Cheaper to Lease?
On the Economics of Automobile Leasing

2.1 Computing a Lease Payment

The lease payment can be calculated exactly, or by means of an approximation. To get the exact payment one divides it into two parts: one part is analogous to the payment of an amortized loan in which the principal is the difference between the net capitalized cost and the residual. The other part is simply the monthly lease rate times the residual.

For lease payments made at the end of the period, the payment is given by:

For lease payments made at the beginning of the period, the payment would be given by:

The approximation for the payment is given by mulitplying the money factor (i.e., one half the monthly lease rate) by the sum of the next capitalized cost and the residual, and then adding that amount to a depreciation component calculated by the straight line method. The payment approximation is given by:

End of period payment for a lease with annualized lease rate of 9.6%, net capital cost of $30,000, and a residual of $15,000.

Same lease with payments at the beginning of the period:

Same lease using the approximation:

We see that the approximation is very close to what the exact formula gives for a beginning of period payment. Plotting different values varying the monthly interest rate from 0.1% to 1% and looking at lease terms ranging from 36 to 39 months, we see the difference ranges from -$0.50 to $0.50.

When the lease rate is low, the difference between the exact amount and the approximation can be negative. The following graph shows the difference as a function of the monthly lease rate.

Converted by Mathematica May 29, 2001
F.C. Maclachlan
Department of Economics and Finance,
Manhattan College, NYC, NY