A comprehensive lease/purchase model

(Equations 23 and 24 omitted)

Note that for t* = 0, (23) and (24) reduce to the basic model (6) and (7) when R sub r = R sub e = R. If losses can be carried forward hen the excess carry forward losses (CFL) of the buy alternative over the lease alternative during the first t* periods is Sigma(D2 sub t + I sub t - L sub t ), and the PV of the tax credit differential will be T sub e x CFL x R sup t*+1 . Subtracting this quantity from the C sub b - C sub L expression as given by the difference between (23) and (24), substituting D sub t = P sub t = V/n and rearranging terms results in the following expression fully derived in Appendix A:

(Equaiton 25 omitted)

Eq. (24) implies that Delta increases with T sub e and independent of T sub r ; for t* = 0, Delta = 0, as in the basic model. Dependency on T sub r , however, will exist when the assumption of D sub t = P sub t is relaxed. In this case of t* > 0 , it can be shown that Delta > 0 for any t*. That is, when the lessee has no revenues from other activities in the first t* periods of the lease agreement (under which case he pays no taxes), but starts to have positive profits afterwards this will make leasing more attractive. The intuition behind the two results -- for the lessor and the lessee, is the same. The lease agreement is characterized by decreasing tax shelters for the purchaser (the lessor) and a constant tax shelter for the user (the lessee). Therefore, it will be advantageous for the lessor to pay taxes at the beginning of the lease agreement (when he actually saves taxes) and not to pay at the end. The opposite holds true for the lessee. Clearly, when the two effects are combined the advantage of leasing, as given by (22) and (25) is even greater. This result is obviously strengthened by accelerated depreciation.

The preceding analysis regarding the impact of intertemporal changes in tax rates on the lease vs. buy decision is given for a certain value of t* -- the point in time in the future at which the tax position changes. In reality, however, each party has some sort of subjective probability distribution of t*. Given such a distribution, the expected value of Delta, as given by Eqs. (22) or (25), will be

(Equation omitted)

leaving the basic results essentially unchanged because Delta >= 0 for t* > 0. Needless to say, however, such probability distributions can affect both the size of as estimated by each party, and the allocation of between the two parties.

For a reasonable range of parameter values, Appendix B presents the effects on of intertemporal changes in tax rates as well as other factors of the leasing issue.

CONCLUSION

This paper derives formal expressions for the net advantage of leasing over buying (NAL), Delta, for different characteristics of the leasing issue. The basic model is expressed in terms of a tax rate asymmetry between the lessor and the lessee because this type of asymmetry is the most common and important in the leasing context. The basic model then is extended to derive formal expressions for the NAL in the presence of positive salvage value, varying financial leverage rates, inflation, and different discount rates. An additional major extension of the model is the incorporation of intertemporal changes in tax rates.