Assume that you are considering either buying or leasing a new car from a dealer
ID: 1185876 • Letter: A
Question
Assume that you are considering either buying or leasing a new car from a dealership, and the following date have been compiled:
Option A: Buying (Financing) the vehicle, for a price of $22,000. In this option, you have to pay $2,000 as a down payment, and $608 per month for 36 months to be paid at the END of each month thereafter. No Fees are applicable. The value of the vehicle after 3 years is S.
Option B: Leasing the vehicle for the price of $22,000. In this option, NO downpayment is required and the montlhy payment is $420 per month for 36 months, to be paid at the BEGINNING of each month. In this option, however, you are required to pay one time non-refunedable Documentation Fee of $400. At the end of the lease term, you have the option to pay S to own the vehicle.
For both options, your interest rate is 6% compunded monthly. If the car has a value of S after the 36 months period, what is the value of S that would make both options A and B economically equivalent?
Explanation / Answer
S=$4348.748 would make both the options economically equivalent
For option A
Total investment = 2000+608*pvfa for 36months @ 6% = 2000+(608*14.6210)=$10889.568
For option B
Total investment = 420*pvfa for 36months @ 6% + 400 = $6540.82
If the salvage value after 3 years is 4348.748 (10889.568-6540.82) then both the options will be economically equivalent.