Simon Benninga. Financial Modelling 3-rd edition

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208 Chapter 6

6.4 The Lessor’s Problem: Calculating the Highest Acceptable Lease Rental

The lessor’s problem is the opposite of that of the lessee:

•

The lessee has to decided whether—given a rental rate on the leased

asset—it is preferable to buy the asset or lease it.

•

The lessor has to decide what minimum rental rate justiﬁ es the purchase

of the asset in order to lease it out.

One way of solving the lessor’s problem is to turn the preceding analy-

sis around. We use the Excel Goal Seek (Tools|Goal Seek) to get $134,826

as the lessor’s minimum acceptable rental:

The alternative loan table shown above was constructed in the

following way:

The principal at the beginning of each of years 1–6 is the present

value of the lease-versus-buy outﬂ ows, discounted at (1 − 38

percent)

12 percent. Thus, for example,

532 070

124 000

11040012

40 000

110400

+− ⋅

∑

[ ( .).] [ ( .)

.. ]

[ ( .).] [ (

446 379

124 000

11040012

40 000

110

+− ⋅

+−

∑

.. ) . ]

[ ( .).]

40 0 12

37 313

40 000

11040012

⋅

+− ⋅



Once the principal at the start of each year is known, it is an easy

matter to construct the rest of the columns.

Interest = 12 percent

Principal, beginning of year

Total payment = Interest in year t + Repayment of principal in

year t

After-tax payment, year t = (1 − Tax rate)

Interest + Repayment

of principal

209 The Financial Analysis of Leasing

Here’s what the Goal Seek settings look like:

GFEDCBA

Asset cost 600,000

Interest rate 12%

Lowest acceptable lease payment 134,826

<-- Computed either with

Goal Seek

Solve

Annual depreciation 100,000

Tax rate 40%

Year 0123456

Lessor after-tax cash flows from leasing

After-tax lease rental 80,896 80,896 80,896 80,896 80,896 80,896

Lessor after-tax cash flows from buying the asset

Asset cost -600,000

Depreciation tax shield 40,000 40,000 40,000 40,000 40,000 40,000

Net cash from buying -600,000 40,000 40,000 40,000 40,000 40,000 40,000

Lessor cash flows

Lease + buy -519,104 120,896 120,896 120,896 120,896 120,896 40,000

IRR of differential cash flow 7.22% <-- =IRR(B19:H19,0)

THE LESSOR'S PROBLEM

Calculating the lowest acceptable lease rate

If you’re using Solver to do this problem, it would look like:

210 Chapter 6

Some Peculiarities of the Excel Solver and Excel Goal Seek

1. Neither of these (otherwise wonderful) Excel tools will accept a formula

in the box that speciﬁ es the target. Thus—in the present example—we would

have liked to write the formula =(1-B6)*B3 in the “To value” box of Goal

Seek. But that technique won’t work: We have to specify a numerical value

(in this case, the after-tax interest rate).

2. You may have to ﬁ ddle with Tools|Options|Calculation in order to specify

enough accuracy to get cell B21 to be exactly 7.22 percent. If you do not get

an acceptable answer, set a higher value for the option Maximum change.

3. Goal Seek does not remember its settings between accesses. Therefore, you

will have to reenter the data each time. (Solver, on the other hand, does

remember its settings.)

211 The Financial Analysis of Leasing

6.4.1 Minicase: When Is Leasing Proﬁ table for Both the Lessor and Lessee?

The symmetry between the lessee’s problem and the lessor’s problem

suggests that if the lessee wants to lease, it will not be proﬁ table for the

lessor to purchase the asset in order to lease it out.

In some cases, however, it may be that the differences in tax rates

between the lessee and the lessor make it proﬁ table for both to enter

into a leasing arrangement. Here is an example: Greenville Electric

Corporation is a public utility that pays no taxes. Its credit rating is

of the highest order, since all of Greenville’s debts are guaranteed by

the city of Greenville. Greenville Electric has decided that it requires

a new turbine. The turbine costs $10 million and will be depreciated to

zero salvage value over ﬁ ve years. Greenville Electric borrows at 6

percent.

Greenville can either lease or buy the plant. The lease offer it has is

$1.8 million per year for six years (starting today); the lessee is a captive

leasing subsidiary of United Turbine Corporation, the manufacturer of

the turbine. United Turbine Leasing also borrows at 6 percent and has a

tax rate of 40 percent.

As can be seen in the following spreadsheet, the lease is proﬁ table to

both lessor and lessee. Greenville Electric gets ﬁ nancing at a cost of 3.19

percent, compared to its borrowing cost of 6 percent; United Turbine gets

an after-tax return of 4.3 percent, compared to its after-tax borrowing

cost of 3.6 percent. Both Greenville Electric and United Turbine

proﬁ t.

3. Who loses? The government, of course! What makes the lease proﬁ table is the utiliza-

tion of otherwise unused depreciation tax shields.

212 Chapter 6

BACDEFG

Turbine cost 10,000,000

Greenville's borrowing rate 6.00%

Lease payment 1,800,000

Year 0 1 2 3 4 5 6

Lessee after-tax lease costs

After-tax lease rental -1,800,000 -1,800,000 -1,800,000 -1,800,000 -1,800,000 -1,800,000

Lessee after-tax purchase costs

Asset cost -10,000,000

Depreciation tax shield (Greenville Electric's tax rate = 0) 0 0 0 0 0 0

Net cash from buying -10,000,000 0 0 0 0 0 0

Cash saved by leasing

Lease - purchase cash flows 8,200,000 -1,800,000 -1,800,000 -1,800,000 -1,800,000 -1,800,000 0

IRR of differential cash flow 3.19% <-- =IRR(B16:H16,0)

Greenville's after-tax borrowing cost 6.00% <-- =B3

Turbine cost 10,000,000

Lease payment 1,800,000

Depreciation (straight line, 5 years) 2,000,000

United Turbine's borrowing rate 6.00%

United Turbine's corporate tax rate 40%

Year 0 1 2 3 4 5 6

Lessor cash flows

Equipment cost -10,000,000

Lease payment, after tax 1,080,000 1,080,000 1,080,000 1,080,000 1,080,000 1,080,000

Depreciation tax shield 800,000 800,000 800,000 800,000 800,000 800,000

Total lessor cash flow -8,920,000 1,880,000 1,880,000 1,880,000 1,880,000 1,880,000 800,000

IRR of lessor cash flows 4.30% <-- =IRR(B33:H33)

United Turbine's after-tax borrowing cost 3.60% <-- =B25*(1-B26)

GREENVILLE ELECTRIC CORPORATION

UNITED TURBINE LEASING CORPORATION

6.5 Asset Residual Value and Other Considerations

In the example of sections 6.3 and 6.4 we ignored the residual value of

the asset—its anticipated market value at the end of the lease term. In

a mechanical sense, it is easy to include the residual value in the calcula-

tions (but you have to be careful—see the warning after the numerical

example). Suppose, for example, you think that the asset will have a

market value of $100,000 in year 7; assuming that this value is fully taxed

(after all, we’ve depreciated the asset to zero value over the ﬁ rst six

years), the after-tax residual value will be (1 − Tax rate)

$100,000 =

$60,000.

213 The Financial Analysis of Leasing

ABCDEFGH

Asset cost 600,000

Interest rate 12%

Lease rental payment 140,000

Annual depreciation 100,000

Tax rate 40%

Residual value 100,000 <-- Anticipated to be realized in year 7; fully taxed

Year 01234567

After-tax cash flows from leasing

After-tax lease rental -84,000 -84,000 -84,000 -84,000 -84,000 -84,000

After-tax cash flows from buying the asset

Asset cost -600,000

Depreciation tax shield 40,000 40,000 40,000 40,000 40,000 40,000

After-tax residual 60,000

Net cash from buying -600,000 40,000 40,000 40,000 40,000 40,000 40,000 60,000

Differential cash flow

Lease minus buy 516,000 -124,000 -124,000 -124,000 -124,000 -124,000 -40,000 -60,000

IRR of differential cash flow 10.49% <-- =IRR(B21:I21,0)

Decision?? Buy <-- =IF(B23<(1-B6)*B3,"Lease","Buy")

RESIDUAL VALUES IN LEASE ANALYSIS

Not surprisingly, the possibility of realizing an extra cash ﬂ ow from

asset ownership makes the lease even less attractive than before (you

can see this difference by noting that the return rate in cell B23, the IRR

of the differential cash ﬂ ows, has increased from 8.30 percent in our

original example to 10.49 percent).

Be a bit careful here, however; the spreadsheet treats the residual

value as if it has the same certainty of realization as the depreciation tax

shields and the lease rentals. This assumption can be far from the truth!

There is no good practical solution to this problem; an ad hoc way of

dealing with it might be to reduce the $100,000 by a factor that expresses

the uncertainty about its realization. The ﬁ nance technical jargon for this

is “certainty-equivalence factor,” and you can ﬁ nd it referenced in any

basic ﬁ nance text.

The last spreadsheet snapshot in this chapter (which

follows) assumes that you’ve decided that the certainty-equivalence

factor for the residual value is 0.7:

4. For further references on certainty equivalents, see Brealey, Myers, Allen (2005, chapter

9). However, note that neither this work nor the present text (nor anyone else) can tell

you precisely how to calculate the certainty-equivalence factor. It depends on your

attitudes toward risk.

214 Chapter 6

6.6 Summary

This chapter has looked at the lease-purchase decision. We have exam-

ined the decision to lease as a purely ﬁ nancing decision, assuming (1)

that all operational factors between leasing and buying are equivalent,

and (2) that the essential ﬁ rm decision to acquire the use of the asset has

already been made. On the basis of these assumptions, the lease-purchase

decision can be made using the equivalent-loan method.

Exercises

1. Your company is considering either purchasing or leasing an asset that costs

$1,000,000. The asset, if purchased, will be depreciated on a straight-line basis over

six years to a zero residual value. A leasing company is willing to lease the asset for

$300,000 per year; the ﬁ rst payment on the lease is due at the time the lease is

undertaken (i.e., year 0), and the remaining ﬁ ve payments are due at the beginning

of years 1–5. Your company has a tax rate t

= 40 percent and can borrow at 10

percent from its bank.

a. Should your company lease or purchase the asset?

b. What is the maximum lease payment it will agree to pay?

2. ABC Corporation is considering leasing an asset from XYZ Corporation. Here are

the relevant facts:

ABCDEFGHIJ

Asset cost 600,000

Interest rate 12%

Lease rental payment 140,000

Annual depreciation 100,000

Tax rate 40%

Residual value 100,000 <-- Anticipated to be realized in year 7; fully taxed

Certainty-equivalence factor 0.70

Year 01234567

After-tax cash flows from leasing

After-tax lease rental -84,000 -84,000 -84,000 -84,000 -84,000 -84,000

After-tax cash flows from buying the asset

Asset cost -600,000

Depreciation tax shield 40,000 40,000 40,000 40,000 40,000 40,000

After-tax residual 42,000 <-- =(1-B6)*B7*B8

Net cash from buying -600,000 40,000 40,000 40,000 40,000 40,000 40,000 42,000

Differential cash flow

Lease minus buy 516,000 -124,000 -124,000 -124,000 -124,000 -124,000 -40,000 -42,000

IRR of differential cash flow 9.88% <-- =IRR(B22:I22,0)

RESIDUAL VALUES IN LEASE ANALYSIS

Estimated residual value multiplied by certainty-equivalence factor which represents

uncertainty about realizing residual

215 The Financial Analysis of Leasing

Asset cost $1,000,000

Depreciation schedule Year 1: 20%

Year 2: 32%

Year 3: 19.20%

Year 4: 11.52%

Year 5: 11.52%

Year 6: 5.76%

Lease term 6 years

Lease payment $200,000 per year, at the beginning of years 0, 1, . . . , 5

Asset residual value Zero

Tax rates

ABC: t

= 0% (ABC has tax-loss carryforwards that

prevent it from utilizing any additional tax shields)

XYZ: t

= 40%

Show that it will be advantageous both for ABC to lease the asset and for XYZ to

purchase the asset in order to lease it out to ABC.

3. Continuing with the same example: Find the maximum rental that ABC will pay

and the minimum rental that XYZ will accept.

4. Perform a sensitivity analysis (using Data|Table, see Chapter 31) on the certainty-

equivalence factor in section 6.5, showing how the IRR of the differential cash ﬂ ows

varies with the CE factor.

Appendix: The Tax and Accounting Treatment of Leases

This chapter discusses the case where the lessor retains the tax beneﬁ ts

of ownership; that is, the lessor is able to take the depreciation on the

leased asset, and the lessee deducts the lease payments from his income

as an expense. In order for these things to happen, it is critical that the

Internal Revenue Service be willing to recognize the lease as a true

lease.

Although the speciﬁ c IRS rules change from time to time, the principle

underlying the rules remains that the lessor should be accorded the

beneﬁ ts of ownership only if he bears some of the economic risks of

ownership. This principle has led the IRS to develop a series of tests to

determine whether or not the lessor has transferred essentially all of the

ownership risks to the lessee. If this is the case, the IRS treats the “lease”

arrangement as a sale of the asset by the “lessor” to the “lessee.” If the

ownership risks have not all been transferred to the lessee, then the lease

is a true lease and the analysis of the chapter holds.

216 Chapter 6

Revenue Ruling 55–540 sets out seven conditions under which a trans-

action will be found to be a sale rather than a lease for tax purposes:

1. Portions of the rental payments are speciﬁ cally applicable to an equity

interest to be acquired by the lessee.

2. The lessee will acquire title upon payment of a stated amount of

rentals.

3. A substantial proportion of the asset’s purchase price is paid in rentals

in a relatively short period of time from the inception of the lease.

4. The rental payments exceed a “fair” rental value.

5. There is a bargain-purchase option; the option price is nominal in

relation to the fair market value of the asset at the time when the option

can be exercised.

6. Some part of the payments is designated as interest.

7. The lease may be renewed at nominal rentals over the useful life of

the asset.

In addition to these conditions, Revenue Ruling 55–541 deals with the

relation of the lease term to the useful life of the asset. The ruling would

seem to suggest that the transaction will be classiﬁ ed as a conditional

sale and not as a lease if the useful life of the asset is not in excess of the

lease term.

One lease packager states that the IRS will generally classify a lease

as a true lease if all the following criteria are met:

•

The estimated fair market value of the leased asset at the end of the

lease term will equal at least 20 percent of the original cost of the leased

property.

•

The lease term does not exceed 80 percent of the estimated useful life

of the asset.

•

There is no bargain-purchase option.

•

The lessor’s equity in the leased asset is at least 20 percent.

The Accounting Treatment of Leases

Accountants have found leases troublesome. Before the advent of

Financial Accounting Standards Board Statement 13 (FASB 13) in

1976, it was common for ﬁ rms to leave leases off their balance sheets

217 The Financial Analysis of Leasing

altogether and to record only as footnotes to the ﬁ nancial statement the

fact that some assets were leased. This practice created an asymmetry

between the accounting treatment of a lease and the accounting treat-

ment of a purchase of an asset with debt. Since the economic similarity

between these two transactions is great, this asymmetric treatment is

illogical.

FASB 13 attempts to solve this problem. The statement is long and

complex, and it is beyond the purview of this book to fully present the

statement’s solutions. We will sketch here the solution to the problem as

outlined in FASB 13; the next chapter deals with FASB 13’s treatment

of the leveraged leases.

The basic idea behind the FASB 13 treatment of leases is that in some

cases the lessee should record a leased asset on his balance sheet, even

though legally the asset belongs to another party. The cases in which this

should happen are those in which the economic substance of the lease

transaction (as opposed to the legal ﬁ ction) is that the lessee effectively

owns the asset. An example would be a 10-year noncancelable lease of

an automobile. By the time the car is returned to the lessor, it is likely

to be practically worthless; hence, FASB 13 would require the lessee to

record the asset on his balance sheet.

Formally, FASB 13 requires the lessee to put the lease on his balance

sheet (the terminology is that in this case the lease is a capital lease) if

one of four criteria applies:

1. The lease transfers ownership of the property to the lessee at the end

of the lease term.

2. The lease contains a bargain-purchase option, which allows the lessee

to purchase the leased asset at a very low price at the end of the lease

term.

3. The lease term exceeds 75 percent of the life of the asset.

4. The present value of the lease payments (at the lessee’s incremental

borrowing rate) exceeds 90 percent of the asset’s fair value.

If a lease is a capital lease under the FASB 13 rules, then the lessee

records the capital lease as an asset and records a corresponding liability

on his balance sheet. The asset is then depreciated, and the liability is

amortized over the lease term. It is as if the asset in question has been

bought with 100 percent loan ﬁ nancing.