week. The tires for life incentive program is a classic example, as it calls for answering the question "How much does the dealer have to add to the price of the car to finance the incentive program?"

Some simplifying assumptions. For example, let's assume the following:

One customer is going to take advantage of the deal, and the car purchase is to take place today.

Then length of time the car is expected to be owned is 6 years.
Replacement tires will be needed every 2 years.
A set of replacement tires costs $200.
Funds set aside to finance the incentive program can be invested at 5%.

Now, assume you are a financial analyst working for the car dealership and the CEO has asked you to report how much they need to add to the price of a car to finance this initiative. They need an answer by the end of this week.