Question

You decided to buy a new car, and you can either lease the car or purchase it on a three- year loan. The car you wish to buy costs $32,000. The dealer has a special leasing arrangement where you pay $99 today and $450 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 7 percent APR. You believe you will be able to sell the car for $23,000 in three years. Should you buy or lease the car? What break-even resale price in three years would make you indifferent between buying and leasing?

Answer 1

Refer to the following calculations for both buying & leasing case:

Note that we are using 7% as the discounting rate for both the cases.

Buying Car price (PV of loan) car selling price after 3 years PV of 23000 (resale value) @7% NPV of cash flows of buying the car Formulas $ 32,000.00 $ 23,000.00 $ 18,774.85 =23000/(1+7%)^3 $ -13,225.15 - 32000+18774.85 Leasing Lease down payment Monthly payments PV of monthly payments NPV of leasing -99 -450 -5,865.84 =PV(7%, 12*3,450) = 450*PV Annuity factor (7%/12,12*3) -5,964.84 = PV of monthly payments + Down payment $ $

As the NPV of Leasing is higher (less negative) than NPV of cash flows of buying, So the car should be leased.

To find the break-even resale price in three years that would make you indifferent between buying and leasing, you just need to set the NPV of buying equal to the NPV of leasing i.e.

NPV of buying = NPV of leasing

-32000 + PV of Resale price = -5964.84

So, PV of resale price = 32000-5964.84

=26,035.16

As this is the PV of resale price, we need to compound it back to 3 years @7%

So, Resale Price = 26,035.16 * (1+7%)^3 = $31,894.19

Resale Price for indifference = $31,894.19