Measuring Lease Yields with a Hybrid PVBy David Holmgren
For the purposes of this article, please click here to refer to two charts.
The depreciation allowances that Congress recently liberalized for economic stimulation have refocused attention on the need for a sound method for calculating an after-tax yield. Many of the difficulties surrounding lease yield measurements have to do with whether the perspective is from the individual pricing the deal or from the organization concerned with overall financial metrics. Of course, there have long been controversies between leasing and non-leasing divisions of financial services companies, with non-leasing groups accusing the leasing groups of using techniques that weren’t standard for the organization (and that perhaps favored leasing) and leasing groups complaining that others did not understand lease analytics. Important rates, such as incremental borrowing rates, discount rates and money cost, figure into leasing metrics, making it critical to choose the rates carefully to reflect the perspective being considered. This article describes an alternative yield that may help to bridge that gap.
Common Lease Yields
Of all the different metrics that lessors use, two have established themselves as regulars: the Multiple Investment Sinking Fund (MISF) and the Internal Rate of Return (IRR) of Pre-Tax Cash Flows (PTCF). For decades, the MISF has been the preeminent method for measuring after-tax lease yields. It is standardized, well understood by lessors, independent of organization-specific rates such as discount or debt rates (although it does require the tax rate) and capable of producing a single yield on a stream of complex after-tax cash flows with multiple sign changes. The IRR is simple and facilitates comparisons with non-leasing operations and investments.
Each of these has its disadvantages, however. The MISF assumes that the tax benefits received early in a lease are equivalent to cash, which is the case if they reduce cash outflows for other, new leases—realistic only if a company has an ongoing stream of new business. However, in an isolated transaction, tax benefits are only income deferrals, not cash refunds. Various methods have been proposed over the years to correct for the MISF shortcoming that it values the tax benefits at “full value” (equivalent to cash). The shortcoming of the IRR, on the other hand, is that it does not capture taxes at all. Perhaps the fact that both have persisted for so long indicates that neither is perfect on its own, but that in tandem they are helpful in portraying lease profitability.
Tax Benefits & Tax Payments
For purposes of this article, we’ll consider the taxes in a lease to comprise the tax benefits (occurring early in the lease, due to the large deductions for depreciation and sometimes interest) and tax payments (occurring later in the lease, due to the residual income and the declining deductions).
The pre-tax cash flows are clear and unquestioned; even the taxes and therefore the after-tax cash flows are agreed on. The tax payments occurring later in the lease are not controversial, as they are treated as cash by the yield calculation. The difficulty is valuing the tax benefits, or in finding a yield which values them appropriately for the purposes of the user.
Replacing Taxes with a Present Value
Now let’s consider replacing the taxes with a present value equivalent, using the following sample case: $1,000,000 equipment cost, 5-year lease term, level quarterly rents of $45,000, 5-year Modified Accelerated Cost Recovery System (MACRS) depreciation, 30% residual, and a 35% federal tax rate. For simplification, we use January 1 as delivery date with the first rent paid in arrears on March 31. The taxes are scheduled as four equal payments on the same dates as the rents, avoiding complexities with compounding. The total transaction PTCF is $200,000; total taxes are -$70,000; total ATCF is $130,000. This case produces a classic pattern: three years of benefits, followed by two years of payments.
The PV method finds a present value equivalent of all taxes, both benefits and payments (Chart 1). The base rate is the IRR that discounts the after-tax cash flows to the equipment cost (4.1922%). The taxes are split into two blocks, benefits and payments. Using the base rate, each amount is discounted and the sum is loaded in on delivery date. It is important to note that the hybrid rate on the resulting stream equals the base rate. This confirms that for yield purposes, we can replace the taxes with the PV of all the taxes.
The Hybrid PV Method
This separation of benefits and payments offers the interesting opportunity of discounting them at different rates, thus the name hybrid PV. The rate for the benefits is the benefit rate, the rate for the payments is the payment rate, and the resulting yield is called the hybrid IRR. As we set the discount rate higher, the present value drops, providing control over the value of the tax benefits. The user can certainly specify the benefit rate directly, but perhaps more interesting, the user can specify the share of the tax benefits to recognize. This is achieved easily by multiplying the base rate by the reciprocal of the desired share. For example, to recognize 70% of the benefits with a base rate of 4.1922%, a benefit rate of 6.45% (4.1922%/0.7) would be used.
Inasmuch as the resulting hybrid cash flows are well structured (i.e., a single negative followed by positives), the IRR will have no difficulty arriving at a unique yield. This avoids the IRR’s inherent weakness (which in part propelled the MISF to predominance) with cash flows of changing signs. The user has full flexibility of valuing the tax benefits, depending on organizational preferences or policies. Chart 2 shows the same transaction, modified to recognize 70% of the tax benefits. Note the benefit rate of 6.4496% and the correspondingly lower hybrid IRR of 4.1326%.
The resulting hybrid IRR is an after-tax yield, so it needs to be converted to its pre-tax equivalent by dividing by (1 – composite tax rate) to compare the lease to investments that are measured with pre-tax metrics. At a 35% composite tax rate, 4.1326% after-tax is equivalent to 6.3578% pre-tax.
The hybrid IRR method can bring value to organizations active in both lending and leasing which have struggled to find a common metric. It offers a convenient, easily understood, and flexible way to value the tax benefits in a lease. It does not remove the subjectivity of the discount rate, but allows analysts to experiment with different scenarios and arrive at a solution acceptable to multiple operating groups within an organization. If an organization can settle on a certain value of the tax benefits (perhaps reviewed periodically), then the hybrid IRR could serve the purpose of what formerly required two yields.