Why is the residual added to the capitalized cost of a vehicle to compute the lease's rent charge

Question

I am trying to understand how lease payments are computed. As described here and confirmed here you compute the lease payment by adding the appropriate fraction of the depreciation to a rent fee that is based on the cost of the vehicle, the residual, and the money factor.

My prior understanding of a lease was that you were essentially financing the depreciation on the vehicle over the first 3 years (or however long the lease is). If you're buying a $30,000 vehicle and the residual value (how much it is estimated it will be worth at the end of the lease term) is $16,000, then you are essentially buying 3 years worth of depreciation amounting to $14,000. At least that was how I used to think about it. I assumed you were basically taking a 3-year loan for $14,000 (at some mysterious interest rate obscured by the money factor). However, that is not actually the case.

When computing the base payment for the lease, you do indeed take the $14,000 depreciation and divide it by the number of months in the lease.

However, when computing the rent, you multiply the money factor by the cost of the vehicle plus the residual value. So in my example, you'd multiply the money factor by $30,000 + 16,000 or $46,000. That number could also be expressed as the depreciation ($14,000) plus twice the residual ($16,000 x 2 = $32,000) which of course also sums to $46,000.

My question is: what is the logic behind this? Why do you pay interest/rent on twice the residual?

Can someone suggest a good way of thinking about this?

Thanks!

Answer 1

No, you are not loaning yourself $14,000, you take out a loan for the full $30,000 (as that is what the dealer wants for the car, and what he gets from the lease provider/bank, and even if the dealer is the "bank" himself), and at the end of the lease, you are basically making a bulk repayment of the remaining $16,000 (by trading-in the car), closing out the loan.

So at the start of the loan, you owe interest on the full $30,000, but since you pay the principal/depreciation during the runtime of the lease, this gets lower by time, e.g. after 18 month, you owe only $23,000 (and interest on that), and at end, you owe $16,000 (and an even lower interest on that).

The "trick" is in the money factor, as described in the question you linked. It contains a factor of 2, e.g. to convert from a yearly interest rate to a monthly rate, you divide by 24 instead of 12 - knowing that this money factor will be used on the sum of price and residual value (and only makes sense in that context).

This has the effect of getting an average value (as Alex B tried to explained in his answer in your linked question): if your intended interest rate is e.g. 10%, you can think of it as paying an interest rate of 5% on ($30,000 + $16,000). That's obviously the same as an interest rate of 10% on ($30,000 + $16,000)/2 = $23,000, e.g. the intended interest rate on the average loan amount. (And in monthly rates, that's 10%/12/2 on the sum, which is how the money factor is calculated.)

E.g. to give you a fixed monthly rate, you "underpay" interest during the first half of the lease (where you owed monthly decreasing interest on $30,000 down to $23,000), and "overpay" interest in the second half of the lease (where you owed interest on $23,000 down to $16,000).