A CONTINGENT-CLAIMS VALUATION OF ALTERNATIVE LEASING CONTRACTS

JAMES STANLEY SCHALLHEIM, Purdue University

Abstract

Leasing has long been a topic of considerable interest to the financial community. In addition, the volume of leases has grown enormously in recent years. However, the lease valuation models developed by finance academics differ substantially. In addition, typical models applied to actual leases have led to the conclusion that leasing is a result of market imperfections or inefficiencies. This study addresses these issues through the development of a valuation model for risky leases. One basic issue that has led to different valuation models of leases is the "equivalent" debt notion. Many have argued that the lease contract is equivalent to a term loan. By attempting to address this issue, it is made abundantly clear that very distinct types of leases exist in practice. After categorizing several different types of leases, each type is shown to be equivalent to other types of financial securities, including, in particular, options. Then each type of lease is compared to debt and equity. One result of this analysis is that a very simple one-period is equivalent to neither debt nor equity. Another result concerning the multi-period lease establishes that the lease contract is equivalent to a specific type of loan. Under specific assumptions, the debt contract which is equivalent to the lease contract can be characterized as "riskier" than "normal" debt. Thus, some lease contracts are equivalent to certain debt securities, providing an analytical basis for the equivalent loan concept. After establishing equivalent securities to the lease contract, this study derives valuation equations for each type of lease. The valuation process begins with the derivation of a single-period, equilibrium lease payment with payment made at the beginning of the period. The valuation of the option to purchase the leased asset and the option to extend the lease are valued using the Option Pricing Model. Combining the value of the options with the beginning-of-period lease payment, contingent-claim valuation models for different types of leases are constructed. The valuation of the long-term (multiple payment) lease is more complicated, but begins with the valuation of the option to extend the lease. The value of each future lease payment can be considered an option to extend the lease. In addition, each preceding lease payment purchases not only the use of the asset over a period, but also purchases the option to extend the lease by making the next lease payment. Using the Geske Compound Option Pricing Formula, the contingent-claim valuation of the long-term lease is accomplished. Having derived a general valution model for risky leases, the next step is to use the model to address some very important issues in leasing. In particular, empirical studies on leasing suggest that the yields in leases are "high". In fact, the model developed in this study is used to illustrate that "high" yields can be computed on leases where the equilibrium lease payments are derived under perfect market assumptions. In addition, the yield on a lease is shown to decline as additional periods (and lease payments) are added. According to the yield criteria, the longer-term lease may appear as a better "deal." In actuality, all leases in the example are constructed to have a zero net present value. In sum, the yield appears to be misleading when used in the evaluation of leases.

Degree

Ph.D.

Subject Area

Management

COinS