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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.

For depreciation, you're paying that because while you have the vehicle, it's depreciating. The lessor still owns the vehicle that you're renting. They could have sold it and kept all the value, but instead they're holding it while it depreciates, so they naturally need to be compensated for that depreciation. 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 other part is the rent charge that you pay the lessor for the privilege of using the vehicle. This is where people usually get tripped up in lease math because it's not obvious why it is calculated this way. 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.