Pricing a Lease Contract in Presence of Late Payment Extra-Charges

Abstract

Partial insolvency in leasing contracts may entail to afford additional late payment costs. In this paper we focus on the case that the lessee makes partial payments in due time and settles the debt augumented by the late payment interests later. The presence of the extra-costs drives the lease Effective Annual interest Rate (EAR) to deviate from the lease contract rate. The aim of this work is to illustrate how design the contract payback amortization to stick EAR to the lease contract rate, when the lease contract rate, the late payment rate and the contract term are exogeneously fixed. First we achieve a proxy for EAR given by the lease contract rate plus an extra-charge rate addendum. We show that this latter addendum is sensitive to the payback Macaulay Duration, a weighted size and timing average. Specifically, the longer the Macaulay Duration, the smaller the extra-charge rate addendum. As a consequence, two general rules to drive EAR close to the lease contract rate roll out, specifically: (1) the payment pattern should be set with a long Macaulay Duration; and (2) the surrender value of the leased good should be put large. As the contract settlement is given, we show that EAR is delimited by a lower bound and an upper bound. Then the payback amortizations with fixed instalments are studied. To get insight on the importance of EAR inputs we roll sensitivity analysis out through illustrative applications. The results of the paper are useful to provide policymakers a better knowledge about the effects on EAR of the contract conditions on the pattern of payments.