4-65. An auto dealership is running a promo- tional deal whereby they will repla

Question

4-65. An auto dealership is running a promo- tional deal whereby they will replace your tires free of charge for the life of the vehicle when you urchase your car from them. You expect the original tires to last for 30,000 miles, and then they will need replacement every 30,000 miles thereafter. Your driving mileage averages 15,000 miles per year. A set of new tires costs $400. If you trade in the car at 150,000 miles with new tires then, what is the lump-sum present value of this deal if your personal interest rate is 12% per year? (4.10)

Explanation / Answer

ANSWER:

Since the tires are to be replaced after 30,000 miles and the average is 15,000 miles per year , it means the tires will be replaced every 2 years and since it is supposed to travel 150,000 miles it will travel for 10 years as 150,000 / 15,000 = 10 years

cost of replacing tires is $400.

i = 12%

pv = cost of replacing in year 2(p/f,i,n) + cost of replacing in year 4(p/f,i,n) + cost of replacing in year 6(p/f,i,n) + cost of replacing in year 8(p/f,i,n) + cost of replacing in year 10(p/f,i,n)

pv = 400(p/f,12%,2) + 400(p/f,12%,4) + 400(p/f,12%,6) + 400(p/f,12%,8) + 400(p/f,12%,10)

pv = 400 * 0.7972 + 400 * 0.6355 + 400 * 0.5066 + 400 * 0.4039 + 400 * 0.322

pv = 318.88 + 254.2 + 202.64 + 161.56 + 128.8

pv = $1,066.08

so the lump sum present value of the deal is $1,066.08

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