Question

Buy Versus Lease Amanda Forsythe of Springfield, Missouri, must decide whether to buy or lease a car she has selected. She has negotiated a purchase price (gross capitalized cost) of $40,000 and could borrow the money to buy from her credit union by putting $3,300 down and paying $878.83 per month for 48 months at 7 percent APR. Alternatively, she could lease the car for 48 months at $625 per month by paying a $3,300 capitalized cost reduction and a $350 disposition fee on the car, which is projected to have a residual value of $12,500 at the end of the lease. Use the Run the Numbers worksheet to advise Amanda about whether she should finance or lease the car. Round your answers to the nearest cent.

Answer 1

Buy versus Lease problem:

Purchase price = Gross capitalised cost = $40,000

Buy case:

Down payment = $3300 => Present value of borrowing from credit union = 40,000 - 3300 = $36700

EMI payment = $878.83, No of months = 48, Annual percentage rate (APR) = 7%

So Monthly Percentage rate = 7%/12 = 0.5833%

Let’s find future value at the end of 48 months =>

Using Excel, given PV=36,700, N=48, I/Y=0.5833%, PMT=878.83

FV = -0.15574 which is equivalent to Zero (given that EMI payment was rounded off to 2 digits, FV has resulted slightly different from zero)

Essentially, at the end of four years, the car has no residual value as per the buy option

Finance charges of borrowing the car = Sum of all the EMI payments – principal payment

= $878.83*48 - $36,700 = $5483.70

Lease case:

Capitalized cost reduction = $3300 (capitalized cost is paid by customers to reduce the lease rates while leasing cars)

Disposition fee on the car = $350 (Disposition fee is charged at the end of lease period to recondition the car by dealers if the leased customer do not buy the car or extend the lease)

Residual value = $12,500

Hence PV = $40,000 - $3300 = $36,700, EMI = $625, Number of months leased = 48

FV = Residual value – Disposition fee = $12,500 - $350 = $12,150

Hence dollar cost of leasing = Sum of all the EMI payments – principal payment based on value at the end of the lease period = 625 * 48 – (36700 – 12150) = $5450.00

Since cost of financing for buying is higher than leasing , Amanda she should lease the car.