This is an old revision of the document!

The other option to buying a car is to lease it. Leasing a car is basically renting it for a period of time (the term), usually 2 or 3 years (24 or 36 months).

Of course, a vehicle is an asset with a variable value, so it has to get complicated.

A vehicle lease is financially structured like this. The y-axis is dollars.

                 ___ $ msrp
                ░
                ░___ $ adjusted cap cost
               ╏░
               ╏░
Depreciation -<╏░___ $ midpoint
   Cost        ╏░
               ╏░
               ╏░___ $ residual
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓
                ▓___ $ 0

Start with the sticker price of the vehicle, that's MSRP. It's how much the vehicle is worth at the start of the lease.

Subtract any discounts & incentives and your down payment (if any). That is adjusted capitalized cost. Don't worry about why it's called this, just understand that is what that number means.

The residual is a prediction of the fair market value of the car at the end of the term. Cars are depreciating assets and lose value as a function of time, mileage, wear, etc.

The last number is the money factor. This is a small decimal like .00329 that determines how much you pay in rent to the lessor. If the number is bigger you pay more, smaller you pay less.

When you lease a car you pay the lessor for two things:

• The depreciation of the vehicle over the time that you have it
• Rent charges for the privilege of renting the vehicle

There's also taxes and insurance but we can ignore those for now.

To understand depreciation charges, first consider that the lessor still owns the vehicle that you're renting throughout the term. That's their asset. They could have sold it for cash (which does not depreciate), or used it for its useful purpose and bore the depreciation cost themselves. Instead they're letting you use the asset during the term. During that time its value is decreasing, so it's only fair that they be compensated for that depreciation. The most fair way to do this would be to assess the depreciation of the car each month relative to the premium month, and charge you that much. However, business is done with contracts and most people who want to lease cars would not be happy about a company getting to decide what to charge them each month on the fly. They want to agree on what they will pay in advance. Thus it is necessary for the lessor to make a prediction about how much the car will depreciate over the term and decide how much they think it will be worth at the end of the term - the residual. Once you understand that, calculating how much you pay in depreciation is easy. It's (adjusted capitalized cost - residual). In the graph this is represented as “depreciation cost.” Note that this is not equal to the actual depreciation of the vehicle! That would be (MSRP - residual). The incentives & down payment are working in your favor here.

The other part is the rent charge. This is charged to compensate the lessor for the privilege of using the vehicle. Basically this is the profit for the lessor. Calculating this quantity is where people usually get tripped up in lease math because it's not obvious why it is calculated the way that it is. To calculate how much you pay in rent in total, it's (adjusted cap cost + residual) x money factor x term. It's calculated this way because the money factor itself is defined as APR/(12*2). The 2 in the denominator of the money factor divides the sum of adjusted cap cost and residual to get the midpoint shown in the bar chart. Why is the money factor defined this way? Because the “principal” (to use loan terms - this is not a loan) of the asset - ie the car's value currently being held by the lessor - decreases from the adjusted cap cost down to the residual over the lifetime of the lease, and the intention is to charge rent on the total value of the asset currently being leased at any given time, and the average of that is the midpoint, so they decided it was easier to take the % of the “loaned” value they wanted to charge you annually, divide it by 12 to get monthly, then divide it again by 2 to account for you paying the depreciation. The upshot of this is that the midpoint defines how much rent you pay - anything that lowers the midpoint will reduce the rent charges.

Obviously to get the total amount you pay over the lifetime of the lease, add the depreciation cost and rent charge. To get it monthly divide by the term (in months).

That's it. That's all there is to leases. It took way too long for me to figure this out. The math has numerous interesting consequences. Note that any discounts off the MSRP (and your down payment, if any) work double duty to reduce both the depreciation cost and the rent charge. Also note that the rent charge cannot be completely eliminated even if you prepay the entire lease.

Other things to know about leases:

1. The lessor owns the vehicle throughout the lease period.
2. You insure the vehicle on your policy.
3. Down payments are not required.
4. If the vehicle is totaled during the lease period, you lose any down payment.