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 $30,000 and could borrow the money to buy from her credit union by putting $3,300 down and paying $614.88 per month for 48 months at 5 percent APR. Alternatively, she could lease the car for 48 months at $330 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 $12,400 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.

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

Explanation:

Solution

Buy versus Lease problem:

Now,

Buy case

The Purchase price = Gross capitalized cost = $30,000

The Down payment = $3300

The  Present value of borrowing from credit union = 30,000 - 3300 = $26700

The EMI payment = $614.88,

No of months = 48, Annual percentage rate (APR) = 5%

The Monthly Percentage rate = 5%/12 = 0.4%

Then

We find future value at the end of 48 months

By applying Excel,

PV=26700, N=48, I/Y=0.4%, PMT=614.88

FV = -0.14079 which is approximate to Zero (given that EMI payment was rounded off to digit of  2 , FV has resulted slightly differ from zero)

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

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

= $61488*48 - 26700 = $2924.724

The lease case

The  cost reduction  capital= $3300 (capitalized cost is paid by customers to decrease the rate of lease while leasing cars)

Fee disposition on the car = $350

The Residual value = $12,400

Then,

PV = $30,000 - $3300 = $26,700, EMI = $330, Number of months leased = 48

FV = Residual value – Disposition fee = $12,400 - $350 = $12,050

The cost of dollar of leasing = Sum of all the  payments of EMI - payment based on principal value at the end of the lease period = 330 * 48 – (26700 – 12050) = $1190

Therefore, since the cost of financing for leasing is higher than buying, Amanda she should finance the car.

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