Math 1030 Project

Leasing a car can be a little more intimidating than buying because of the seeming complexity of its costs.  Some may also shy away from leasing because at the end of the leasing period the vehicle is returned and the leaser has nothing to show for the money he or she invested.  These apparent difficulties, however, may scare car-owners away whom, if they had a better understanding of the costs and financial implications of leasing, might find it to be a sound investment.

The first number to consider when leasing is the MSRP or Manufacturer Recommended Retail Price (leaseguide.com).  The MSRP of our 2008 Volkswagen Passat is $29,100 which represents the full price if you were to purchase the car outright (internetautoguide.com).  Fortunately, the MSRP is almost always negotiable so for our calculations, we’re going to assume the dealer has been talked down to $27,000.  In 48 months it will cost an estimated $13,013.31 less, selling for only $12,986.69 (NCBuy.com/auto).  The amount vehicles decrease in value over time is called depreciation and the new lowered selling price is called residual value (leaseguide.com).  So we see by taking the current MSRP and subtracting the estimated residual value…

$27000.00 (MSRP) – $12986.69 (residual) = $13013.31 (depreciation)

…we get the depreciation of the car over 48 months.  This number is important because during the lease, what you’re paying for is the estimated depreciation of the vehicle during that period of time. 

            Some leases will have a down payment.  The lease offered at Strong Volkswagen in Salt Lake City has no down payment so we’ll go with that (strongvw.com).  There will however be a title and registration fee of approximately $600 for a 2008 Passat which will be rolled into the monthly payments.  If we add that to the depreciation…

            $600.00 (title and registration) + $13013.31 (depreciation) = $13613.31

…we get the total amount that will be paid over the whole period of the loan.

            Monthly payments for all leases are subject to sales tax which, for Salt Lake County, Utah, is currently 6.8% (tax.utah.gov).

            Now that we have all our variables defined all our variables, we can calculate our monthly payments.  Leases are usually paid off in the same manner as installment loans so we will use the loan payment formula which will give us a constant amount to be paid each month.  The formula is as follows.

   ___P X (APR/n)______                                                      (-nY)

PMT    =    [1 – (1 + APR/n)      ]

PMT    =    regular payment

P          =    amount to be paid

APR    =    annual percentage rate (sales tax rate)

n          =    number of payment periods per year

Y         =    lease term in years

When we plug in the numbers it gives us

                          __13613.31 X (0.068/12)___           

                                                              (-12 * 4)

PMT    =      [1 – (1 + 0.068/12)          ]

               __13613.31 X (0.00567)___

                                           (-48)

            =      [1 – (1.00567)      ]

               __77.14209__

            =      0.23756

            =  $324.7268  monthly payment

One of the advantages of leasing over taking out a loan to buy is lower monthly payments.  Buyers pay more so they can own the vehicle at the end of the pay period, leaving them with equity.  If they were to resell their vehicle right after paying it off, however, they would lose the same amount of money the leaser paid during their lease.  The longer they wait to sell the car, the more money they lose on the investment until it breaks down completely and yields negligible returns.  The cost of repairs for owners adds expenses that leasers don’t have to deal with.

            When considering whether to lease or buy, one must keep in mind that they will lose money no matter what, in the long run.

            For college students such as myself, the quality of the vehicle is of much less importance than it’s ability to get me from point A to point B.  Therefore, buying a really old hippy van for a couple thousand bucks will always be more financially viable than leasing.