Revisiting The Standard Lease Valuation Model: Necessary Conditions, Asset Characteristics, And Contract Provisions.
James A. Miles
Professor of Finance
Department of Finance
Smeal College of Business
Penn State
University Park, PA 16802.
(814) 863-3565
John R. Ezzell
Professor of Finance
Department of Finance
Smeal College of Business
Penn State
University Park, PA 16802.
(814) 863-7969
Premal P. Vora[(]
Assistant Professor of Finance
Penn State Harrisburg
777 W. Harrisburg Pike
Middletown, PA 17057.
(717) 948-6148
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Revisiting The Standard Lease Valuation Model: Necessary Conditions, Asset Characteristics, And Contract Provisions.
Abstract
We revisit the standard model for valuing lease contracts to explore the necessary conditions it implies for a lease to have a non-negative net tax advantage. We conclude that it is the interest tax savings related to the debt supported by lease payments that are necessary for the lease to have a net tax advantage, not the transferred depreciation write-offs. We demonstrate that asset characteristics and contract provisions also have an effect on the net tax advantage of a lease. Because asset characteristics and contract provisions have implications for the agency effects of leasing, our analysis demonstrates that an interaction exists between the tax and agency effects of leasing.
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Revisiting The Standard Lease Valuation Model: Necessary Conditions, Asset Characteristics, And Contract Provisions.
More than twenty-five years have passed since what is now considered to be the textbook or the standard model of valuing lease contracts was published by Myers, Dill, and Bautista(1976). Although a number of innovations in valuing lease contracts have subsequently appeared in the literature (see, for example, Franks and Hodges (1978) and Lewis and Schallheim (1992)), the popularity and resilience of this model is testimony to its intuitive structure, flexibility, and ease of use.[1] Despite this popularity, little has been written about the necessary or sufficient conditions that are implied by the model for leasing to have a net tax advantage. We explore this question and arrive at some novel and interesting—even surprising—conclusions.
The standard model implies that lease contracts between lessees and lessors having the same tax rate cannot be explained in terms of a tax savings motivation.[2] When the lessee and lessor are taxed at different rates, this model is commonly understood to mean that some assets are leased because of the tax savings on the depreciation write-offs that lease contracts transfer from low tax rate lessees to high tax rate lessors. We demonstrate in this paper, however, that the transferred depreciation write-offs are never sufficient for lease contracts to have a net tax advantage. Further, we demonstrate that the standard leasing model actually implies it is the interest tax savings on the debt capacity that a lease contract transfers from the low tax rate lessee to the high tax rate lessor that are necessary for leasing to have tax advantages, i.e., unless the lessor levers the lease it is impossible for the contract to have a net tax advantage. The necessity of the interest tax savings in explaining why some assets are leased instead of purchased has been obscured by the emphasis the literature commonly places on the depreciation tax savings benefit (Brealey and Myers (2003, p. 731), Brigham and Ehrhardt (2002, p. 788), Grinblatt and Titman (2002, p. 524)).
Further, while the value of the depreciation tax savings depends mainly on the tax code, the value of interest tax savings depends critically on such economic asset characteristics as asset life, cash flow timing and risk, the magnitude and risk of salvage value, and on such lease contract provisions as lease payment schedules, penalty clauses, asset use restrictions, tie-in sales, metering and maintenance clauses. However, asset characteristics and contract provisions also have implications for the agency effects of leasing. Thus, our analysis demonstrates that an interaction exists between the tax and agency effects of leasing. Prior literature on leasing has failed to recognize this interaction as a possible source of gains from leasing.[3]
Our exploration and analysis of the model’s implications is useful to the equipment leasing industry (lessees, lessors, brokers, etc.) and to academia (business faculty and students). It is useful to the equipment leasing industry because it addresses prior misconceptions about the source of the tax advantage of leasing and it provides insights into structuring a lease in a way that maximizes its tax advantage. It is useful to academia—in addition to both of the reasons cited for the industry—because our analysis of the standard leasing model finally gives an intuitive explanation of why the net tax advantage to leasing is negative for a number of textbook problems. We also discuss what parameter changes in these problems are likely to produce a non-negative net advantage.
The paper proceeds as follows: In Section I we show that the lessor’s unlevered net advantage to leasing (NAL) is necessarily negative. In Section II we show that interest tax savings on debt supported by the after tax lease payments is necessary for the lessor's NAL to be non-negative and that the magnitude of the interest tax savings depends on the time pattern of the lease payments. In Sections III and IV we consider the effects of various asset characteristics and lease contract provisions on the magnitude of interest tax savings on lessor debt. We conclude in Section V.
I. The Unlevered Gain from Leasing
We begin this section with our analysis of the standard leasing model which demonstrates that when the non-taxpaying lessee’s NAL is zero, the taxpaying lessor’s unlevered NAL is necessarily negative. We make the non-taxpaying lessee’s NAL zero so that no room exists for increasing the lease payment to increase the taxpaying lessor’s NAL—any increase in the lease payments would render the lease unacceptable to the lessee because it would make the lessee’s NAL negative. We assume in this section that the salvage value of the leased asset is zero, the lessee is responsible for maintaining the asset, and the maintenance costs are independent of the lease-purchase decision. In the section dealing with asset characteristics and contract provisions we examine the effect of salvage value and maintenance clauses on the tax gains from leasing.
To specify the lessor’s unlevered NAL, we let
Lt = the time t lease payment
Dt = the time t depreciation tax deduction
A = the asset's initial cost
r = the discount rate on riskless cash payoffs
t = the corporate income tax rate
n = the term of the lease
m = the depreciable life of the asset.
The taxpaying lessor’s unlevered NAL, is
NALLessor, Unlevered= / (1)Equation (1) shows that the lessor receives taxable lease payments and depreciation tax deductions in exchange for the asset's initial cost. The terms in equation (1) can be regrouped as follows:
NALLessor, Unlevered / (2)Equation (2) partitions the effects of the lease contract into a non-tax component (the terms in the first set of parentheses) and a tax component (the terms in the second set of parentheses).
Since the lessee pays no taxes, a break-even lease contract to the lessee implies that the present value of the lease payments is equal to the asset's initial cost or
/ (3)Equation (3) implies that equation (2) can be rewritten as
NALLessor, Unlevered / (4)Thus, the non-tax component of equation (2) is zero while the tax component must be negative because and, hence, the present value of depreciation deductions is always less than the initial cost of the asset. Therefore, the unlevered NAL to a taxpaying lessor is negative if the lease is a break-even transaction to a non-taxpaying lessee, and no adjustment to the lease payment schedule will produce non-negative NALs for both parties. Since the present value of the lease payments is necessarily greater than the present value of the depreciation deductions, the tax advantage of the depreciation deductions to the lessor are always dominated by the tax liability on the lease payments. Hence, the depreciation write-offs allowed on a leased asset to a taxpaying lessor can never produce sufficient tax savings to explain why that asset was leased instead of purchased.
We illustrate this result in the context of the Nodhead College problem (Brealey and Myers (2003, p. 748)):
Nodhead College needs a new computer. It can either buy it for $250,000 or lease it from Compulease. The lease terms require Nodhead to make six annual payments (prepaid) of $62,000. Nodhead pays no tax. Compulease pays tax at 35 percent. Compulease can depreciate the computer for tax purposes over five years. The computer will have no residual value at the end of year 5. The interest rate is 8 percent.
Under the terms specified above, the lessee’s NAL is
NALLessee = +$250,000 – = –$59,548, while the lessor’s unlevered NAL is
NALLessor, Unlevered = = $21,079.[4] The net tax advantage to leasing (the sum of the net advantages to the lessee and lessor) is –$59,548 + $21,079 = –$38,469. Although this lease is acceptable to the lessor, it is clearly unacceptable to the lessee.
In Figure 1 we plot the lessee’s NAL, the lessor’s unlevered NAL, and the net tax advantage against a level lease payment that varies from $46,000 to $62,000 per year. As the lease payment decreases, the lessee’s NAL rises. It can be shown that at a lease payment of $50,073 the lessee’s NAL is zero, but the lessor’s unlevered NAL is –$17,628. While decreasing the lease payments further will increase the lessee’s NAL, the lessor’s unlevered NAL will become more negative. Thus, there is no level lease payment schedule over five years (prepaid) that would be acceptable to both the lessee and the lessor assuming that the lease is unlevered.
II. Leasing with Debt Financing
When corporate taxes are the only market imperfection, a riskless levered cash flow stream i can be correctly valued if its unlevered component is discounted at the leverage adjusted rate, where Gi is the market value of the debt supported by stream i expressed as a fraction of stream i’s levered market value, i.e., Gi is the market value leverage ratio.[5] For a riskless cash flow stream, we assume that Gi=1, i.e., the firm borrows 100 percent of the levered value of the cash flow stream. We now demonstrate that the present value of the interest tax shield generated by depreciation write-offs is insufficient to make the NAL of the lease non-negative.
The standard leasing model implies that the lessor’s levered NAL can be expressed as
NALLessor, Levered
where . However, the levered NAL to a lessor can also be expressed as a function of the unlevered NAL:
NALLessor, Levered= NALLessor, Unlevered + PVTS(L) + PVTS(D) / (5)where PVTS(L) and PVTS(D) are, respectively, the present value of the interest tax shields on debt supported by the lease payments and the present value of the interest tax shields on the debt supported by the tax savings on depreciation. The present value of the interest tax savings on debt supported by the depreciation tax shield is the difference between the levered and unlevered values of the present value of the depreciation tax shields. Therefore,
PVTS(D) / (6)Likewise, the present value of the interest tax savings on debt supported by lease payments is the difference between the levered and unlevered value of the present value of the lease payments. Therefore,
PVTS(L) / (7)By substituting equations (4) and (6) into (5), NALLessor, Levered can be expressed as
NALLessor, Levered = PVTS(L)
where the second term on the right hand side is NALLessor, Unlevered + PVTS(D). Because the value of the annual depreciation write-offs discounted at the levered rate r* is less than the cost of the asset, NALLessor, Unlevered + PVTS(D) is always negative. Therefore, even when depreciation tax savings are used to support debt, the lessor’s NAL is negative unless PVTS(L) is sufficiently large to offset the negative value of NALLessor, Unlevered + PVTS(D). In lease contracts that are structured largely due to tax considerations, if the net tax advantage is negative, it is likely that PVTS(L) is not large enough to offset the negative value of NALLessor, Unlevered + PVTS(D).
We now illustrate this result with further analysis of the Nodhead College problem. We previously found that with a lease payment of $50,073, NALLessee = 0, while NALLessor, Unlevered = –17,628. From equation (6),
PVTS(D) = = $5,476.
The sum of NALLessor, Unlevered and PVTS(D) = –$17,628 + $5,476 = –$12,152. In order for NALLessor, Levered > 0, PVTS(L) must be greater than $12,152. From equation (7),
PVTS(L) = = $10,185.
Clearly, PVTS(L) is not large enough to offset the negative value of NALLessor, Unlevered + PVTS(D) and the lease results in NALLessor, Levered = –$1,967 (–$12,152 + $10,185 = –$1,967).[6]
III. Asset Characteristics and Contract Provisions
A. The Lease Payment Schedule
Any number of lease payment schedules satisfy the condition in (3) implied by the assumption that the non-taxpaying lessee’s NAL is zero. Suppose a portion Dj of lease payment Lj is deferred k periods. Lease payment Lj+k will increase by Dj(1 + r)k to satisfy the assumption that the tax-exempt lessee’s NAL is zero. However, the change in the lessor’s NAL is
DPVTS(L)
=
where
Because Rk increases with k, the present value of the interest tax shields on debt supported by the after tax lease payments increases with both the size of the deferral, Dj, and the number periods it is deferred, k. The intuition of this result is that deferring an unlevered cash payment extends the number of periods in which it supports debt and, therefore, generates interest tax savings. When the unlevered value of the cash payoff is preserved the extended stream of interest tax savings has a greater present value than the original stream.[7]