What is a lease?

The Mathematics of Leasing

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The Mathematics of Leasing

Let me tell you up front that this is the tricky part. If you hated math in school, you will definitely hate this chapter. I made it as simple as possible to avoid the reader’s eyes glazing over in the first paragraph. But, this is very important. You should be able to make a fair appraisal of the value of a lease proposal just by looking at the figures presented by the leasing company.

Let’s discuss the elements of your lease calculation at a high level.

Cap Cost/Selling Price – This is the price you pay for the vehicle you are leasing.

Residual Value – This is the amount you owe at the end of your lease term. This is usually calculated as a percentage of the Manufacturers Suggested Retail Price (MSRP)of the vehicle. This is an arbitrary percentage derived from some very intelligent people sitting around a room looking into a crystal ball which will tell them what your vehicle will be worth in a predetermined amount of time in the future.

Depreciation – This is the difference between the Cap Cost/Selling Price and the Residual Value.

Example:         Your new car has a MSRP of                         $40,000.00

                        And you have a Selling Price of                    $40,000.00

                        The Residual Value is 50%                         -$20,000.00

                        The Depreciation is what is left                     $20,000.00

So, from this example you can see that the residual, and by extension, the amount of depreciation, is a very important factor in your lease since the total depreciation is divided equally among your monthly payments. In this case you the monthly portion of your depreciation for a 36 month lease would be $555.55.

Now if the residual had been 60%, the depreciation would have been $16,000, or $444.44 per month. So a more popular car, or a better lease program just made a $100.00 per month difference in your monthly payment. Now to money factor.

Money Factor - The money factor is a figure derived by dividing your Annual Interest Rate by 12 (as in twelve month) to give you a monthly APR. The percentage is then converted to a decimal by dividing by 100. Since the finance charges are determined based on the average amount financed, (or level yield), the cap cost plus the residual divided by two, would give you the average amoun financed. Or, APR/12 x 1/100, which is the same as APR/1200.

For our purposes and the entire leasing world we use the much simplified:

                              (Cap Cost + Residual) X APR / 2400

Now you can take your money factor backwards and determine your Annual Percentage Rate. Let's use a money factor of .003, which is pretty common these days.

                                    .003 X 2400 = 7.2% APR


                                     7.2% APR / 2400 = .003 MF

This is all you will ever need to know about Money Factors, but once again, we are about understanding what make a lease what it is.

Now, using the same numbers from our previous example, let's calculate the rental portion of our lease, or the "Monthly Use Fee":

Example:         The CAP COST is                                        $40,000.00

                        The Residual is                                            $20,000.00

                        The Depreciation is 50% or                            $20,000.00

                        The calculation goes like this:

                               $ 40,000 + 20,000 = $60,000 X .003 = $180

Some of you may be thinking, if the Residual is high, as I've indicated is should be, then the Money Use Fee would be higher also. What gives?

This is true, but the monthly depreciation has a much bigger impact on your payment than does the monthly use fee. Here are two examples. The same car with two different residuals and money factors. Which one do you like best?

Cap Cost $40,000


$20,000 (50%)
$24,000 (60%)
Money Factor .003 .0025
Monthly Depreciation 555.55 444.44
Monthly Use Fee 180.00 160.00
Monthly Payment (36 mo.) $735.55 $604.44

Over the term of the lease this represents a $4719.96 difference, which is a savings to you, or a profit for the dealer or leasing company. You should be able to see by now that a very subtle change can make a huge difference. Just for practice try a money factor of .0033 or .0035, with a residual of 55% or 65%.

The rest of your lease payment is made up of acquisition fees and taxes. If you have the ready cash, pay these fees up front.

Now let's see what affect the Cap Reduction can have on these scenarios. Let's just use $5,000 in our example above:

Cap Cost $40,000
Cap Reduction $  5,000 $  5,000
Adjusted Cap $35,000 $35,000


$20,000 (50%)
$24,000 (60%)
Depreciation $15,000 $11,000
Money Factor           .003         .0025
Monthly Depreciation $    416.66 $    305.55
Monthly Use Fee $    165.00 $    147.50
Monthly Payment (36 mo.) $    581.66 $    453.55

As you can see in the examples your payments are reduced by $153.89 and $150.89 respectively, or $5540.04 and $5430.04 in total savings. So your $5,000 investment in the lease saved you some money. Not a bad investment. There is, in fact, a point at which leasing company will limit the amount of cap reduction you can apply to a lease. Play with the numbers and you'll see why.


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