Your sister just bought a new car having a sticker price (manufacturer\'s sugges

Question

Your sister just bought a new car having a sticker price (manufacturer's suggested retail price) of 36,000. She was crafty and was able to negotiate a sales price of 33,500 from the auto dealership. In addition, she received 4,5000 for here old trade-in car under the U.S. government's "Cash for Clunkers" program. If her new car will have a resale value of 3,5000 after seven years when your sister will shop for a replacement car, what is the annual capital recovery cost of your sister's purchase? The relevant interest rate is 8% per year, and your sister can afford to spend a maximum of 5,000 per year to finance the car (operating and other costs are extra).

Explanation / Answer

Net cost is initial cost minus the present value of the salvage value 33,500- 4,500- 3,500/(1.08)^7= 26,957.78 Recovery ratio is (1+i)^n* i/((1+i)^n-1) n=7 and i=.08 Recovery ratio is .192072402 So annual capital recovery cost is net cost times recovery ratio. 26957.78* .192072402= 5177.85

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