Question

You are interested in a new Ford Taurus. After visiting your Ford dealer, doing your research on the best leases available, you have three options. (i) Purchase the car for cash and receive a $1,600 cash rebate from Dealer A. The price of the car is $16,000. (ii) Lease the car from Dealer B. Under this option, you pay the dealer $450 now and $200 a month for each of the next 36 months (the first $200 payment occurs 1 month from today). After 36 months you may buy the car for $9,100. (iii) Purchase the car from Dealer C who will lend you the entire purchase price of the car for a zero-interest 36-month loan with monthly payments. The car price is $16,000. Suppose the market interest rate is 8%. What is the net cost today of the cheapest option?

Answer 1

The net cost of each option is the PV of the cash ouflows
discounted at 8%/12 per month.
Dealer A:
PV = 16000-1600 =	$           14,400
Dealer B:
PV = 450+200*((1+0.08/12)^36-1)/((0.08/12)*(1+0.08/12)^36)+9100/(1+0.08/12)^36 =	$           13,996
Dealer C:
PV = (16000/36)*((1+0.08/12)^36-1)/((0.08/12)*(1+0.08/12)^36) =	$           14,183
CHEAPEST OPTION IS THAT OF DEALER B.