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Financial Analysis, Planning and

Forecasting

Theory and Application

By

Alice C. Lee

San Francisco State UniversityJohn C. Lee

J.P. Morgan Chase

Cheng F. Lee

Rutgers University

Chapter 14

Leasing: Practices and Theoretical Developments

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Outline

14.1 Introduction 14.2 Types of leasing arrangements and accounting

treatments Three leasing forms

Accounting for leases

14.3 Cash-flow estimation and valuation methods 14.4 The Modigliani and Miller propositions and the

theoretical considerations of leasing

14.5 Lease vs. buy decisions under uncertainty: the

CAPM approach 14.6 Summary and conclusion

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14.1 IntroductionFabozzi (1981) has discussed the conventional reasons for leasing in detail.

Here we shall discuss them only briefly.a. True lease financing might be cheaper than borrowing or purchasing the

asset. This kind of advantage is primarily due to different marginal tax rates

faced by the lessor and lessee.

b. Since leasing generally does not require the firm to make a down payment

(as most lending institutions do), the effect is to conserve working capital,

although, in general, lease payments are prepaid and in that sense are like

a down payment (although generally smaller than those required in most

purchase arrangements).

c. Leasing may preserve the credit and debt capacity of the firm. This, as we

shall see, is a result of the accounting conventions in use today.

d. Leasing can reduce the risk of obsolescence and capital-equipment

disposal problems. Almost always the term of the lease is less than the life

of the asset, particularly so in the case of leases that are cancelable at

certain times at the option of the lessee.

e. Leasing is more flexible and convenient than buying an asset. Most lessors

deal with leasing arrangements on a regular basis and are used to tailoring

these arrangements, within reason, to their clients best interest.

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14.2 Types of leasing arrangements and

accounting treatments

Three leasing formsa) Direct Leasing

b) Sale and Leasebackc) Leveraged Leasing

Accounting for leases

a) Capital Lease Treatmentb) Accounting for Operating Leases

c) Accounting for Leases from the LessorsStandpoint

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accounting treatments9

101

$75,000 $15,000

$450,000 $75,000 . (14.1)(1 (1) )NN R R

TABLE 14.1

Docksider corporation depreciation schedule Assumption:

1. et value is479,448.2. Expected value end of year 10 is15,000.3. Depreciation method is sum-of the-ears-digits.

Year end Depreciation Expense Capital Equipment under Leases

0 0.00 479,448.00

1 84,445.09 395,002.91

2 76,000.58 319,002.33

3 67,556.07 251,446.26

4 59,111.56 192,334.70

5 50,667.06 141,667.65

6 42,222.55 99,445.11

7 33,778.04 65,667.07

8 25,333.53 40,333.54

9 19,889.02 23,444.52

10 8,444.52 15,000.00

Total Dpe. 464,448,00

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accounting treatmentsTABLE 14.2

Lease amortization schedule

Assumption:1. Original lease value of $479,448.

2. Interest rate is 12 percent.

3. Annual lease payments of $75,000, with final payment of $15,000 on final day of year 10.

End of

year

Cash

payment

Interest on

lease

Lease obligation

reduction

Outstanding lease

obligation

0 75,000.00 0.00 75,000.00 404,448.00

( Day 1)

1 75,000.00 48,533.76 26,466.24 377,981.76

2 75,000.00 45,357.81 29,642.19 348,339.57

3 75,000.00 41,800.75 33,199.25 315,140.32

4 75,000.00 37,816.84 37,183.16 277,957.16

5 75,000.00 33,345.86 41,465.14 236,312.02

6 75,000.00 28,357.44 46,642.56 189,669.46

7 75,000.00 22,760.34 52,239.66 137,429.80

8 75,000.00 16,491.58 58,508.42 78,921.38

9 75,000.00 9,470.57 65,529.43 13,391.94

10 15,000.00 1,670.03 13,392.97 0.00

479,488.00

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accounting treatmentsTABLE 14.3

Principal repayment figures on annual basis:

Balance Sheets for ten years of lease arrangementAssumptions:

1. Initial asset value of $479,488.

2. Depreciation schedule in Table 14.1 used to update asset value.

3. Total liability figures taken from implicit interest schedule.

End of

yearAssets

Current

Lease

obligation

Noncurrent

Lease

obligation

Total

Liabilities

0 $479,488.00 $75,000 0.00 $404,488.00

( Day 1)

1 395,002.91 75,000 377,981.76 452,981.76

2 319,002.33 75,000 348,339.57 423,339.57

3 251,446.26 75,000 315,140.32 390,140.32

4 192,334.70 75,000 277,957.16 352,957.16

5 141,667.65 75,000 236,312.02 311,312.02

6 99,445.11 75,000 189,669.46 264,669.46

7 65,667.07 75,000 137,429.80 212,429.80

8 40,333.54 75,000 78,921.38 153,921.38

9 23,444.52 75,000 13,391.95 88,391.95

10 $15,000.00 $15,000 0.00 $15,000.00

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TABLE 14.4Income-statement expenses on annual basisoperating lease optionYear Lease Payment

1 75,000

2 75,000

3 75,000

9 75,000

10 75,000*

Total expenses 750,000

*The15,000 payment for the machine at the end of the lease contract

period would have to amortized as any other asset at this point and is

therefore not included as a deduction from income.

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TABLE 14.5Income statement expenses on annual basis Capital lease option

YearDepreciation

ExpenseInterest Expense Total Expenses

1 84,445.09 48,553.76 132,978.85

2 76,000.58 45,357.81 121,358.393 67,556.07 41,800.75 109,356.82

4 59,111.56 37,816.84 96,928.40

5 50,667.06 33,354.86 84,021.92

6 42,222.55 28,357.44 70,579.99

7 33,778.04 22,760.34 56,538.38

8 25,333.53 16,491.58 41,825.11

9 16,889.02 9,470.57 26,359.59

10 8,444.52 1,607.03 10,051.55*

750,000.00

*Also excluded from the capitalized lease expense option is the purchase price

of the asset.

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TABLE 14.6

Income differential under two different accounting treatments, capitalization and noncapitalization

Assumptions:Income figures from Table 14.4 and 14.5 used for comparative purposes.

Year Capitalized Expenses Noncapitalized Expenses Difference

Cumulative

Difference,

Capitalized lessNoncapitalized

1 132,978.85 75,000 57,978.85 57,978.85

2 121,385.39 75,000 46,358.39 104,337.24

3 109,356.82 75,000 34,356.82 138,694.06

4 96,928.40 75,000 21,928.40 160,622.46

5 84,021.92 75,000 9,021.92 169,644.38

6 70,579.99 75,000 4,420.01 165,224.37

7 56,538.38 75,000 18,461.62 146,762.75

8 41,825.11 75,000 33,174.89 113,587.86

9 26,359.59 75,000 48,640.41 64,947.45

10 10,051.55 75,000 64,947.45 0.00

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14.3 Cash-flow estimation and valuation methods

TABLE 14.7Lease cash flows

Assumptions:

1. The firms marginal tax is 25 percent.

2. The before-tax required return on Docksiders debt is 12 percent.

3. The lease payments are made at the beginning of the indicated year, and the shields from these payments are not

recognized.

Year Lease Cash Flow Tax Shield After-tax Cash OutflowsPresent Value of

after-tax Outflows

1 75,000 18,750 56,250 57,789.16

2 75,000 18,750 56,250 53,025.84

3 75,000 18,750 56,250 48,647.56

4 75,000 18,750 56,250 44,630.78

5 75,000 18,750 56,250 40,945.67

6 75,000 18,750 56,250 37,564.83

7 75,000 18,750 56,250 34,463.15

8 75,000 18,750 56,250 31,617.57

9 75,000 18,750 56,250 29,006.95

10 75,000 22,500 67,500 31,364.01

409,064.52

*Here we allow deduction of the15,000 asset price for illustrative purposes, assuming, in a sense, that the present value of the tax

shield is not a significant factor, or that it will be written off in a very short time. We also allow the instantaneous deduction in the

following purchase-option cash-flow evaluation for perfect comparability.

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whereA = Net cash outflow at t=0,

RtCt= Periods net operating inflows,

Dt = Periods depreciation expense,

Sn = Expected salvage value at time n,tc = Ordinary income tax rate, and

k = After-tax cost of capital for the firm.

1

( - - )(1- )- , (14.2)

(1 (1) )

nt t tt c n

P t nt

C SR D D= ANPV

k k

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14.3 Cash-flow estimation and valuation methodsTABLE 14.8

Purchase-option cash flows with 100 percent debt financing

Assumptions:

1. The assets initial value is 500,000 and the depreciation method is sum-of-the-years-digits.

2. The firm is unable to utilize the investment tax credit.

3. 15,000 final payment still applies.4. Ten equal, prepaid annual loan repayments will be made.

5. Marginal borrowing rate is 12 percent and the applicable tax rate is 25 percent.

YearCash

Payment

Depreciation

Expanse

Interest

Expanse

Tax

Shield

Present value

of after-tax flows

1 78,247.61 90,909.09 50,610.29 35,379.85 45,789.03

2 78,247.61 81,818.18 47,293.81 32,278.00 44,619.05

3 78,247.61 72,727.27 43,579.35 29,061.66 43,418.51

4 78,247.61 63,636.36 39,419.16 25,763.88 42,169.73

5 78,247.61 54,545.45 34,759.75 22,326.30 40,922.02

6 78,247.61 45,454.55 29,541.20 18,748.94 39,676.20

7 78,247.61 36,363.64 23,696.44 15,015.02 38,442.76

8 78,247.61 27,272.73 17,150.29 11,105.76 37,230.52

9 78,247.61 18,181.82 9,818.62 7,000.11 36,046.79

10 78,247.61 9,090.91 1,607.14 2,674.52 41,233.79

+15,000.00

409,548.40

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1

1 0

(14.3)n n

t tc t t cL t t

t t

(1 - ) ( - + ) (1 - )C OR L= ,NPV

(1 + k (1 + r ) )

1 1

(14.4)n n

ttt c c n cL P t t ttt t

(1 - )(1 - ) - LO SD- = - + A - .NPV NPV

(1 + k (1 + k ) ) (1 + r)

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14.4 The Modigliani and Miller propositions and the


Vu = Total value of an unleveraged firm,

= A perpetual stream of after-tax cash

flows, and

k = Investors required return on equity.

1 (14.5)u

( - )X =V

k

(1 - )X

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(14.6)

(14.7)

V VL U = + D

(1- )and .U

l MiV Mi D

k i

L(1 - )Mi Mi

= +Vk i

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1L (1 - ) dMi dMidV

= + = ,dM k dM i dM

1(1 - )i

+ = ,k

(1 - )i = (1 - )k

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1L (1 - ) dMi dMidV

= + = ;

dM k dM i(1 - ) dM

(14.8)(1 - 2 )k

(1 - )i = (1 - )

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whereC = Net initial outlay,

c= Applicable corporate tax rate,

Rt= Cash flows before depreciation and taxes,

Dt= Depreciation expense accruing in time t,= A weighted discount rate, weighted according to the

risk of the component flows, and

n = The life of the project.

(14.9)

tc cn tP t=1 t

(1 - ) ( ) + DR= -C +NPV

(1 - k)

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(14.10)

whereL0= Lease payment at day 1,

Lt= Lease payment at the end of time period t,

Ft= Executory costs paid by the lessor,

Pj= Purchase price of asset at end of lease term,D = Depreciation expense in time period t,

i = Discount rate for a riskless cash flow,

k = Discount rate for a risky cash flow, and

j = term of lease.

0

1 1

1 1

(1 ) (1 )(1 )(1 ) (1 )

(1 ),

(1 ) (1 ) (1 )

j n

c t c t L c t t

t t

j njc t c t

t j tt t j

L RNPV Li k

PF D

i k k

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where

Mt = Payment of interest and principal on

the loan during period t, andAt = Amortization of the loan for tax

purposes in period t.

1

1 1

1

(1 )

(1 ) (1 )

t t tcj

t0P c

j

n nc t c t

t tt t

(1 - ) ( - ) +M A A

= - ( - ) - (1 + i)NPV L

R D

k i

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(14.12)

(14.13)

(14.14)

1

1

1

.(1 ) (1 )

n tcL P t

t

jt t t t c c

tt

njc

t jt

D- =NPL NPV(1 + k)

(1 - ) ( - - ) -L M F A )

(1 + i)

PD

i k

1

1n t tcL P t

t

( - ) ( - )M L =NPV NPV (1 + i)

0 0

n n

Lt tc cL t t

t t

D D=A

(1 + i (1 + k ) )

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(14.15)

where

Pt = Lease payment at time t,

c = The lessors marginal tax rate,

Bt = Depreciation expense on the asset at time t,

R

D

= Before-tax cost of debt,(1 - c)RD = Investors after-tax required return on debt,and

= Lessees marginal tax rate.

0 0

1 1

1 1 1 1

n n * *t t t tc c

L t tD Dc ct t

( - ) + ( - ) +P B P B=V

( + ( - ) ( + ( - )) )R R

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(14.16)

(14.16)

(14.17)

(14.18)

0

nt

tDct

1 BD = .

A (1 + (1 - ))R

DA

B

r

t

et

t

n

( ) .10

0

nt c

t cet

A(1 - D)P= ,

1 -(1 + )r

t

et

*

*t

nP

(1 + r) =

A(1 - D)

1 -,

1

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(14.19)

(14.19)

(14.20)

A(1 - D)1 -

> P(1 + r)

,*

*

t

et

t

n

0

t=0

n t

et

c

c

P

(1 + r) =

A(1 - D)

1 - ,

*c

*c

1 - D1 - D> .

1 -1 -

*

c

*c

(1 - D)(1 - D)A [ - ] .

1 -1 -

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14.5 Lease vs. buy decisions under uncertainty:

the CAPM approach

(14.21)

where

Lit= Lease payment at time t,

Xit = Assets purchase price, and

dit = Economic depreciation of the asset in

time t.

ijit

it

itR =L

X - d ,

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the CAPM approach

(14.22)

E(Rit) = Rf- Bit[E(Rm) - Rf] (14.23)

Lit= Xit[Rf- Bit(E(Rm) - Rf) + E(dit)] (14.24)

( ( ))it it it m m it d d B R E R e

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the CAPM approach

(14.25)

E(Vij) = 1 + Rf+ Bj(E(Rm) - Rf). (14.26)

(14.27)

1

0

j

f m fj

j

E( )V= 1 + + B (E( ) - ),R R R

V

0i

it it m f

f

V =E(V ) - B [E(R ) - R ]

1 + R,

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the CAPM approach

(14.28)

(14.29)

(14.30)

it it it it = [E( ) + E( )]C dR X

it m f it itL

f f

E( ) - (E( ) - )V B R R L= ;V

1 + 1 +R R

itt m f it it it itP

f f

E( ) - (E( ) - ) (E( ) + E( ))V B R R dX R= ,V

1 + 1 +R R

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the CAPM approach

(14.31)

(14.32)

(14.33)

L it it it itNA = X [E(R ) + E(d)] - L ,

i t m f iti t

f f

E( ) [E( ) ]V B R RL= .

1 + 1 +R R

f it m fit it

f

1(n) = [ (E( ) ) + E( )].C dR B R R

1 +R

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14.6 Summary and conclusion

In this chapter we have uncovered many of the interesting facets of

leasing. The conventional rationales for leasing deal primarily withreducing the risk of making use of an asset vis--visthat of actuallyowning said asset, and with maintaining greater borrowing capacitythan would otherwise be possible. The latter rationale is subject togreater question, given the recent emphasis, in the field of leasingaccounting, on making these fixed obligations known to all viewers ofthe firms financial statements, rather than allowing quasi-debtinstruments to be, for the most part, hidden in footnotes. There stillshould exist some concern, however, as to the effects that leases haveon the various financial statements, for bond covenants and otherrestrictions may become binding if leases that could conceivably betreated in more than one way for accounting purposes are not optimallytreated. The risk factor, the element of lease contracts that attracts

most of the attention, raises the question of whether compensatingreturns must be made between the agreeing parties, while theexistence of the various forms of leasing arrangements testify toward awillingness on the parts of these parties to engage in leasing activities,with the knowledge that such risk transfers exist.

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14.6 Summary and conclusionIn the area of lease valuation we found that the minimum discount rate applied to the

cash flows of a leasing scheme was the risk-free rate, and not some other rate deflatedby the interest-tax-break percentage so that this figure would be less than the risk-freerate. In confronting the problem of valuation under conditions of market equilibrium,whether it is the specification of Modigliani and Miller, or of the more specialized CAPMframework, we found no rationale for leasing in competitive markets. Even including theoften troublesome market imperfection known as taxation, this result was seen to hold,and no abnormal returns were found to be possible through leasing, due to thecompetitive element of the market.

Unfortunately, the types of taxation considered in these market-equilibrium modelsgenerally avoid those irregular tax considerations such as investment tax credits, theinclusion of which greatly complicates the analysis because the element of negotiation isinvolved. All is not lost though, as the Myers et al. formulation shows where suchsubsidies are taken account of in a general form.

With the existence of specialized leasing companies, either as a subsidiary of a

manufacturer or as a separate entity altogether, we find it difficult to accept the restrictiveview that leasing offers no net benefit to selected lessor-lessee consortiums. As such,the lease-versus-buy decision does require separate analysis for each leasingopportunity, and analysts must consider each proposal (lease versus buy) separately ifthey believe there are differences between the net costs and/or benefits from leasing andthose of legal ownership.

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Appendix 14A. The Application of Adjusted Present Value

(APV) Method to Lead versus Buy Decision

(14.A.1)

where

Rt = pretax operating cash revenue gathered by the

project during time period tCt = pretax operating cash expenses due to the project

during time period t

dept= additional depreciation due to the project during time

period t

= the market rate of return on unlevered flows of the

indicated risk class.

r = the interest rate paid on debt

= corporate tax rate

c

.)r+(1

rD+I-)+(1

dep+)-)(1dep-C-R(=APV ttcN

=1tt

tcttt

N

=1t

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Table 14.A.1

N Nt t c tct t

t tt=1 t=1

N

t 1 2 3 4 5t=1

( - - )(1 - ) +dep depCR rD

APV = - I +(1 + (1 + r) )

400 9.60 7.68 5.76 3.84 1.92 - 1200 + + + + +(1.08 (1.04 (1.04 (1.04 (1.04 (1.04) ) ) ) ) )

423.40

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Out Standing balance of loan $600 $480 $360 $240 $120 $0

interest payment $24 $19 $14 $10 $5

Tax deduction on interest $9.60 $7.68 $5.76 $3.84 $1.92

After-tax interest expense $14.40 $11.52 $8.64 $5.76 $2.88

Repayment of loan $120 $120 $120 $120 $120

A di 14A Th A li ti f Adj t d P t V l

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Table 14.A.2

NPV of the leaseAdditional effects when

APV of the lease relaive to the purchase purchase is financedrelaive to the purchase when purchase is financed

with some debtby all equity

Lease Minus Buy Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Lease

Lease Payment -$12,500 -$12,500 -$12,500 -$12,500 -$12,500

Tax benefit of lease payment $4,250 $4,250 $4,250 $4,250 $4,250

Buy (minus) $50,000

Cost of machine

Lost depreciation tax benefit -$1,700 -$1,700 -$1,700 -$1,700 -$1,700

Total $50,000 -$9,950 -$9,950 -$9,950 -$9,950 -$9,950

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2

3 4 5

$9,950 $9,950All-Equity NPV $50,000

1.065 1.065

$9,950 $9,950 $9,950 $8650.99

1.065 1.065 1.065

2 3 4 5

$1,105 $933 $753 $565 $369$3,191.551.065 1.065 1.065 1.065 1.065

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Table 14.A.3.

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Out Standing balance of loan $50,000 $42,195 $34,055 $25,566 $16,713 $0

interest payment $3,250 $2,743 $2,214 $1,662 $1,086

Tax deduction on interest $1,105 $933 $753 $565 $369

After-tax interest expense $2,145 $1,810 $1,461 $1,097 $717

Extra cash that purchasing firm $9,950 $9,950 $9,950 $9,950 $9,950

gernerates over leasing firm

Repayment of loan $7,805 $8,140 $8,489 $8,853 $16,713

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