Financial Analysis, Planning and
Forecasting
Theory and Application
Chapter 14
Leasing: Practices and Theoretical Developments
By
Alice C. Lee
San Francisco State University
John C. Lee
J.P. Morgan Chase
Cheng F. Lee
Rutgers University
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

14.1
Introduction
Fabozzi (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 client’s best interest.
14.2 Types of leasing arrangements and
accounting treatments
 Three leasing forms
a) Direct Leasing
b) Sale and Leaseback
c) Leveraged Leasing
 Accounting for leases
a) Capital Lease Treatment
b) Accounting for Operating Leases
c) Accounting for Leases from the Lessor’s
Standpoint
14.2 Types of leasing arrangements and
accounting treatments
9
$75,000 $15,000

.
N
10
(1  R)
N 1 (1  R)
$450,000  $75,000  
(14.1)
TABLE 14.1
Docksider corporation depreciation schedule Assumption:
1.
et value is＄479,448.
2.
Expected value end of year 10 is＄15,000.
3.
Depreciation method is sum-of –the-ears’-digits.
Year end
0
Depreciation Expense
＄
0.00
Capital Equipment under Leases
＄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
－
14.2 Types of leasing arrangements and
accounting treatments
TABLE 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
0
Cash
payment
＄75,000.00
Interest on
lease
＄
0.00
Lease obligation
reduction
Outstanding lease
obligation
＄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
14.2 Types of leasing arrangements and
accounting treatments
TABLE 14.3
Principal repayment figures on annual basis:
Balance Sheets for ten years of lease arrangement
Assumptions:
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
year
Assets
Current
Lease
obligation
Noncurrent
Lease
obligation
＄
Total
Liabilities
0.00
$404,488.00
75,000
377,981.76
452,981.76
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
0
$479,488.00
$75,000
1
395,002.91
2
( Day 1)
14.2 Types of leasing arrangements and
accounting treatments
TABLE 14.4
Income-statement expenses on annual basis－operating lease option
Year
Lease Payment
1
75,000
2
75,000
3
75,000
•
•
•
•
•
•
9
75,000
10
75,000*
Total expenses
＄750,000
*The ＄15,000 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.
14.2 Types of leasing arrangements and
accounting treatments
TABLE 14.5
Income statement expenses on annual basis－ Capital lease option
Year
Depreciation
Expense
Interest Expense
Total Expenses
1
＄84,445.09
＄48,553.76
＄132,978.85
2
76,000.58
45,357.81
121,358.39
3
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.
14.2 Types of leasing arrangements and
accounting treatments
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
Difference
Cumulative
Difference,
Capitalized less
Noncapitalized
Capitalized Expenses
Noncapitalized Expenses
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
14.3 Cash-flow estimation and valuation methods
TABLE 14.7
Lease cash flows
Assumptions:
1.
The firm’s marginal tax is 25 percent.
2.
The before-tax required return on Docksider’s 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 Outflows
Present 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 the ＄15,000 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.
14.3 Cash-flow estimation and valuation methods
( Rt - C t - Dt )(1-  c)  Dt
Sn
=
A


,
NPV P

t
n
(1  k )
(1  k )
t 1
n
(14.2)
where
A = Net cash outflow at t=0,
Rt – Ct = Period’s net operating inflows,
Dt = Period’s depreciation expense,
Sn = Expected salvage value at time n,
tc = Ordinary income tax rate, and
k = After-tax cost of capital for the firm.
14.3 Cash-flow estimation and valuation methods
TABLE 14.8
Purchase-option cash flows with 100 percent debt financing
Assumptions:
1.
The asset’s 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.
Year
Cash
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
14.3 Cash-flow estimation and valuation methods
(1 -  c ) ( R t - C t + O t ) n 1 L t(1 -  c )

,
NPV L = 
t
t
t 1
t  0 (1 + r )
(1 + k )
n
(14.3)
n
L t(1 - c )
O t(1 -  c ) -  c D t
Sn
+ A- 
.
NPV L - NPV P = 
t
t
t
t
t 1
t 1 (1 + r )
(1 + k )
(1 + k )
n
(14.4)
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
( 1 -  )X
V =
k
u
(14.5)
Vu = Total value of an unleveraged firm,
(1 -  )X = A perpetual stream of after-tax cash
flows, and
k = Investor’s required return on equity.
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
V
V
U
L
= V
U
+ D
(1-l )
 Mi

Mi and  D 
.
k
i
(1 -  )Mi  Mi
+
V =
k
i
L
(14.6)
(14.7)
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
(1 -  ) dMi  dMi
dV
=
+
= 1,
dM
k dM i dM
L
(1 -  )i
+  = 1,
k
(1 -  )i = (1 -  )k
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
(1 -  ) dMi

dMi
dV
=
+
= 1;
dM
k dM i(1 -  ) dM
L
(1 - 2 )k
(1 -  )i =
(1 -  )
(14.8)
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
NPV P = - C + 
n
t=1
(1 -  c ) ( R t ) +  c D t
(1 - kˆ )t
(14.9)
where
C= 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.
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
j
NPVL   L0 (1   c ) 

t 1
j


t 1
(1   c ) Ft
(1  i)
t

(1   c ) Lt
(1  i )t


t 1
n
Pj
(1  k )
n
j

(1   c ) Rt
(1  k )t
 c Dt
 (1  k )
t  j 1
t
(14.10)
,
where
L0 = 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.
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
j
NPV P = - L 0( 1 -  c ) -

(1 -  c ) ( M t - At ) + At
(1 + i )t
j 1
n


t 1
(1   c ) Rt
(1  k )t
n

 c Dt
 (1  i)
t 1
t
where
Mt = Payment of interest and principal on
the loan during period t, and
At = Amortization of the loan for tax
purposes in period t.
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
n
NPL L - NPV P =
 c Dt 
 (1 + k )
t 1
j


t 1
n

t
(1 -  c ) ( L t - M t - F t ) -  c At
t
(1 + i )
cD
 (1  i)
t 1
t

Pj
(1  k )
j
(14.12)
)
.
( 1 -  c ) ( M t - Lt )
NPV L  NPV P = 
t
t 1
(1 + i )
n
n
AL = 
 c D Lt
t
(1
+
i
)
t 0
n

 c Dt
t
(1
+
k
)
t 0
(14.13)
(14.14)
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
P t( 1 -  c ) + B t c
P t( 1 -  * ) + B t *

V L=
t
t
D
D
(
1
+
(
1

)
(
1
+
(
1

)
)
)
R
R
c
c
t 0
t 0
n

n

(14.15)
where
Pt
c
Bt
RD
(1 - c)RD
and

= Lease payment at time t,
= The lessor’s marginal tax rate,
= Depreciation expense on the asset at time t,
= Before-tax cost of debt,
= Investor’s after-tax required return on debt,
= Lessee’s marginal tax rate.
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
1
D=
A
n

Bt
.
t
D
t 0 (1 + R (1 -  c ) )
(14.16)
n
Bt
DA  
.
t
t  0 (1  re )
(14.16)
A(1 -  c D)
Pt
=
,
t
1 -c
t 0 (1 + r e )
(14.17)
A(1 -  * D)
Pt
=
,

t
*
1 - 
t 1 (1 + r e )
(14.18)
n

n
14.4 The Modigliani and Miller propositions and the
theoretical considerations of leasing
n
A(1 -  * D)
Pt
>
,

t
*
1 - 
t  0 (1 + r e )
(14.19)
t=0
n
c
A(1
D)

Pt
=
,
t
c
1 - 
(1 + r e )
1 -  *D 1 -  c D
>
.
*
1 -c
1 -
(14.19)
(1 -  *D) (1 -  c D)
A[
].
*
1 -c
1 -
(14.20)
14.5 Lease vs. buy decisions under uncertainty:
the CAPM approach
Lit
- d it ,
Rij =
X it
(14.21)
where
Lit = Lease payment at time t,
Xit = Asset’s purchase price, and
dit = Economic depreciation of the asset in
time t.
14.5 Lease vs. buy decisions under uncertainty:
the CAPM approach
dit  dit  Bit ( Rm  E ( Rm ))  eit
E(Rit) = Rf - Bit[E(Rm) - Rf]
(14.22)
(14.23)
Lit = Xit [Rf - Bit (E(Rm) - Rf) + E(dit)] (14.24)
14.5 Lease vs. buy decisions under uncertainty:
the CAPM approach
E( V 1 j )
= 1 + R f + B j (E( R m ) - R f ),
(14.25)
E(Vij) = 1 + Rf + Bj (E(Rm) - Rf).
(14.26)
V0j
V 0i
E(V it ) - B it [E( Rm ) - R f ]
=
,
1 + Rf
(14.27)
14.5 Lease vs. buy decisions under uncertainty:
the CAPM approach
C it = [E( R it ) + E( d it )] X it
(14.28)
E( V it ) - Bit(E( R m ) - R f )
it
L

;
V L=
1+ R f
1+ R f
(14.29)
E( V it ) - Bitt(E( R m ) - R f ) X it(E( R it ) + E( d it ))

,
V P=
(14.30)
1+ R f
1+ R f
14.5 Lease vs. buy decisions under uncertainty:
the CAPM approach
NAL = X it [E( Rit ) + E( d it )] - L it , (14.31)
L it = E( V it )  B it [E( R m )  R f ] .
1+ R f
1+ R f
(14.32)
1
[ R f  B it (E( R m )  R f ) + E( d it )].(14.33)
C it (n) =
1+ R f
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 with
reducing the risk of making use of an asset vis-à-vis that of actually
owning said asset, and with maintaining greater borrowing capacity
than would otherwise be possible. The latter rationale is subject to
greater question, given the recent emphasis, in the field of leasing
accounting, on making these fixed obligations known to all viewers of
the firm’s financial statements, rather than allowing quasi-debt
instruments to be, for the most part, hidden in footnotes. There still
should exist some concern, however, as to the effects that leases have
on the various financial statements, for bond covenants and other
restrictions may become binding if leases that could conceivably be
treated in more than one way for accounting purposes are not optimally
treated. The risk factor, the element of lease contracts that attracts
most of the attention, raises the question of whether compensating
returns must be made between the agreeing parties, while the
existence of the various forms of leasing arrangements testify toward a
willingness on the parts of these parties to engage in leasing activities,
with the knowledge that such risk transfers exist.
14.6 Summary and conclusion
In 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 deflated
by the interest-tax-break percentage so that this figure would be less than the risk-free
rate. 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 CAPM
framework, we found no rationale for leasing in competitive markets. Even including the
often 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 the
competitive element of the market.
Unfortunately, the types of taxation considered in these market-equilibrium models
generally avoid those irregular tax considerations such as investment tax credits, the
inclusion of which greatly complicates the analysis because the element of negotiation is
involved. All is not lost though, as the Myers et al. formulation shows where such
subsidies 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 restrictive
view that leasing offers no net benefit to selected lessor-lessee consortiums. As such,
the lease-versus-buy decision does require separate analysis for each leasing
opportunity, and analysts must consider each proposal (lease versus buy) separately if
they believe there are differences between the net costs and/or benefits from leasing and
those of legal ownership.
Appendix 14A. The Application of Adjusted Present Value
(APV) Method to Lead versus Buy Decision
N
( Rt - C t - dept )(1 -  c ) + dept
 c rDt .
APV = 
I
+

t
t
(1
+

(1
+
r
)
)
t=1
t=1
N
(14.A.1)
where
Rt = pretax operating cash revenue gathered by the
project during time period t
Ct = 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
c = corporate tax rate
Appendix 14A. The Application of Adjusted Present Value
(APV) Method to Lead versus Buy Decision
N
(R t - C t - dep t )(1 - c) + dep t
c rD t
APV = 
I
+

t
(1 + ) t
t=1
t=1 (1 + r )
N
N
400
9.60
7.68
5.76
3.84
1.92
1200
+
+
+
+
+
t
(1.04)1 (1.04) 2 (1.04) 3 (1.04) 4 (1.04) 5
t=1 (1.08)
 423.40

Table 14.A.1
Year 0
Out Standing balance of loan
Year 2
Year 3
Year 4
Year 5
$480
$360
$240
$120
$0
$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
$120
$120
$120
$120
$120
interest payment
Repayment of loan
$600
Year 1
Appendix 14A. The Application of Adjusted Present Value
(APV) Method to Lead versus Buy Decision
 NPV of the lease


  Additional effects when 
APV
of
the
lease
relaive
to
the
purchase

 

   purchase is financed



when purchase is financed  
 relaive to the purchase 


  with some debt

 by all equity

Table 14.A.2
Lease Minus Buy
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Lease
Lease Payment
Tax benefit of lease payment
Buy (minus)
-$12,500
-$12,500
-$12,500
-$12,500
-$12,500
$4,250
$4,250
$4,250
$4,250
$4,250
-$1,700
-$1,700
-$1,700
-$1,700
-$1,700
-$9,950
-$9,950
-$9,950
-$9,950
-$9,950
$50,000
Cost of machine
Lost depreciation tax benefit
Total
$50,000
Appendix 14A. The Application of Adjusted Present Value
(APV) Method to Lead versus Buy Decision
$9,950 $9,950
All-Equity NPV  $50, 000 

1.065 1.065 2

$9,950
1.065
3

$9,950
1.065
4

$9,950
1.065
5
 $8650.99
$1,105
$933
$753
$565
$369




 $3,191.55
2
3
4
5
1.065 1.065  1.065  1.065  1.065 
Appendix 14A. The Application of Adjusted Present Value
(APV) Method to Lead versus Buy Decision
Table 14.A.3.
Year 0
Year 1
Year 2
Year 3
Year 4
$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
$7,805
$8,140
$8,489
$8,853
$16,713
Out Standing balance of loan
$50,000
Year 5
gernerates over leasing firm
Repayment of loan