I saw a commercial on TV last night in which a local car dealer was trying to at
ID: 2633117 • Letter: I
Question
I saw 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.
Explanation / Answer
After the car is sold to the customer, it will need replacements twice in its lifetime - once after 2 years, and the second time after 4 years (after 6 years, it is anyway fit to be discarded so no point in fitting it with new tyres then).
The cost of fitting with replacement tyres both times = $ 200
Present value of cost of first replacement in 2 years = 200 / (1+5%)^2 = 181.41
Present value of cost of second replacement in 4 years = 200 / (1+5%)^4 = 164.54
So total present value of cost of replacement = 181.41 + 164.54 = $ 345.95
Answer: Extra amount to be added to car price = $ 345.95
Hope this helped ! Let me know in case of any queries.