Reprinted from Equipment Leasing / Leveraged Leasing, 4th Edition, by Ian Shank and Arnold G. Gough. Copyright 1999 by Practising Law Institute. Published by Practising Law Institute, 810 7th Ave., New York, N.Y. 10019. Reprinted with the permission of the Publisher.

Chapter 6


By James C. Ahlstrom and Iris C. Engelson

6.1 Introduction

A leveraged lease generally involves the acquisition of an item of capital equipment for a period equal to most, but not all, of the equipmentís anticipated economic life and the sale of the residual value and the tax benefits of ownership to another party in exchange for a lease rate that is lower than the debt rate that would have applied to a purchase of the equipment. Although a leveraged lease is a rather complex form of financing with documents that are measured in inches rather than pages, its particular economics arise from only three of its features: (a) the involvement of three parties: a lessor, a lessee, and a lender who provides (b) non-recourse debt at a (c) substantial degree of leverage. Firstly we will consider leveraged leasing from the point of view of the lessor (owner) to find out why it chooses to own equipment that will spend most of its life in someone else's employ, how it analyzes its return, and how it chooses the leverage and debt amortization schedule. Next, we will look at the transaction from the lessee's viewpoint to understand why the lessee chooses to rent, rather than own, its equipment. Finally, we will look at lessee lease-buy analysis.

6.2 The Classic United States Leveraged Lease

Let us consider a fifteen year lease of new equipment with a tax life of seven years. Let us assume the equipment costs $1 million, and the lessor wishes to purchase it with $200,000 of its own cash and $800,000 borrowed from lenders at 7.5 percent interest. The lessor assumes that it sells the equipment for $200,000 (the residual value). The lessee has an early buyout option (an "EBO") after ten years. The lessor pays a fee of $5,000 to the broker. Immediately upon purchase, the lessor will lease the equipment to the lessee for fifteen years. Rents are paid on the same day the debt services are due, and the rents always are sufficient to pay debt service. The rents and debt services have been calculated using optimization techniques (see below).

The most important feature of the loan to the lessor is its non-recourse nature. That is, the lender agrees that the lessor is not personally liable for repayment of the loan and that the lender will look only to the rent received from the lessee for repayment. To secure this type of loan, the lessor must assign its interest in the lease to the lender. Rent and other payments made under the lease go directly to the lender (or its agent) and debt services due are deducted before the difference (if any) is sent to the lessor. The lessor also must give a first mortgage of the equipment to the lender.

The effect is substantially to remove the credit of the lessor from the transaction. The lessor will not record the loan as a liability nor the equipment as an asset for financial reporting purposes. However, the lessor will report the cash investment as an asset and the deferred taxes as a liability.

Because the lessor, not the lessee, has borrowed the money on a non-recourse basis, the lender must look to the credit of the lessee for repayment of its loan. Thus, if rents are not paid and therefore the loans are in default, the lender may claim damages only against the lessee through the lease because the obligation to pay rent is in the lease. However, because the lender does not sign the lease, its claim depends on the lessor's assignment of its rights under the lease to the lender. The lender may also claim title to the specific equipment subject to the lease. Since the lender will have lent no more than 80 percent of the equipmentís cost, it has a favorable collateral ratio. As a practical matter, in the event of a lessee bankruptcy, the trustees have often elected to continue lease payments rather than risk the loss of the equipment.

6.2.1 Before-Tax Analysis

The first step in the economic analysis of this lease is to calculate the amount of the lessor's investment. The lessor has invested $200,000 in cash, has paid a brokerís fee of $5,000 and has borrowed $800,000 on a non-recourse basis. Is its investment $205,000 or $1,005,000? In this regard, the importance of the non-recourse nature of the debt cannot be over emphasized. Had the lessor borrowed the $800,000 from its bank and bought the equipment, all the cash flows would be the same, including the cash flows arising from the tax aspects of ownership, but then the lessor's investment would be the purchase price of the equipment plus fee, the lease would not be a leveraged lease, and the economic analysis would give drastically different results. If an ordinary leveraged lease were analyzed in terms of recourse loans, the economic yield to the lessor would be minuscule. In our example, the lessor's investment is $205,000 which equals the equipment cost plus brokerís fee less the amount of non-recourse debt.

We now have the lessor's investment of $205,000 and the before-tax cash flows from the lease consisting of the excess of rent over debt services of $88,477 and the residual value of $200,000 (see section 6.9.2). By ordinary present worth techniques, we can calculate the yield to be 2.519 percent per year. The "multiple investment sinking fund" method of analysis discussed below would provide the same result. This rate of return is lower than the debt interest rate, indicating an inferior rate of return for the lessor. Lessors generally require a return rate higher than the debt rate to compensate for the greater risk arising from the lessorís secondary credit position (the lenders have the first mortgage) and the uncertainty that the residual value will be as large as assumed. In the foregoing example, the yield would be zero with a residual value of $116,523 and the lessor would suffer a loss with a lower residual value.

The foregoing result demonstrates that a leveraged lease provides an unsatisfactory rate of return when analyzed without including the tax aspects of equipment ownership. This result arises from the fact that lease rates on the leveraged leases are lower than debt rates on the loan. From the point of view of the lessee, this is the main motivation to lease, rather than purchase, the asset in the first place. Accordingly, we will now discuss the modifications to the lessor's normal tax payments that occur as a result of the lease.

6.2.2 Tax Benefits

Current tax law in the United States subsidizes the purchase of new capital equipment for tax paying companies. Since 1980, we have seen large and rapid changes in the amount of tax benefits available. The Economic Recovery Tax Act of 1981 introduced the Accelerated Cost Recovery System ("ACRS"). Under this system, assets had a tax life of 3, 5, 10 or 15 years. Most leased equipment had a tax life of 5 years. An Investment Tax Credit ("ITC") was available, and the purchaser of new equipment was entitled to deduct 10 percent of the equipment price from its taxes for the year in which the equipment was placed in service. The Tax Equity and Fiscal Responsibility Act of 1982 reduced the ITC benefit available. The Tax Reform Act of 1986 (the "1986 Act") repealed the ITC except for a limited amount of transitional property. Depreciation schedules were changed and two new tax lives were added. Tax rates were lowered from 46% to 34%, and many base broadening proposals were introduced. Corporate tax rates are currently (1997) 35%. See the other chapters in this book for a more detailed description of the 1986 Act.

Our example will be calculated using the current tax rules. The meaning of the economic analysis does not change when other tax assumptions are used, although the exact tax numbers do change.

The only real tax benefit available to purchasers of new equipment under the 1986 Act is an accelerated depreciation deduction. This confers a benefit provided that the lease term for the equipment is longer than its depreciable life, because substantial taxes would then be deferred. For our lease, the deduction available the first year is $142,857 and the deduction available the second year is $244,898. Our example assumes a basis of $1,000,000 and a seven year tax life. These depreciation deductions are of value to the lessor only if it has income from other sources in excess of these deductions and if the lessor is not subject to the Alternative Minimum Tax. If this is the case, the lessor will pay $50,000 less in taxes the first year and $85,714 less in taxes the second year (at a 35% rate). The amount of taxes saved declines thereafter.

The timing of the tax savings is the relevant benefit in leasing, not the change in total tax liability. The brokerís fee is amortized on a straight line basis over the life of the lease. The other tax benefit available from our lease is the deduction for interest on the loan, which amounts to $60,000 in the first year. The rents paid by the lessee are the fully taxable income of the lessor. The taxable income of the lessor for each year of the lease is shown in section 6.9.1. Under the assumption that the lessor pays substantial taxes each year (including future years), the negative tax payments in the last column are treated as cash inflows. Note the general pattern: taxes are reduced in the first years of the lease and are paid in later years. This pattern is a general feature of leveraged leases, and the benefit will show up in any sort of present value analysis. The tax payments are shown in an annual table. The actual date on which the payments are made depends on the lessor's tax payment method. For a calendar-year corporation, payments of estimated tax are made on the fifteenth day of April, June, September, and December. Any additional tax due is paid on the fifteenth day of March of the following year. Penalties are prescribed for insufficient payments of estimated tax. The table assumes that the lessor pays 100% of its tax liability on a current basis. The yield obtained may be very sensitive to the exact amount of taxes saved on each tax payment date, especially during the first year. This in turn depends on the tax planning and management of the lessor.

6.2.3 After-Tax Yield

We now have all the information needed to calculate the lessor's yield on its investment, namely the amount of its investment and the cash flow due to the investment. The cash flow is shown in section 6.9.2 by year and is equal to the rent plus the residual value less the debt service less the taxes.

The first point of interest in the above cash flow is the rapid return of the investment. The investment is returned by the fifth year and, in fact, cash over and above this amount is paid to the lessor through 2004. Thereafter, the payment of taxes reduces the lessor's cash position until it finally remains with a profit of $54,260 at the end of the lease term.

The usual method used for obtaining the yield on a leveraged lease is the "multiple investment sinking fund" or "MISF" method. This method is very similar to the usual internal rate of return method, but it uses one rate (the yield rate) for the investment stage and another rate (the sinking fund rate) for the sinking fund stage. The MISF method provides the same result as the internal rate of return method when there is only one rate used for two stages in a transaction. Therefore, the MISF method is a generalization of the internal rate of return method rather than a completely new and different method of analysis.

The yield found from the MISF method is the yield on the lessor's investment while the lessor has an outstanding investment (as opposed to a sinking fund). That is, the yield rate when multiplied by the investment outstanding from time to time will equal the lessor's earnings. If, during the lease, the lessor's investment is repaid, and if a sinking fund develops due to the further receipt of cash, the investment balance will be zero and the sinking fund will earn interest at a specified rate, called the sinking fund rate. The sinking fund earnings are compounded back into the sinking fund. When the cash flow eventually becomes negative due to tax payments, these payments will be made from the sinking fund until its balance is reduced to zero. If any further negative cash flows remain, they will be met by further investments by the lessor and the investment balance will increase and accrue earnings at the yield rate. The yield rate is the rate at which both the investment balance and sinking fund balance are zero at the end of the lease. In practice, there may be several investment stages and several sinking fund stages in a single lease analysis depending upon the details of the cash flows.

The calculation for our example is shown in section 6.9.3 on a monthly basis for the first two years of the lease term. The investment in the first month is $205,000 less the advance rent received of $1,735, or $203,265. The earnings of $1,186 in the first month are derived from the investment balance of $203,265 multiplied by the after-tax yield of 7.000% divided by twelve months. Subsequent earnings are calculated in the same way until a sinking fund is established in 2004. At that point, the earnings for the month in which the sinking fund occurs are zero, and the sinking fund earnings are the sinking fund rate multiplied by the sinking fund balance. These calculations are performed for every month of the lease. Section 6.9.4 shows the annual totals for the full term. The sinking fund rate for this example is zero.

A yield for the forgoing cash flow and investment may be found by the usual "internal rate of return" method that is based on present value. However, the resulting yield would not be accepted as an accurate yield in the marketplace and would be higher than, or equal to, the yield found from the MISF method of analysis. The problem is the correct treatment of the lessor's position when it holds funds in excess of its investment plus profit, that is, the correct treatment of the sinking fund. The usual internal rate of return method would evaluate the sinking fund at the same rate as it would value the investment. That is, during the time that the lessor has a negative cash position (the time immediately after the lessor makes its investment), the internal rate of return method would impute earnings to the investment at the internal rate (the yield rate to be found from the analysis). As the lessor receives cash the investment would be paid back (with earnings) until it would be reduced to zero. As more cash is received, a sinking fund develops, which would earn money (interest) at the same rate. Then, as cash flows become negative, the sinking fund would be depleted until finally, at the end of the lease term, both the sinking fund balance and investment balance would be zero. However, implicit in this analysis is the idea that the lessor can earn a return at the yield rate on surplus funds available for a few years (the sinking fund). The lessor would view these funds as only worth approximately the rates on its bank lines, or perhaps the rates on short-term debt instruments, or typically 3.5 percent per year after tax. Therefore, the lessor would reject the internal rate of return yield as too high. Another objection to the normal internal rate of return analysis as applied to leveraged leases is that it may give rise to more than one yield. However, this objection should be viewed as the mathematics trying to tell the analyst that something is wrong rather than as a basic fault with the method. In any case, our example deal has only a small sinking fund.

Please note that in this yield method the sinking fund is not established to "take care of tax payments." For purposes of analysis, tax payments may be met both by the sinking fund and by further investments by the lessor. In fact, the lessor may actually spend its "sinking fund" as it receives it, and then meet tax liabilities as they come due with its own funds. The division into precise sinking fund and investment stages is a mathematical procedure used to find a yield rate, and the lessor may not have an actual sinking fund. However, the lease may temporarily give the lessor cash in excess of its investment plus inherent profit and the lessor may invest these funds while it has them. Therefore, the concepts of a "sinking fund" and "sinking fund rate" are pertinent, even if the exact sinking fund flows used in finding the yield are never achieved or even attempted. The yield derived from the multiple investment sinking fund method has certain desirable mathematical and logical features that recommend its use and the leveraged lease marketplace regards this yield as one of the pertinent measures of lessor return. Statement of Financial Accounting Standards No. 13 ("SFAS No. 13") specifies the multiple investment sinking fund method as the recommended method for recording book earnings except that a zero sinking fund rate must be used.

Apparently, the yield the lessor receives from the lease depends upon the sinking fund rate chosen for the analysis, and ultimately the real yield obtained depends upon the lessorís ability to utilize the surplus funds that become available as a result of the lease. In the past, lessors typically evaluated a lease at a sinking fund rate of zero, and again at a rate of 3.5 percent per year after tax. Currently, the use of a zero sinking fund rate is nearly universal due to four main reasons. First is the requirement of a zero sinking fund rate for reporting book earnings. Second is the loss of the Investment Tax Credit, which delays the repayment of the lessorís investment from tax benefits. Third is the larger residual value assumptions which result in a substantial lessor investment at the end of the lease term and thus less time in the middle of the lease term for a sinking fund to develop. Fourth is the use of optimization methods which seek to adjust rent and debt service to maximize economic benefit. Because the sinking fund rate will always be less than the yield rate and usually less than the debt rate, this has the effect of devoting cash flows to the lessorís investment and debt balance and thus minimizing the amount of the relatively less valuable sinking fund.

6.2.4 Before-Tax Yield

Because the yield on an investment in a leveraged lease is calculated in terms of the after-tax cash flows, the "before-tax yield" is a misnomer. As discussed above, the actual yield calculated on the before-tax cash flows is a very low number. In the mid-1970ís the after-tax yield described above was used as the "yield" and no before-tax yield was used. At that time, after-tax yields were about 20% per year. When the market became more competitive around 1980, it became common to express the after-tax yield as a before-tax "equivalent" yield by dividing it by one minus the tax rate. That is, at a 46% tax rate, a 10% after-tax yield is "equivalent" to an 18.5% before-tax yield. At the same time the yields fell to half their former levels. The new "before-tax" yields were then about 20%. Lessors must often compete for funds with others within their organizations. It is easier to use a yield which is more similar to the usual interest rate on a loan, rather than to try to explain the method of calculating the after-tax yield. In 1986, Congress changed the tax rates, and lessors were confronted with tax rates which varied from 46% to 34% over the term of the deal. The "gross up" procedure no longer worked, but a new "true" before-tax MISF yield was invented which solved this problem. The solution was to perform the same analysis as the after-tax MISF yield described above, but instead of using an after-tax yield, the before-tax yield multiplied by the (variable) tax rate is used. Currently, most lessors seem to be using after-tax yields again.

6.2.5 Effective Yield

A few lessors restate the after tax yield as an "effective" annual yield. In other words, if $1.00 in a savings account earning 10% (nominal annual) interest compounded monthly grows to $1.1047 in one year, the effective annual yield is 10.47% per year. Although this calculation may make sense for savings accounts, it makes no sense for leveraged leases. The investment balance in a leveraged lease changes throughout each year. Most computer programs calculate the yield on a monthly basis. The resulting yield is multiplied by twelve to produce the "nominal" yield. To convert this number to a higher annual effective yield adds nothing to the calculation. Most computer programs can also calculate the yield on a daily basis. This yield is converted to an effective monthly yield to make it more similar to the usual monthly yield.

6.2.6 Book Earnings

In November 1976, the Financial Accounting Standards Board published SFAS No. 13, which addresses leveraged lease accounting. Since then, the lessor's earnings in a leveraged lease are booked in the same way that the lessor analyzes his yield: earnings are obtained by applying a constant yield rate to its outstanding investment on an after-tax basis. An estimated residual value may be included, but the sinking fund rate used must be zero. The effect of this is to conform the accounting treatment to the economic analysis. In practice, a large part of the lessorís earnings are recognized over the first few years of the lease term.

6.2.7 Sinking Fund Risk

Our example has only a small sinking fund, and consequently the yield is not too sensitive to the sinking fund rate used. The after-tax yield changes from 7.000% to 7.132% when the sinking fund rate is increased from zero to 3.0% after tax. In the past, leveraged leases often had larger sinking funds, and lessors often spoke of a "sinking fund risk"; the risk that the lessor would not in fact be able to realize earnings on the sinking fund (surplus cash position) at the rate it originally assumed when it signed the deal. This risk prompted lessors to evaluate leases on the basis of a sinking fund rate of zero even when the short term debt rates were historically high. The resultant yield was safer (and lower), and the lessor could view the sinking fund earnings as a potential upside factor, rather than assuming their existence at the beginning of the lease term.

6.2.8 Residual Value Risk

The lessor owns the equipment at the expiration of a true lease. The sale price of the equipment at that time is called the residual value. In our example, we assumed that this value was $200,000. In the mid-1970ís, lessors were inclined to bid deals without reference to the residual value and to think of the residual as a potential upside factor. However, lessors often included an estimate of the residual value when booking earnings. Over the years, the leveraged leasing market became much more competitive and the rentals were lowered in recognition of a more reasonable residual value estimate. Many items of equipment have now come off lease, and lessors are developing a track record in residual values.

In 1986, changes to the tax law repealed the Investment Tax Credit and lengthened depreciable lives. The amount of tax benefits in a lease therefore decreased. Consequently, to achieve the same yield, the lessor must increase the rent. In order to preserve business, lessors now use a larger and more carefully estimated residual value. By assuming larger residual values the lessor can raise the rent by a smaller amount and still achieve the same yield even with the reduced amount of tax benefits. Inflation can have a substantial effect on residual value. For a ten year lease term, an average inflation rate of 7.18% per year will double the residual value. For a fifteen year lease term, a rate of 4.73% per year will double the residual value. However, estimating inflation rates is difficult. The risk that the residual value will be less than assumed is now one of the greatest risks in a leveraged lease.

6.2.9 Credit Risk

If the lessee ceases to pay rents, the non-recourse loans will be in default, and the lenders will foreclose on the leased equipment. The amount of money that the lessor would lose must be calculated on an after-tax basis, and would include taxes on income resulting from forgiveness of the lease debt. In our example, the amount of loss is 20.5% in the first year, the amount of the investment. In the last year it is 20%, the amount of the residual value. For intermediate years, the amount of loss is about 27%. The point is that the lessor's credit risk is substantial throughout the lease term. Even for leases with a smaller residual value, the risk amount is high through the middle of the term and only falls at the end.

Note that the risk amount is not the same as the investment balance shown in section 6.9.4. The investment balance is the basis for the yield calculation. The lessor has a substantial risk position until the very end of the lease term, even though the investment has been returned through tax savings by 2002. This is true because the tax savings taken to reduce the investment balance (and raise the yield) are recaptured upon the conversion of the asset. All that really reduces the risk amount is cash from the lessee paid to the lessor (cash paid to the lenders does not help) and receipt of the residual value. This is quite different from a loan. In a loan, the risk amount and the investment balance would be identical, since the amount at risk and the investment both equal the loan principal outstanding. The lessor should be aware that, unlike a loan, the yield does not have any relationship to the risk position. The lessor cannot raise the rent to increase the yield a few points to compensate for risk, as it would if it were lending money. With a loan, the amount at risk is the principal outstanding and increasing the interest rate one percent adds additional income exactly proportional to the principal outstanding and thus to the risk amount. Therefore, the lender receives additional income in proportion to the risk. This simple relationship does not hold true for a leveraged lease. Because the risk amount is relatively constant over much of the lease term, it is more sensible for the lessor to add a constant amount to the rent in compensation for risk rather than to look at the yield.

We find that most lessors think that the yield (however measured) is about the same as the interest rate on a loan. That is, a leveraged lease with a yield of 7% per year after-tax is "like" (if not equivalent to) a loan with the same interest rate. This view may be tempered with considerations such as the different risk posture and the extent to which the yield depends upon the realized residual value.

6.2.10 Tax Rate Change Risk

Because some of the economic benefit of leveraged leasing comes from tax benefits, it is to be expected that changes in the tax law or rates can have a substantial economic impact on a transaction. Careful documentation can minimize the risk of tax law changes, since changes before commitment can give risk to unwinds or price adjustments, while changes after commitment are usually "grandfathered."

Tax rate changes are a real risk of leveraged leasing, a point that was brought home when Congress changed the tax rate from 46% to 34% by the 1986 Act. The previous schedules in our example are all based on the current corporate tax rate of 35%. A tax rate change can be a benefit or a detriment to a leveraged lease depending upon when it occurs. An increase in the tax rate at the "cross-over" (the time when the lease stops showing losses and becomes taxable) will decrease the profit and yield because tax savings taken at a lower rate must be repaid at a higher rate. The opposite is true for a decrease in the tax rate at the cross-over.

Leveraged leases vary in their sensitivity to tax rate changes, and generally the sensitivity is less the lower the leverage because interest deductions are lower and because the changes in cash flow are smaller relative to the investment. In some cases, state taxes can have effects similar to a tax rate change. If the lessor cannot consolidate the lease for state tax purposes, the tax losses will not do any good, while state tax payments still must be made in later years depending upon the state carry-forward rules.

Although lessors' concern has focused on adverse tax rate changes, the 1986 Act resulted in windfall profits for lessors with leases written in the sixties and seventies. These leases were often highly tax-intensive, and the tax rate decrease reduced the tax liabilities of these leases. Furthermore, paragraph 46 of SFAS No. 13 requires that all the gain (or loss) must be recognized "in the year in which the assumption is changed." That is, the lessor must use "catch up accounting," and book the gain (or loss) all at once.

Although the tax rate change risk (or reward) can be substantial for a single leveraged lease, the risk for a portfolio of leveraged leases can be much lower. If at the time of the tax rate change the lessor has some leases in the tax-loss phase and some in the tax-gain phase, the effect of the tax rate change will be decreased. Of course, if the lessor has mostly leases of the same type starting at the same time, this cancellation effect will not occur. The lessor can manage its portfolio to minimize tax rate change effects and also to achieve desirable overall cash flow characteristics.

6.2.11 Tax Base Risk

The lessor also runs the risk that it will not continue to have net taxable income from other business activities in excess of the losses in the early years of the lease term. In this case, the tax losses do not immediately give rise to tax savings, the lessor will be in a tax loss carry-forward situation, and the cash inflows we have assumed will be deferred. The yield will be decreased, and if the carry-forwards expire, the inherent profit will be lower. Clearly, the lessor should consider the effect of its leveraged leases in its overall tax planning.

6.2.12 Alternative Minimum Tax Risk

The 1986 Act added an additional risk to leveraged leasing. The 1986 Act provided for a new type of minimum tax which must be paid if it is higher than the regular tax. Basically, the excess of accelerated depreciation over straight line depreciation in a leveraged lease is an item of tax preference. If the lessor has enough tax preferences from its leveraged leases and other business activities, the lessor becomes a minimum tax payer and the cash flows from sections 6.9.1 and 6.9.2 will not occur.

6.2.13 Termination Values

All leveraged leases provide for a lump sum payment to the lessor in the event of equipment destruction, lessee default, or other early termination of the lease. These different cases often provide for different payment amounts, the difference being the amount of built-in residual value that will be provided to the lessor. The termination value is first used to repay the non-recourse debt, and the excess is then the property of the lessor. Termination values are equal to the total of equipment cost plus fees at the start of the lease term. Because termination values protect the lessorís yield and because yield earnings are recognized on an accelerated basis, termination values remain at this level for several years and then gradually diminish until they equal the residual value at the end of the lease term. An example of termination values is shown in section 6.9.6.

In practice, termination values are a negotiated item. Lessors may ask for a higher termination value for a voluntary termination than they do for a casualty loss. Lessees have argued that no residual value should be included in the case of a termination for obsolescence because the lessor should bear this risk; lessors have argued the opposite.

6.2.14 Early Buyout Option

Our example lease includes an early buyout option ("EBO") which permits the lessee to purchase the leased equipment on January 1, 2008 for $627,867. In our example lease, the lessorís yield if the EBO is exercised is the same as the full-term yield, namely 7% after tax, but the deal could have been structured for a different EBO yield. The EBO is similar to a termination value in that it generally protects the lessorís yield as well as repays the lenders. Our EBO is a "deferred EBO", which means that the EBO is paid in five installments, one on January 1, 2008 and four more which match the lessorís tax liability in 2008. The deferred EBO is used because it results in a lower present worth of the EBO to the lessee. It does not lower the lessorís yield because the lessor will be in a sinking fund state, and the sinking fund rate is zero.

The EBO is a structuring technique invented during the 1990ís, and prior to that time lessors claimed that an EBO was contrary to IRS guidelines (see below) because it appears to give the lessee a bargain purchase option, and generally gives the lessee the right to the residual upside. To satisfy IRS guidelines, the deal has been structured with an EBO "compulsion test" which states that the EBO must not be less than the present value of the remaining rents plus an assumed fair market value (higher than the 20% assumed for economic analysis). Therefore, the EBO does not represent a "bargain" purchase option.

6.2.15 IRS Guidelines

The Internal Revenue Service (the "IRS") has published guidelines relating to the structuring of leveraged leases. By following the guidelines, which are contained in Revenue Procedures 75-21, 75- 28, 76-30, and 79-48, the parties may expect to receive a favorable ruling from the IRS to the effect that the transaction is a lease for federal income tax purposes. Today, it is uncommon for a lessor to seek a ruling, but the guidelines are followed for leveraged leases in the institutional market.

The first point made in the guidelines is that the lessor must have a minimum unconditional at-risk investment of at least 20% of the cost of the leased equipment at the beginning of the lease term. That is, the lessor must pay 20% of the cost of the leased equipment (or assume personal liability in the same amount) by the time the equipment is first placed in service and may not be entitled to a return of the investment by any member of the lessee group through any form of unwind. Further, this investment must be maintained throughout the lease term. This means that the lessor may not receive the bulk of the early rentals by deferring debt service and thereby receive the cash sooner.

The leased equipment must have a minimum remaining value at the end of the lease, and the lessor, not the lessee, must bear the risk and reward for this value. The lessor must represent and demonstrate that the leased equipment will have a value of at least 20% of its original cost (without regard for inflation) at the end of the lease term. In addition, the equipment must not be leased for more than 80% of its economic life. These representations must be net of any removal or conversion costs, must contemplate the use of the equipment by parties other than members of the lessee group, and must be supported by commercial feasibility studies when necessary.

The lessor may not have the right, nor presently intend to acquire the right, to require any party to purchase the leased equipment at other than its fair market value (except for performance guarantees by the manufacturer of the equipment). No member of the lessee group may have the right to purchase the equipment for less than its fair market value.

No member of the lessee group may pay for part of the cost of the equipment. This also applies to certain improvements during the lease term, but excludes maintenance. No member of the lessee group may lend to the lessor any of the funds necessary to acquire the equipment or guarantee any indebtedness created in connection with the acquisition of the equipment by the lessor.

The lessor must demonstrate that it expects to receive a profit on the lease apart from tax benefits. This requirement is satisfied if the sum of the rent and expected residual is greater than the sum of the debt service and investment. Also, the lessor must receive significant cash flow from the lease. This requirement is met if the total rent exceeds the total debt service by a reasonable amount. This reasonable amount has been interpreted to be 2% of the investment multiplied by the number of years in the lease term.

If the rents in the lease are not level, the payments may give rise to prepaid or deferred rent. The IRS will not question unequal rent if the annual rent is either (a) always within 10% of the average of the rentals ("90-110" rents) or (b) within 10% of the average for at least the first two-thirds of the lease term, and for the remainder of the lease term, is no higher than the highest rent during the initial portion of the term and no lower than half the average rent during the initial portion. Currently, part (b) of the test is not used, and rent must satisfy part (a). The IRS may allow rents more uneven than the foregoing if there is a good business reason for the variation. In particular, rents that may vary in compensation for floating rates on the lease debt are allowed. Section 467 of the Internal Revenue Code of 1986, as amended (the "Code") may further limit the amount by which rent may increase. If Section 467 applies, then income from the rents must be recognized on a constant present value basis. Some lessors use level rents to avoid Section 467 problems. Others believe that the 10% test in the guidelines provides a safe harbor from Section 467 problems.

The uneven-rent test produces a serious structuring constraint. When the lessee evaluates the cost of the lease by measuring the present worth of the rents, the lessor may obtain a better bid by using a "low-high" rent structure. That is, rents are lower in the beginning of the lease term and higher at the end. Such a rent structure may show a present value cost lower than level rents for a given return to the lessor. However, the uneven-rent test constrains the amount by which the rents can vary.

Our example has been structured with "continuous" rents, meaning that a combination of advance and arrears rents are used in the same lease. Note the rather confusing rent payments in section 6.9.5. The use of both advance and arrears rents creates more freedom to reduce the present value of rent while still passing the IRS uneven rent test.

6.3 Rent and Debt Structuring

Today's leveraged leasing marketplace is highly competitive. Lessees measure the cost of a lease by using the present worth of the rent. Large deals are won or lost on the basis of a few hundred dollars in present worth of rent per million dollars of equipment cost. Today, it is the universal practice to "optimize" a leveraged lease by using a computer program which chooses the amount of leverage, and the exact rent and debt service amounts in order to achieve the lowest present worth of rent. The best lease has the lowest possible present worth of rent, and achieves all the necessary constraints. This result can be obtained using a mathematical procedure known as "linear programming" (see below) as implemented in a computer program.

The variables to be found are the amounts of each rent and each debt service. The lessor usually wants to optimize for the lowest present worth of rent, either the full term rent or the rent for the EBO term plus the EBO amount. However, it is sometimes convenient to optimize for the lowest lease rate, or the highest yield or profit at fixed rents. Of course, the lowest present worth of rent is obtained at zero rent. The lessor must also enter "constraints" into the problem. For example, the constraint that the after-tax yield must be at least 7%. There are usually many other constraints such as the IRS constraints. A representative list of constraints would consist of:

Other constraints sometimes needed are:

These constraints must be chosen carefully. Only the necessary constraints must be put into the computer model so that the resulting structure will meet the lessorís requirements. If too many constraints are entered, it may turn out that a lower present worth of rent could have been obtained with fewer constraints.

6.4 The LILO Structure

Now that we have discussed the classic United States leveraged lease, we turn our attention to the Lease-In Lease-Out ("LILO") structure. Also called the "leasehold" or lease-leaseback structure, it has been used for years in the US real estate marketplace. As a leveraged lease structure, it is used for big ticket ($100 million up) assets with very long useful lives of 35 years or more. Typical assets are aircraft, ships, rolling stock and facilities.

Our example LILO starts with the lease of the asset from its owner (the "User") to an investor (the "Investor") under an agreement called the "headlease." In our example, the asset has a useful life of 37.5 years and the headlease has a term of 30 years. The Investor pays the User two rents under the headlease, one of 84.141304% at closing, and one of 399.449808% after 35 years. The large amount of the second payment is needed for the present worth to be significant. The headlease grants the use of the asset to the Investor for 30 years. The User continues to own the property.

The Investor then subleases (the "Sublease") the equipment to the User for a term of 24 years for a normal pattern of semi-annual rents. The Sublease consists of an initial term of 13.5 years (the "Base Term"), after which the User can purchase the leasehold interest from the Investor for an EBO payment of 26.872%. If the User does not exercise the EBO, the Investor may lease the asset to a third party, or "put" the equipment to the User for the remaining term of 10.5 years (the "Renewal Term").

The Investor funds the transaction by equity of 18.790018% and non-recourse debt of 65.351286%. The non-recourse debt is secured by the Sublease rentals. The Sublease rentals and EBO payment may require additional credit enhancements consisting of the purchase of US Treasury "strips," a letter of credit, a "guaranteed investment contract" (GIC) or deposit of funds, etc.

It is quite difficult to structure, analyze and close a LILO deal due to the many requirements of the User and Investor, and the tax complexity. The computer model of a LILO is many hundreds of lines, many of which are hand-coded constraints. The participation of knowledgeable legal counsel and perhaps a lease arranger to do the structuring will be required.

From the Userís perspective, the LILO will make economic sense if the "net benefit" is large enough, perhaps 5%. The net benefit is the present value of the headlease rents less the payment obligations, including any deposits. The Userís structuring considerations are:

The Investor measures the economic benefit of a LILO by the two MISF yields on its equity investment, first assuming the deal runs to maturity, and next assuming the EBO is exercised. Both yields are eight percent in our example. The cash flows and yield report are shown in section 6.9.7. The Investor will expect to get SFAS-13 accounting treatment, so that the economic earnings shown are also the book earnings. Structuring considerations are:

Despite the different structure of the LILO, the economic analysis does not differ from that of the classic leveraged lease. The net after-tax cash flow shows the typical positive, negative, then positive-at-the-end pattern of a classic leveraged lease. Use of SFAS-13 accounting completes the picture.

6.4.1 Defeasance

A debt defeasance structure may be used in certain deals. Examples are the Japanese Leveraged Lease or "JLL", part of the obligations in a LILO, and the historical TBT. In a debt defeasance structure, the obligations under a loan are guaranteed by a deposit of sufficient funds. As an extreme example, the funds may be returned to the lender who then applies the funds against its own repayment rights. Tax counsel should be sought concerning the reality of a defeased loan.

6.5 Return on Equity and Assets

Other yield methods based on accounting considerations are coming into more common use. The return on assets is a prominent measure of bank performance. Therefore, banks are concerned about the effect of a large number of leveraged leases on this ratio. The first step in the return on assets method is to calculate the book earnings from the lease. Then an allocation of overhead is made, and the interest expense of the investment funds are subtracted from book earnings. Interest expense arises from the assumption that part of the investment is made from borrowed funds. The interest expense is found from an accounting measure of the funds invested in the lease. The book earnings less overhead and interest is called net book earnings. The net book earnings are then divided by the lease assets for each year (or quarter or month). This gives the return on assets for each year of the lease term. Because the return on assets varies, it is necessary to use an average which has been weighted by the dollar lease assets. This number is then used along with yield as a measure of lease value.

Another yield method, "return on equity," has become more popular in the last few years. There are two variations on this method. The first method is similar to the return on assets method. The book earnings are adjusted for overhead and interest expense. The result is then compared to the equity. The investment in the lease is considered to come from internal equity and debt. If the leasing company's leverage is 90%, and if the investment is $280,000, then the investment consists of $28,000 of "true" equity and $252,000 of debt. The book earnings less overhead and interest on the debt gives net book income. This net book income divided by the (small) equity gives the return on equity. The division may involve the present worth of earnings over present worth of equity, or an average may be used. Or an internal rate of return may be used.

The return on assets and return on equity methods described above are attempts to model a real leasing company, and to price deals to achieve specified accounting measures. Different lessors often have different incompatible ways of performing the analysis, depending on the assumptions they make about the financing of the leasing company, and the measure and allocation of overhead.

However, there is a second form of the return on equity calculation which has more general applicability. No allocation of overhead is made. The investment consists of equity and debt as before. The return on equity is a constant number throughout the lease term, and is found in a manner similar to the MISF yield method described above, except that the investment balance is considered to consist of debt and equity in a constant ratio. For each month of the lease term, the after-tax debt interest is the cost of funds multiplied by the debt balance in the previous month multiplied by one minus the tax rate (because interest expense is deductible). The return on equity is an after-tax return on equity rate multiplied by the equity in the previous month. The new investment balance is the old investment balance less the after-tax cash flow plus after-tax interest expense plus the return on equity "earnings". The new debt and equity are the investment balance multiplied by the fixed leverage ratio. The effect is to allocate the cash flow to the debt balance and the equity balance in proportion to the leverage, while calculating the debt expense after tax according to the interest rate and tax rate in effect at that time. The return on equity rate is a yield rate on equity, and for highly leveraged companies it will be several times the MISF yield rate. The return on equity for our example lease is 28.353% after tax. Note that this return on equity method is calculated on the after-tax cash flow, and is a variation on the regular MISF yield calculation.

The return on equity measures became more popular during the early 1980's when many industrial companies were entering the leveraged lease marketplace. These companies often evaluate investments using a hurdle rate of perhaps 20% for a return on their equity. The after-tax yields available were not at this level, so a return on equity measure was devised which was 20% and was more similar to what these non-financial companies were accustomed to seeing.

It is possible to derive the return on equity from a simple equation. If we write down the assumptions of the analysis as follows:

Capital = Equity + Debt

Debt = Capital X Leverage

Earnings on Capital = Yield X Capital

Debt Interest = Debt X Debt Rate X (1 - Tax Rate)

Return on Equity Earnings = Equity X Return on Equity Rate

Earnings on Capital = Debt Interest + Return on Equity Earnings

The above equations say that the capital invested is composed of equity and debt in a constant ratio, and that the return on equity is the return on capital less debt interest. The above equations can be solved to give:

Return On Equity = Yield on Capital - (Debt Rate X Leverage)
1 - Leverage

For our example, the yield on capital is the after-tax yield rate of 7.000%. The tax rate is 35%, and the after-tax debt rate is 7.5% times one minus the tax rate or 4.875%. The leverage is 90%, so the calculated return on equity is 26.13%. The point is that the return on equity method is so similar to the yield method that it does not contain any additional information. It simply re-states a perfectly valid yield on capital as an equivalent yield on equity, given a simple model of the capital structure of the lessor.

We believe that the return on equity method of yield is not superior to the MISF yield, and that it is essentially equivalent to the MISF yield. It contains no new information. The lessor has two choices. Calculate the return on equity and compare it to the hurdle return on equity, but understand what the return on equity is. Do not think that the yield is "really" higher just because the analysis method has changed. Alternatively, calculate the required return on capital given the hurdle return on equity and the known debt cost and leverage. Then compare the MISF yield with that yield on capital hurdle.

6.6 The Meaning of Yield

All single investor leases are pure investments because no significant sinking fund develops. The principal feature of the investment in a leveraged lease is its short life. Tax savings are large and result in a rapid payback of the initial investment. Our fifteen-year example lease has after-tax earnings of $54,260 and a yield of 7.000% per year after-tax on an investment of $205,000. Multiplying 7.000% by $205,000 we obtain earnings of $14,350 for one year. The average life is $54,260 divided by $14,350, or 3.78 years. We conclude that a leveraged lease has a yield for only a short amount of time, and, therefore, even a fifteen-year lease is to be viewed as a short-term investment. A single investor lease has a much longer average life and stands between leveraged leases and loans from an investment point of view.

Note that even though leveraged leases have a relatively small amount of earnings they can have a large yield because the investment is outstanding for a small amount of time. An extreme case would be a twenty-year lease with zero assumed residual value, in which the investment was repaid with earnings in one year and all subsequent positive cash flow was used to pay taxes. Then the yield could be very high even if the earnings were small. However, the value of the leveraged lease would be low. Why would anyone invest money in a complicated deal and receive it back in one year? Note that the credit risk, tax-rate-change risk and other risks continue for the full twenty years, and that the yield calculation has ignored this. The yield calculation only measures the yield on the investment while there is an investment. If the investment exists only for a very short time, the yield becomes irrelevant.

However, many lessors demand a certain level of earnings as a condition to investing in a leveraged lease. This is equivalent to specifying a minimum average life. Combined with a minimum yield requirement, this is equivalent to the criterion that the yield must be adequate but also meaningful.

Of course, although the yield exists in this extreme example only for one year, the investment is returned in one year also. Therefore, it is possible to invest in another leveraged lease after one year. If another leveraged lease identical to the first is available after the first year, the lessor may invest in it and obtain the high yield for two years. Of course, the risk is twice as great, and this has again been ignored by the yield calculation. If another leveraged lease at the original yield is not available, the lessor would have done better to invest in a leveraged lease at a lower yield but with a two-year life. Note the similarity to deciding whether to lend money for one year or two years; the decision depends upon yield rates at the end of the first year.

Although the foregoing discussion brings out an important point about leveraged (and other) leases, we must reconsider our conclusions when a secondary investment occurs. Most leveraged leases have an ending positive cash flow due to the receipt of the residual value. This results in another investment period just prior to the end of the lease term. Our conclusion that the average life of a leveraged lease is short remains true, but it is significant that the lessor is committing itself to two investments at the start of the lease term. We have discussed the first investment above. The second investment must be made (due to tax payments) years later, often well past the lessor's planning horizon. Use of the MISF method ensures that the second investment will have the same yield as the first investment, but market conditions at the time of the second investment are unknown.

For some lessors, the principal motivation to invest in a leveraged lease is the residual value. A lessor may manage its portfolio to obtain the most residual value at the least cost, and ignore yield consideration. Since most leveraged leases are bid on and booked with an assumed residual value, the lessor must obtain a residual of at least this value in order not to suffer a reversal of earnings. But inflation may substantially increase the realized dollar value of certain assets. This makes the economic analysis one of estimating realized residual value rather than analyzing yields. Leveraged leases of real estate are in this category. However, it is still necessary to monitor risk and to budget for the large lease cash flows and tax liabilities.

In summary, we have found it convenient to discuss leveraged leases as a pure source of funds, as a pure short-term investment, as two short term investments, and as a complicated way to buy a residual value. Single investor leases are always pure investments plus a residual value. For many leases, one of these elements dominates the investment decision, and economic analysis is relatively simple. However, many other leases contain several elements. It is not possible to compare different elements of a lease on a consistent basis unless a way is found to assign standard values to each element. This is just another example that "you can't add apples and oranges." Lessors evaluate the different elements by "feel" and reach an investment decision.

The process of valuing diverse leveraged lease elements must be specific to the investor and to assumed future market conditions. The various yield and analysis methods make use of simple models of the investor. The MISF method assumes that the investor has either an investment at the yield rate or a sinking fund at a sinking fund rate. The yield is then found by assuming a rate at which to value the sinking fund. The present worth method values both the investment and sinking fund at the same rate, and brings the result to the present as a dollar amount. The future worth method is similar. More elaborate models of the investor might be useful. In particular, a model including a simple adjustment for risk would improve the lessor's ability to choose leveraged lease investments, because it would make the yield more like the yield (interest rate) on a loan. Of course, a leveraged lease will never be a loan, and a sense of "feel" will always be needed in order to properly make a leveraged lease investment.

6.7 Lessee Economics

The principal reason a company will acquire property by lease rather than purchase is an inability to use the tax benefits of ownership on a timely basis. Thus, the primary objective in a leasing transaction is often the sale of tax benefits to the lessor in exchange for a lease rate that is lower than the lessee's borrowing rate. If the lessee is subject to the Alternative Minimum Tax and the lessor is not, then a lease will result in a further tax benefit to the lessee. Usually, although not always, the cost of leasing to the lessee is greater than the cost of direct ownership if the lessee can use the tax benefits as effectively as the lessor, if the lessee's incremental tax rate is equal to or greater than the lessor's and if the asset has significant value to the lessee at the end of the lease term.

As we have seen, the analysis of the economics of a leveraged lease for a lessor must be made on an after-tax basis in order to properly evaluate the value of the deal. The situation is somewhat different on the lessee side. Most lessees enter into a leasing arrangement, as opposed to a direct purchase of the equipment, because they are not in a position to take advantage of the tax benefits of ownership; they expect to be in a tax loss position for a substantial portion of the lease term. In such a situation, a before-tax analysis will suffice to value the deal.

If a lessee anticipates turning taxable in the relatively near term, however, the picture changes substantially. Rent payments made by the lessee during a year in which it is taxable will represent a lower overall cost to the lessee than payments made during tax loss years. When the present value of the lessee cost is calculated on an after-tax basis, a deal which was optimally structured on a before-tax basis may suddenly appear suboptimal by a significant amount. A prudent lessee will consider the "real" benefit of a leveraged lease on an after-tax basis.

There are other reasons for leasing an asset rather than owning it. If the lessee knows that it will not need the asset after the lease term, it may seek a rent rate that includes a discount for the anticipated value of the residual. How much discount is available will depend on the lease term, and on the availability of lease funds at the time. This amounts to a sale of the residual value to the lessor rather than (or combined with) the sale of tax benefits. As a further reason for leasing, the lessee may find that greater financial leverage is available to it through a combination of leasing and traditional financing.

This last point is especially important for a lessee whose main problem is the availability of sufficient capital for its needs. The lessee may be able to obtain more funds through debt and equity sales in addition to leveraged leasing than it could through debt and equity sales alone. Because buyers of leveraged lease equity would not usually be investors in the lessee's securities, the lessee is going to a different market for funds. The extent to which additional funds may be acquired through leveraged leasing depends on the capital markets at the time.

Other reasons for leveraged leasing may arise from institutional or contractual constraints. For example, the lessee may have indenture restrictions against additional borrowing, but not corresponding restrictions against leasing. Or a manager may be able to acquire property through lease because a lease is an item of the expense budget, whereas a purchase would need to be approved as an item of the capital budget. Regulated industries may have differences in the accounting treatment of leasing versus ownership for rate-making or rate-base purposes, which may give an advantage to one or the other.

A leveraged lease can play a special role in a project financing or joint venture, since it can reduce the dollar size of the fixed financial obligation that must be provided through various purchase or supply contracts with third parties. This may make it possible to rely exclusively on third-party credit to finance the project.

The FASB in its Statement 13 has established accounting standards that would require the capitalization of some leveraged leases. That is, some leveraged leases would be recorded as assets or liabilities on the lessee's balance sheet, and the asset would be depreciated as if it were owned. Under the standards, leveraged leases must be capitalized if the equipment is leased for 75% or more it its estimated economic life, or if the present worth of the rentals is 90% or more of the equipment value less the ITC retained by the lessor (the "7d" test).

The discount rate specified in the standards is not necessarily the lease debt rate, but is either the lessee's secured debt rate for a loan with similar repayment terms or the lessor's implicit rate. The lessor's implicit rate is the internal rate of the rentals plus estimated residual value versus the equipment value less the ITC retained by the lessor. The lessee must use the secured debt rate, unless it is practicable to learn the implicit rate used by the lessor. In this case, the lessee must use the lessor's implicit rate if it is lower than the secured debt rate.

6.7.1 The Lessee's Rent Cost Comparison

When lessees evaluate different leveraged leasing proposals, they usually evaluate the cost of the rents by either the present worth method or the internal rate method on a before-tax basis. Under the present worth method, the cost of the rents is given by the present worth of the rentals at the lessee's cost of capital. Under the internal rate method, the cost of the rents is given by the internal rate of the rentals versus the equipment cost. If the rents are level and equal in number, the two methods give the same cost comparison between two leveraged leases. That is, if lease A has a present worth cost lower than lease B, then it will have a lower internal rate also. This is simply equivalent to looking at one rent as the cost comparison.

If the rents are not level, it is possible (and likely) that if lease A has a present worth cost lower than lease B, then lease A may still have an internal rate higher than lease B. In this case, should the lessee choose lease A or lease B? The corresponding problem for the lessor was discussed above, and the mathematics of the "Capital Budgeting Problem" is completely applicable to the comparison of leveraged lease proposals and to lease-buy analysis. Lessees should evaluate rent costs by using the present-worth method, not the internal rate method.

In our example lease, the present worth of the rents is $841,172. If the EBO is exercised, the present worth of the rents up to the EBO date plus the EBO payments is $922,297. Both are at a discount rate of 7.5%.

6.7.2 Lease-Buy Analysis

In evaluating the economics of a leveraged leasing transaction, the lessee should not combine the analysis of how to finance the equipment with the analysis of whether to acquire the equipment. Whether to lease or to own equipment which the prospective lessee has already decided to acquire is basically a financial decision. Having decided to acquire equipment, there are two common ways to evaluate the cost of financing, the "present-worth" method and the "basic-interest-rate" method. Neither has the relevance and market acceptance of the methods used to evaluate lessor economics.

The conventional method of comparing the costs of leasing and ownership is to discount the cash flows associated with the two alternatives to present worth at the lessee's opportunity rate. The present-worth cost of leasing is simply the present worth of the rentals plus the present worth of the residual value, all on an after-tax basis. The present worth of cost of ownership is the down payment plus the present worth of the debt services less the present worth of the tax benefits (if they can be used). The tax benefits are the same as those that would be available to the lessor. Note that if the lessee is subject to the Alternative Minimum Tax, then taxes must be calculated for both the lease and buy cases using that method. The prospective lessee then chooses the alternative with the lower present-worth cost.

Although the present-worth method is the most common method, it is undoubtedly incorrect, unless the down payment amount is correctly chosen. The amount of down payment included in the analysis has a substantial effect on the apparent present-worth cost. The appropriate down payment amount should be associated with the prospective lessee's debt-to-equity ratio, rather than the actual down payment made on the equipment. In addition, the method has been criticized by Richard F. Vancil (9) on the grounds that it intermingles the effects of tax savings with the amount of funds provided. That is, if the prospective lessee always has alternative sources of financing available, the amount of financing obtained should not affect the results. In his view, the main difference between leasing and ownership is the difference in permissible income tax deductions.

Under Vancil's method of analysis, which he calls the "basic interest rate method", the cost of ownership is the price of the equipment less the present worth of the tax savings due to depreciation. This has the consequence that the cost of ownership is independent of the amount of the down payment. The cost of leasing is the price of the equipment less the present worth of the tax savings due to the deductibility of the principal portion of the rent. That is, the rents are divided into principal and interest payments as if they were debt services at a rate called the basic interest rate equal to the incremental borrowing cost. The principal portion is actually deductible, because it is really part of the rent, whereas it would not be deductible under ownership. The interest component of the rent would be deductible under either lease or ownership. This is the key feature of the lease according to this method of analysis. The method compares the total deductibility of rent versus the availability of depreciation. In this discussion we have ignored a problematic but crucial correction to the method (discussed in the reference by Vancil). It arises because the division of the rent into principal and interest payments leaves a balance other than zero at the end of the lease term unless the basic interest rate is equal to the lease implicit rate. The basic-interest-rate method is subject to criticism because it ignores the difference (if any) in the amount of financing provided and the effects of leasing and debt financing on the prospective lessee's capital structure. That is, it may not address the reasons the lessee may decide to lease in the first place.

In general, the quantitative analysis of the lease-buy decision has not reached the uniformity and market acceptance of the methods used to evaluate lessor economics. The findings of a study of lease-buy analysis methods was published (10) in 1980. This study attempted to find out the method of lease-buy analysis actually used by large firms, and to present a model based on a sound conceptual framework.

In practice, lessees rarely go through the detailed quantitative analysis described above. Instead, they often decide to lease for some basic economic or other reason, such as the inability to use the tax benefits of ownership. They then attempt to obtain the best deal available by seeking lease rate bids, by using leveraged lease professionals, and by negotiation. Nevertheless, an important part of the decision to seek capital through equity or debt sales is the price comparison between the two. The lease equity market has its ups and downs as do other capital markets. If the lessee has the ability to compare confidently the prices of equity and debt with leveraged leasing, it will be able to obtain capital through leveraged leasing at the most advantageous times.

6.8 Example Reports

6.8.1 Taxable Income for the United States Leveraged Lease

 Period             Depre-   Interest   & other   Taxable    Taxes
  Ends    Income   ciation    on Loan   Expense    Income     Paid
12/1998    84886    142857      60000       333   -118305    -41407
12/1999    84886    244898      58264       333   -218609    -76513
12/2000    84886    174927      56267       333   -146642    -51325
12/2001    84886    124948      54121       333    -94516    -33081
12/2002    84886     89249      51813       333    -56510    -19778
12/2003    84886     89249      44640       333    -49337    -17268
12/2004   103749     89249      40035       333    -25868     -9054
12/2005    84886     44624      36540       333      3388      1186
12/2006    94317         0      32267       333     61716     21601
12/2007   103749         0      28584       333     74832     26191
12/2008   103749         0      24302       333     79114     27690
12/2009   103749         0      19444       333     83971     29390
12/2010   103749         0      13309       333     90107     31537
12/2011   103749         0       6695       333     96720     33852
12/2012   103749         0          0       333    103416     36196
12/2013   200000         0          0         0    200000     70000
         =======    =======   =======    ======   =======   =======
Total    1614758    1000000    526281      5000     83477     29217

6.8.2 Cash Flows for the United States Leveraged Lease

Period   Taxes   Rental   Debt    Other   B.T.    A.T.  Invest.  Net Cash
  Ends    Paid    Cash   Service  Cash    Cash    Cash   + Fee   Balance
12/1998  -41407   31735   30000       0    1735   43141  205000  -161859
12/1999  -76513   82283   82283       0       0   76513       0   -85345
12/2000  -51325   83887   83887       0       0   51325       0   -34021
12/2001  -33081   83812   83812       0       0   33081       0     -940
12/2002  -19778   83732   83732       0       0   19778       0    18838
12/2003  -17268  143865  143865       0       0   17268       0    36106
12/2004   -9054  103749  103749       0       0    9054       0    45160
12/2005    1186   84886   84886       0       0   -1186       0    43974
12/2006   21601   94317   91368       0    2950  -18651       0    25323
12/2007   26191  103749   79541       0   24208   -1983       0    23340
12/2008   27690  103749   83538       0   20210   -7480       0    15860
12/2009   29390  103749   86636       0   17113  -12277       0     3583
12/2010   31537  103749   98184       0    5565  -25972       0   -22389
12/2011   33852  103749   98184       0    5565  -28287       0   -50676
12/2012   36196  103749   92617       0   11131  -25064       0   -75740
12/2013   70000       0       0  200000  200000  130000       0    54260
         ====== ======= ======= =======  ====== =======  =======
Total     29217 1414758 1326281  200000  288477  259260   205000


6.8.3 Multiple Investment Sinking Fund Method - Monthly

            Nominal Monthly After-Tax Yield         .583333 % /month
            Nominal Annual After-Tax Yield         7.000000 % /year
            After-Tax Sinking Fund Rate             .000000 % /year

                   After   Invest. Payment of   Ending   Sinking S. Fund
 Date Investment tax Cash Earnings Investment Investment  Fund  Earnings
 1/98     205000     1735        0       1735     203265      0       0
 2/98          0        0     1186      -1186     204451      0       0
 3/98          0        0     1193      -1193     205644      0       0
 4/98          0    10352     1200       9152     196492      0       0
 5/98          0        0     1146      -1146     197638      0       0
 6/98          0    10352     1153       9199     188439      0       0
 7/98          0        0     1099      -1099     189538      0       0
 8/98          0        0     1106      -1106     190644      0       0
 9/98          0    10352     1112       9240     181404      0       0
10/98          0        0     1058      -1058     182463      0       0
11/98          0        0     1064      -1064     183527      0       0
12/98          0    10352     1071       9281     174246      0       0
 1/99          0        0     1016      -1016     175262      0       0
 2/99          0        0     1022      -1022     176285      0       0
 3/99          0        0     1028      -1028     177313      0       0
 4/99          0    19128     1034      18094     159219      0       0
 5/99          0        0      929       -929     160148      0       0
 6/99          0    19128      934      18194     141954      0       0
 7/99          0        0      828       -828     142782      0       0
 8/99          0        0      833       -833     143615      0       0
 9/99          0    19128      838      18291     125324      0       0
10/99          0        0      731       -731     126055      0       0
11/99          0        0      735       -735     126790      0       0
12/99          0    19128      740      18389     108402      0       0
. . .
12/13                                                  0      0
        ======== ========   ======    =======                      ======
Total     205000   259260    54260     205000                          0

6.8.4 Multiple Investment Sinking Fund Method - Annual Totals

            Nominal Monthly After-Tax Yield         .583333 % /month
            Nominal Annual After-Tax Yield         7.000000 % /year
            After-Tax Sinking Fund Rate             .000000 % /year

                   After   Invest. Payment of   Ending  Sinking  S. Fund
 Date Investment tax Cash Earnings Investment Investment  Fund  Earnings
12/98     205000    43141    12387      30754     174246      0        0
12/99          0    76513    10669      65844     108402      0        0
12/ 0          0    51325     6544      44781      63621      0        0
12/ 1          0    33081     3766      29315      34306      0        0
12/ 2          0    19778     1982      17797      16509      0        0
12/ 3          0    17268      759      16509          0      0        0
12/ 4          0     9054        0          0          0   9054        0
12/ 5          0    -1186        0          0          0   7868        0
12/ 6          0   -18651      112     -10895      10895      0        0
12/ 7          0    -1983      332      -2315      13211      0        0
12/ 8          0    -7480      445      -7924      21135      0        0
12/ 9          0   -12277     1137     -13414      34549      0        0
12/10          0   -25972     2924     -28896      63446      0        0
12/11          0   -28287     5071     -33358      96804      0        0
12/12          0   -25064     7378     -32442     129246      0        0
12/13          0   130000      754     129246          0      0        0
       ========= =========  ======   ========                     ======
Total     205000   259260    54260     205000                          0

6.8.5 Rentals for the United States Leveraged Lease

   Date      Arrears    Advance     Total
 1/ 1/1998     .000000    .173459    .173459
 7/ 1/1998    3.000000    .000000   3.000000
 1/ 1/1999    5.315101    .000000   5.315101
 7/ 1/1999    2.913184    .000000   2.913184
 1/ 1/2000    5.575376    .000000   5.575376
 7/ 1/2000     .000000   2.813352   2.813352
 1/ 1/2001    5.675209    .000000   5.675209
 7/ 1/2001    2.706032    .000000   2.706032
 1/ 1/2002    5.782528    .000000   5.782528
 7/ 1/2002    2.590663    .000000   2.590663
 1/ 1/2003    5.897896   6.256538  12.154434
 7/ 1/2003    2.232022    .000000   2.232022
 1/ 1/2004     .000000   8.373145   8.373145
 7/ 1/2004    2.001730    .000000   2.001730
 1/ 1/2005     .000000   6.661574   6.661574
 7/ 1/2005    1.826986    .000000   1.826986
 1/ 1/2006     .000000   7.523381   7.523381
 7/ 1/2006    1.908336    .000000   1.908336
 1/ 1/2007     .000000   7.620788   7.620788
 7/ 1/2007    2.754087    .000000   2.754087
 1/ 1/2008     .000000   9.159795   9.159795
 7/ 1/2008     .000000   1.215080   1.215080
 1/ 1/2009     .000000   9.402656   9.402656
 7/ 1/2009     .972219    .000000    .972219
 1/ 1/2010     .000000   9.709432   9.709432
 7/ 1/2010     .665443    .000000    .665443
 1/ 1/2011     .000000  10.040113  10.040113
 7/ 1/2011     .334762    .000000    .334762
 1/ 1/2012     .000000   9.818262   9.818262
 7/ 1/2012     .000000    .556613    .556613
 1/ 1/2013     .000000    .000000    .000000
            ========== ========== ==========
Total        52.151574  89.324188 141.475762

6.8.6 Termination Values

      Date      Termination Value 
     1/ 1/98     100.500000000
     7/ 1/98     101.399811000
     1/ 1/99     100.073524000
     7/ 1/99     100.962147000
     1/ 1/ 0      98.993643000
     7/ 1/ 0     102.356468000
     1/ 1/ 1      97.098322000
     7/ 1/ 1      97.418132000
     1/ 1/ 2      94.574887000
     7/ 1/ 2      94.745591000
     1/ 1/ 3      91.556576000
     7/ 1/ 3      85.375206000
     1/ 1/ 4      87.633942000
     7/ 1/ 4      79.260804000
     1/ 1/ 5      81.262526000
     7/ 1/ 5      74.600961000
     1/ 1/ 6      76.427941000
     7/ 1/ 6      68.612231000
     1/ 1/ 7      70.249997000
     7/ 1/ 7      61.327921000
     1/ 1/ 8      62.786695000
     7/ 1/ 8      54.848204000
     1/ 1/ 9      54.917519000
     7/ 1/ 9      45.564007000
     1/ 1/10      46.674109000
     7/ 1/10      37.152577000
     1/ 1/11      38.105933000
     7/ 1/11      28.414616000
     1/ 1/12      29.210737000
     7/ 1/12      19.926704000
     1/ 1/13      20.000005000

6.8.7 Multiple Investment Sinking Fund Method

            Nominal Monthly After-Tax Yield         .666667 % /month
            Nominal Annual After-Tax Yield         8.000001 % /year
            After-Tax Sinking Fund Rate             .000000 % /year

                  After    Invest.  Payment of   Ending  Sinking  S. Fund
 Date Investment tax Cash Earnings  Investment Investment Fund   Earnings

12/97     207900    27099     6750      20349     187552       0       0
12/98          0    54531    13993      40537     147014       0       0
12/99          0    53897    10647      43250     103764       0       0
12/ 0          0    53216     7077      46139      57626       0       0
12/ 1          0    52480     3269      49211       8415       0       0
12/ 2          0    10648      391       8415          0    1842       0
12/ 3          0    -2774        5       -937        937       0       0
12/ 4          0    -9134      341      -9476      10412       0       0
12/ 5          0   -10869     1178     -12047      22459       0       0
12/ 6          0   -11135     2185     -13320      35779       0       0
12/ 7          0   -11372     3298     -14670      50449       0       0
12/ 8          0   -11591     4522     -16113      66562       0       0
12/ 9          0   -11771     5864     -17635      84197       0       0
12/10          0   -10724     7298     -18022     102219       0       0
12/11          0    26140     5709      20431      81788       0       0
12/12          0    63388     1092      62296      19492       0       0
12/13          0   -19040     1930     -20969      40461       0       0
12/14          0   -25688     4099     -29787      70249       0       0
12/15          0   -27377     6620     -33998     104246       0       0
12/16          0   -29188     9495     -38683     142929       0       0
12/17          0   -31141    12762     -43903     186832       0       0
12/18          0   -37526    16590     -54115     240948       0       0
12/19          0    78556    12337      66219     174729       0       0
12/20          0    94221     5727      88495      86234       0       0
12/21          0    53996     2571      51425      34810       0       0
12/22          0    13957     2487      11471      23339       0       0
12/23          0    16110     1472      14638       8701       0       0
12/24          0    18500      292       8701          0    9507       0
12/25          0    21124        0          0          0   30631       0
12/26          0    24040        0          0          0   54671       0
12/27          0     8968        0          0          0   63639       0
12/28          0   -10073        0          0          0   53566       0
12/29          0   -12153        0          0          0   41414       0
12/30          0   -14507        0          0          0   26907       0
12/31          0   -17167        0          0          0    9740       0
12/32          0    -9740        0          0          0       0       0
        ======== ========  =======  =========                      ======
Total     207900   357900   150000     207900                          0




1. Teichroew, Robichek and Montalbano, Mathematical Analysis of Rates of Return under Certainty, 11 MANAGEMENT SCIENCE 395-403 (1965).

2. Teichroew, Robichek, and Montalbano, An Analysis of Criteria for Investment and Financing Decisions under Certainty, 12 MANAGEMENT SCIENCE 151-179 (1965).

3. Lorie and Savage, Three Problems in Capital Rationing, 28 J. BUS. 4 (1955).

4. H. Weingartner, Mathematical Programming and the Analysis of Capital Budgeting Problems (1963, 1967).

5. Bernhard, Discount Methods for Expenditure Evaluation - A Clarification of Their Assumptions, 28 J. INDUS. ENG. 19-27 (1962).

6. H. Markowitz, Portfolio Selection: Efficient Diversification Of Investments (1959).

7. L. Bussey, The Economic Analysis of Industrial Projects (1978).

8. J. Mao, Quantitative Analysis of Financial Decisions (1969).

9. Vancil, Lease or Borrow - New Method of Analysis, 39 HARV. BUS, REV. 122-36 (1961).

10. William L. Ferrara, James B. Thies, and Mark W. Dirsmith, The Lease-Purchase Decision, published by the National Association of Accountants and The Society of Management Accountants of Canada (1980).


James C. Ahlstrom received his Ph.D from Cornell University in 1972, and is now back at Interet Corporation. Interested in the use of mathematics in finance and business, he is the co-author (with Iris C. Engelson and Ladislav V. Belcsak) of a widely used lease analysis computer program.

Iris C. Engelson received her B.S.E. in chemical engineering from Princeton University in 1983. Until joining Interet in 1987, she worked for Haverly Systems in the development of linear programming computer codes.

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