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
or
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 
$40,000

Residual

$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 
$40,000

Cap Reduction 
$ 5,000 
$ 5,000 
Adjusted Cap 
$35,000 
$35,000 
Residual

$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.
