After deciding to buy a new car, you can either lease the car or purchase it on

Question

After deciding to buy a new car, you can either lease the car or purchase it on a three-year loan. The car you wish to buy costs $38,000. The dealer has a special leasing arrangement where you pay $105 today and $505 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at a 6 percent APR. You believe you will be able to sell the car for $26,000 in three years.

What break-even resale price in three years would make you indifferent between buying and leasing?

What is the present value of purchasing the car?

Explanation / Answer

Find the PV of both options and compare: PV lease (Note: use the interest rate on the loan to compute the PV of the lease) Enter: N = 36; I/Y = 0.5; PMT = $505; FV = 0;CPT; PV= 105+ 505 PVIFA(.5%,36) = $16599.86+ $105= $16704.86 PV loan (Price of the Car – PV of the Resale Price) Enter: N = 36; I/Y = 0.5; PV = 0; PMT = 0; FV = $26,000;CPT; PV= 38000- 26000 PVIF(.5%,36) = $38,000 - $21726.768 = $16,273.23 Answer: Lease What break-even resale price will make you indifferent between buying and leasing? Find the FV of the PV of the Resale Price that makes (Price of the Car – PV of the Resale Price) = PV of the Lease $38,000 – PV of the Resale Price = $16704.86 PV of the Resale Price = $21295.14 To find FV Enter: N = 36; I/Y = 0.5; PV = 21295.14; PMT = 0;CPT; FV FV= 21295.14x1.005^36 = $25483.48

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