A comprehensive lease/purchase model

(Equations 2 through 4 omitted)

which is the PV of the break-even lease payments to the lessor. Using the annuity formula (Equation omitted) and inserting it into the LHS of Eq. (4) yields:

(Equation 5 omitted)

where (characters omitted) is the break-even lease rate for period t.

From the lessee's view point, the least-cost alternative (leasing or buying) will be preferred. The PV of the leasing alternative (C sub L will be:

(Equation 6 omitted)

which is the after tax PV of the lease payments, and where T sub e is the lessee's relevant tax rate, R sub e = (1 + r sub e ) sup -1 , and r sub e , is the lessee's discount rate. The cost of the buy alternative (C sub b ) is the purchase price of the asset minus the interest and depreciation tax shields, i.e.,

(Equation 7 omitted)

The advantage of the leasing over the buying alternative, or, equivalently, the net advantage of leasing (NAL), Delta, will be given by C sub b - C sub L . Substituting (7) and (6) for C sub b and C sub L respectively, adding and subtracting (Equation omitted), and following the same procedure as above yields

(Equation 8 omitted)

Substituting (characters omitted) from (5) for L sub t into (8), and using again (Equation omitted), we get

(Equation 9 omitted)

Eq. (9) is the model's basic lease valuation formula.

To focus solely on the consequences of a discount-rate asymmetry it will further be assumed that a symmetry in all other aspects including the tax rate exists. Thus, when both the lessor and the lessee are subject to the same tax rate, T sub r = T sub e = T, and Eq. (9) reduces to:

(Equation 10 omitted)

Note that Delta = 0 when a discount rate symmetry (R sub t = R sub e ) exists. When R sub r -= R sub e Eq. (10) demonstrates that Delta 0 as r sub r >/

In practice, for some sectors of the leasing industry (such as automobiles), second only to the classic tax-rate differential as a determinant for leasing economy is a differential in average rate of return (MARR). In the U.S., for example, many automobiles leased to private citizens whose benefits from the automobiles are untaxed (thus providing a strong classic leasing incentive from the fact that the depreciation shield is available only to the lessor) are leased not for the classic reason but basically because the lessor can borrow more cheaply than the lessee could. It is usual for a potential lessor to expect to earn a greater rate of return than the cost of borrowed money (r) (i.e., MARR > r), and a potential lessee can either be a saver with a very low MARR or a consumer-debt debtor with a MARR in the same range as that for corporations. An analysis of MARR asymmetry in conjunction with a discount rate asymmetry is relevant to a lease/purchase economy in the case in which the differences between the MARR and r values of the lessor and the lessee are substantial. In such a case, a lease/purchase analysis which incorporates both the MARR and r asymmetries is undoubtedly an important topic for future research.

It should be noted that the basic model implicitly assumes that the depreciation schedule is the same for both lessor and lessee. Often the lease/ purchase decision is influenced in favor of leasing by the lessor's being able (via more complete recordkeeping, accounting effort, and negotiation with the tax authority) to use, with full approval, more favorable depreciation schedules than the lessee could use. Regardless of relative tax rates, if the lessor can depreciate the asset enough faster than the lessee can, the lessor/lessee combination derives a net gain at the expense of he tax authority, so that by proper pricing of the lease both parties can benefit. An extension of the basic model which incorporates a depreciation-schedule asymmetry clearly can be an interesting and relevant issue in future research.