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J B GUPTA CLASSES 98184931932, drjaibhagwan@gmail.com,
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Copyright: Dr JB Gupta
Chapter 9Chapter 9Chapter 9Chapter 9 Lease DecisionsLease DecisionsLease DecisionsLease Decisions
Chapter IndexChapter IndexChapter IndexChapter Index
� Three Methods of Lease V/S Purchase Evaluation
� Calculation of Lease Rent – 4 Situations
� Lease V/S Hire Purchase
� Monthly Lease Installments
� Calculation of Cost of the Machine
� Cross – Border Lease
� Extra Practice (Must Do)
� Extra Practice (Optional)
� Theoretical Aspects
(i) Financial Lease v/s Operating Lease
(ii) Advantages of Lease Fancying
(iii) IRR Method of Lease Evaluation
(iv) Cross-Border Lease
There are three methods of lease decisions :
(i) NPV : Find NPV by the method discussed in capital budgeting chapter. If
the question is silent about loan repayment including interest, it may be
assumed that loan will be repaid including interest in the same period as
the term of lease. This assumption places loan on an equivalent basis with
lease.
(ii) Cost of Lease by IRR Method: Find incremental cash flows of lease assuming purchase
with the help of own funds. Find cost of lease by IIRR Method.
(iii) Williomson Method (B.S.W. Method) Under this method, we find operating
result and financial result. Tax is totally ignored for calculating financial
result. Financial result in “PV of loan repayments including interest – PV
of lease payment”. Operating result is PV of “Tax saving in case of lease
– tax saving in case of purchase”. Find sum of both results. If the sum is
2
positive, lease is preferred. If sum is zero, the decision is taken on the
basis of non-financial considerations. If the sum is negative, purchase is
preferred.
Lease v/s buy decision: The key issue in lease v/s buy decision is the appropriate
discount rate. In this connection there are two views :
(i) We have to decide regarding acquiring a fixed asset. We use the capital
budgeting technique. Hence, the appropriate discounting rate is cost of
capital.
(ii) The other view is quite different. A lease versus buy analysis is
performed when the decision is made to acquire an asset. “It is not a
capital expenditure decision. It is financing decision. Whether nor not to
acquire the asset is not part of typical lease analysis – in a lease
analysis we are simply concerned with whether to obtain the use of the
asset through lease or by purchase.1” Rather we can say the analysis
does not aim to decide lease or purchase (as the purchase has already
been decided); it is to decided whether lease or borrow. The cash flows
of this analysis are more like debt service cash flows than operating
cash flows2. Hence the appropriate discount rate is the after tax cost of
debt.
The second view seems to be more appropriate.
[The students are advised to follow the second view except in the following cases:
(i) We are given discount rate in the question, we should discount the cash
flows at the given discount rate ( For example Question No.19, please the
first sentence of the question) (ii) Post – tax cost of debt is neither given in
the question nor it can be calculated ( for example : Questions No.10,33) and
(iii) We are given the present value factors (PVFs) in the question and these
are not of “post –tax cost of debt”. (For example : Question No.18) We should
discount the cash flows on the basis of these PVFs.]
The above-mentioned difference of opinion does not apply to decision from lessor
point of view. From the lessor point of view, the lease analysis is a capital
expenditure decision (capital budgeting decision). Hence, the appropriate
discount rate is the cost of capital of the firm.
THREE METHODS OF LEASE V/S PURCHASE EVALUATIONTHREE METHODS OF LEASE V/S PURCHASE EVALUATIONTHREE METHODS OF LEASE V/S PURCHASE EVALUATIONTHREE METHODS OF LEASE V/S PURCHASE EVALUATION
Q. No. 1: Q. No. 1: Q. No. 1: Q. No. 1: An industrial unit desires to acquire a machine costing Rs.5 Lakh which has
an economic life of 10 years, scrap value nil. The unit is considering the alternative
choice of:
1 Financial Management – Brigham and Ehrhardt.
2 There is almost no uncertainty in debt –service like cash flows as the cash flows are governed by
the contracts. The operating cash flows are estimated ones, these are not contractual, hence these
are uncertain.
3
(a) Taking machine on lease of
(b) Purchasing the asset by raising loan.
Lease payments are to be made in advance and the lessor requires the asset to the
completely amortized over its useful life and that the asset will yield him a return of 10 per
cent.
Rate of interest is 16 per cent p.a. Tax 50 per cent. Straight line method of
depreciation may be adopted. Evaluate the proposal by all three methods of
evaluation of lease v/s buy. (May, 1984)(May, 1984)(May, 1984)(May, 1984)
AnswerAnswerAnswerAnswer
Working Notes 1
Annual lease rent = 5,00,000 × ———— = 73976
1 + 5.759
Tax savings on annual lease rent = 36,988
1 3Annual payment to bank= 5,00,000 × ————--- = 89,174 1 + 4.607
Table showing interest in various bank payments:
Amt. Due Principal Interest Tax Saving of Interest. I 5,00,000
89,174 89,174 — —
II 4,10,826
23,442 23,442 65,732 32,866
III 3,87,384
27,193 27,193 61,981 30,991
IV 3,60,191
31,543 31,543 57,631 28,816
V 3,28,648
36,590 36,590 52,584 26,292
VI 2,92,058
42,444 42,444 46,730 23,365
VII 2,49,614
49,236 49,236 39,938 19,969
VIII 2,00,378
57,113 57,113 32,061 16,031
IX 1,43,265
66,252 66,252 22,922 11,461
3 As the question is silent about the schedule of loan repayment including interest, it has been
assumed that loan will be repaid including interest in the same period as the term of lease. This
assumption places loan on an equivalent basis with lease.
4
X 77,013
77,013 77,013 12,161 6,081
NPV METHODNPV METHODNPV METHODNPV METHOD
DCF ANALYSIS OF LEASDCF ANALYSIS OF LEASDCF ANALYSIS OF LEASDCF ANALYSIS OF LEASE PROPOSAL E PROPOSAL E PROPOSAL E PROPOSAL
PERIIOD PVF/A CASHFLOW PV
Lease rent 0-9 7.247 -73976 annually -5,36,104
Tax savings 1-10 6.710 +36988 annually +2,48,189
-2,87,915
DCF ANALYSIS OF PURCDCF ANALYSIS OF PURCDCF ANALYSIS OF PURCDCF ANALYSIS OF PURCHASE PROPOSAL HASE PROPOSAL HASE PROPOSAL HASE PROPOSAL
PERIIOD PVF/A CASHFLOW PV
Bank payments 0-9 7.247 -89,17489,17489,17489,174 annually -6,46,244
Tax savings 1 0.926 +57,866 +53,584
2 0.857 +55,911 +47,916
3 0.794 +53,816 +42,730
4 0.735 +51,292 +37,700
5 0.681 +48,365 +32,937
6 0.630 +44,969 +28,330
7 0.583 +41,031 +23,921
8 0.540 +36,461 +19,689
9 0.500 +31,081 +15,541
10 0.463 +25,000 +11,575
-332321
Lease is recommended on account of its lower net present value of cost.
TeachinTeachinTeachinTeachingggg note:note:note:note: not to be given in the exam: the interest included in 2nd payment
will be allowed as deduction for income tax purposes against I year’s taxable
income. It is the interest for the first year and it is being paid before the last date
of submitting the Income Tax return.
Similarly, the interest included in 3rd payment will be allowed as deduction for
income tax purposes against the II year’s taxable income.
And so on.
[Section 43(b) of Income tax Act,1961]
5
COST OF LEASE METHODCOST OF LEASE METHODCOST OF LEASE METHODCOST OF LEASE METHOD
(ALSO KNOWN AS IRR M(ALSO KNOWN AS IRR M(ALSO KNOWN AS IRR M(ALSO KNOWN AS IRR METHOD OF LEASE EVALUETHOD OF LEASE EVALUETHOD OF LEASE EVALUETHOD OF LEASE EVALUATIONATIONATIONATION)
INCRREMENTAL CASHFLOWS
PERIIOD LEASE PURCHASE INCREMENTAL CASHFLOW
0 -73,976 -5,00,000 +4,26,024
1 -36,988 +25,000 -61988
2 -36,988 +25,000 -61988
3 -36,988 +25,000 -61988
4 -36,988 +25,000 -61988
5 -36,988 +25,000 -61988
6 -36,988 +25,000 -61988
7 -36,988 +25,000 -61988
8 -36,988 +25,000 -61988
9 -36,988 +25,000 -61988
10 +36,988 +25,000 +11988
FAKE PAYBACK PERIOD = 4,26,024/61988 = 6.87
Consulting the annuity table, approximate rate = 6%
NPV at 6%
+426024
-61988x6.802
+11988x0.558
= +11,071
NPV at 4%
+426024
-61988x7.435
+11988x0.676
= -26753
Cost of Lease :
-26,753
= 4 + ---------------------------x 2 = 5.42 %
-26753 – 11071
Cost of lease = 5.42%
Cost of borrowing = 8%. Lease is recommended.
WILLIOMSON METHODWILLIOMSON METHODWILLIOMSON METHODWILLIOMSON METHOD (B.S.W METHOD)(B.S.W METHOD)(B.S.W METHOD)(B.S.W METHOD)
Financial result = 89,174 (1 + 4.607) – 73,976 (1 + 4.607) = + 85,217.
6
Computation of operating result:
Year Tax Saving Tax Saving Net Tax P.V. (8%) (Lease) (Purchase) Savings 1. 36,988 25,000 + 32,866 – 20,878 – 19,333
2. 36,988 25,000 + 30,911 – 19,003 – 16,286
3. 36,988 25,000 + 28,816 – 16,828 – 13,361
4. 36,988 25,000 + 26,292 – 14,304 – 10,513
5. 36,988 25,000 + 23,365 – 11,377 – 7,748
6. 36,988 25,000 + 19,969 – 7,981 – 5,028
7. 36,988 25,000 + 16,031 – 4,042 – 2,154
8. 36,988 25,000 + 11,461 527 + 285
9. 36,988 25,000 + 6,081 5,907 + 2,954
10. 36,988 25,000 + 0 11,988 + 5,550 —————
– 65,634
Total Result = 85,217 + (– 65,634) = 19,583
As total result is positive, lease may be preferred.
CALCULATION OF LEASE RENT CALCULATION OF LEASE RENT CALCULATION OF LEASE RENT CALCULATION OF LEASE RENT –––– 4 SITUATIONS4 SITUATIONS4 SITUATIONS4 SITUATIONS
I.I.I.I. Calculation of lease rent which matches with purchase/loan option : Assume
lease rental to be x. Equate “ present value of purchase/loan option” with
“present value of lease option (based on lease rent x )”. Find the value of x.
This is referred as break-even lease rental.
Example : Example : Example : Example : Q. No. 2, 3
II.II.II.II. Calculating equal lease rent to provide pre tax return to lessor:
Lease rent = Apply IRR method ( ignore the tax of Lessor)
Example:Example:Example:Example: Q. No. 1.
III. III. III. III. Calculating unequal lease rent to provide pre tax return to lessor:
Apply IRR method. Example:Example:Example:Example: Q. No. 4. ( ignore the tax of Lessor)
IV. IV. IV. IV. Calculating lease rent to provide post tax return to the lessor.
Apply IRR method.
Example :Example :Example :Example : Q. No. 5,6 (iii) ( consider the tax of Lessor)
TEACHING NOTETEACHING NOTETEACHING NOTETEACHING NOTE: Before calculating lease rent, we should find whether we have
to calculate lease rent from lessee point of view or lessor point of view.
If the question is silent on the point whether we have to calculate pre-tax or post
tax lease rent:
(i) Calculate pre-tax lease rent if we have to take the decision from
lessee point of view ( calculate lease rent ignoring tax)
(ii) Calculate post-tax lease rent if we have to take the decision from lessor
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point of view.
If the question has some specific requirement regarding pre-tax or post-tax lease
rent, we should follow that instruction.
Q .No. 2: Q .No. 2: Q .No. 2: Q .No. 2: Beta Limited is considering the acquisition of a personal computer costing
Rs. 50,000. The effective life of the computer is expected to be five years. The
company plans to acquire the same either by borrowing Rs. 50,000 from its bankers
at 15 per cent interest per annum or by lease. The company wishes to know the
lease rentals to be paid annually which will match the loan option. The following
further information is provided to you:
(a) The principal amount of the loan will be paid in five annual equal installments.
(b) Interest, lease rental, principal repayment are to be paid on the last day of each
year.
(c) The full cost of the computer will be written off over the effective life of
computer on a straight line basis and the same will be allowed for tax purposes.
(d) The company’s effective tax rate is 40 per cent and the after tax cost of capital
is 9 per cent.
(e) The computer will be sold for Rs.1,700 at the end of the fifth year. The
commission on such sales is 9 per cent on the sale value and the same will be
paid.
Compute the annual lease rental payable by Beta Limited which will result in
indifference to the loan option. Discount factors: .92, .84, .77, .71, .65.
Answer:Answer:Answer:Answer:
Borrow Rs.50,000 from bank
Period Loan
repayment
Interest Tax Saving on Interest
& Depreciation
CF
1 10000 7500 7000 10500
2 10000 6000 6400 9600
3 10000 4500 5800 8700
4 10000 3000 5200 7800
5 10000 1500 4600 6900
Period 5 : sale of scrap net of com. and tax = 1700x.91x.60 = Rs.928
Present value of cost under purchase proposal:
Period PV of cost
1 10500x0.92
2 9600x0.84
3 8700x0.77
4 7800x0.71
5 6900x.0.65
5 -928x0.65
33,843
8
Let equal. Lease rent (annual) =X
(0.60X)(3.89) = 33843 X = 14500
Hence annual lease rent (equal. To purchase proposal) = Rs.14500
TEACHING NOTETEACHING NOTETEACHING NOTETEACHING NOTE – not to be given in the exam: Cost Rs.50,000. Depreciation
claimed in 5 years Rs.50,000 (because the question says that the full cost of the
computer will be written off over the effective life of computer on a straight line
basis).
WDV = Nil
Net sale value of scrap = 1,700 x 0.91 = 1547
STCG = 1547
( The capital gain / loss on the depreciable asset is treated as STC gain/ STC loss
for Income tax purposes)
Tax on STCG = 619
Net realization = 1547 – 619 = Rs.928
Q. No.3Q. No.3Q. No.3Q. No.3:::: Welsh Limited is faced with a decision to purchase or acquire on lease a
mini car. The cost of mini car is Rs.1,26,965. It has a life of 5 years. The mini car
can be obtained on lease by paying equal lease rentals annually. The leasing
company desires a return of 10 per cent on the gross value of the asset. Welsh
Limited can also obtain 100 per cent finance from its regular banking channel. The
rate of interest will be 15 per cent p.a. and the loan will be paid in five annual equal
installments, inclusive of interest. The effective tax rate of the company is 40 per
cent. For the purpose of taxation it is to be assumed that the asset will be written off
over a period of 5 years on a straight line basis.
(a) Advise Welsh Limited about the method of acquiring the car.
(b) What should be the annual lease rental to be charged by the leasing company to
match the loan option? ((((May 1996May 1996May 1996May 1996)))) (20 Marks)
Answer :Answer :Answer :Answer :
(a)Working notes :(a)Working notes :(a)Working notes :(a)Working notes :
Assumption :lease rent is payable in the beginning of the year.
Annual lease rent = ( 1,26,965 ) / ( 1 + 3.17 ) = 30,447
4Loan installment = ( 1,26,965 ) / ( 1 + 2.855) = 32,935
4 As the question is silent about the schedule of loan repayment including interest, it has been
assumed that loan will be repaid including interest in the same period as the term of lease. This
assumption places loan on an equivalent basis with lease.
9
CaCaCaCalculation of interest lculation of interest lculation of interest lculation of interest : : : :
Amount due Principal Interest
Total borrowing
I Payment
II Payment
III Payment
IV Payment
V payment
1,26,965
32,935
94,030
18,830
75,200
21,655
53,545
24,903
28,642
28,642
32,935
18,830
21,655
24,903
28,642
Nil
14,105
11,280
8,032
4,293
Year Dep. Dep. + int. Tax savings PV
1 25393 39498 15799 14488
2 25393 36673 14669 12351
3 25393 33425 13370 10322
4 25393 29686 11874 8407
5 25393 10157 6602
DCF ANALYSIS OF PURCDCF ANALYSIS OF PURCDCF ANALYSIS OF PURCDCF ANALYSIS OF PURCHASE PROPOSAL HASE PROPOSAL HASE PROPOSAL HASE PROPOSAL
PERIIOD PVF/A CASHFLOW PV
Bank payments 0-4 4.24 -32,935 -1,39,644
Tax savings +52,170
NPV OF COST -87474
DCF ANALYSIS OF LEASDCF ANALYSIS OF LEASDCF ANALYSIS OF LEASDCF ANALYSIS OF LEASE PROPOSAL E PROPOSAL E PROPOSAL E PROPOSAL
PERIIOD PVF/A CASHFLOW PV
Lease rent 0-4 4.24 -30,447 Annually -1,29,095
Tax savings 1-5 3.89 +12,179
Annually
+47,376
NPV OF COST -81,719
Lease is recommended on account of its lower net present value of cost.
Answer (b) Answer (b) Answer (b) Answer (b)
Let the required lease rent = y
10
-87474 = -y(4.24) + 0.40y(3.89)
-2.684y = -87474
y = 32591
Annual lease rent (payable in the beginning of each year) = Rs.32,591
Q. No. 4: Q. No. 4: Q. No. 4: Q. No. 4: X Ltd is to acquire a machine, costing Rs.1,00,000 on 5 years lease.
Calculate annual lease rent if the lessor expects pre-tax return of 10% and the lease
rents are to be in the ratio of 1:2:3:4:5 for 1st , 2nd,….. 5th year respectively.
AnswerAnswerAnswerAnswer
Assumption: Lease rent is to be paid in the beginning of the year.
Let annual lease rent = y
0 = - 1,00,000 + y + 2.y.(0.909) + 3.y.(0.826) +4.y.(0.751) + 5.y.(0.683)
- 11.715.y = -1,00,000
y =8,536
Year Lease rent payable in the beginning of the year
1 Rs. 8,536
2 Rs.17,072
3 Rs.25,608
4 Rs.34,144
5 Rs.42,680
Q. No.5: Q. No.5: Q. No.5: Q. No.5: Fair Finance, a leasing company, has been approached by a prospective
customer intending to acquire a machine whose cash down price is Rs.3 Crores.
The customer, in order to leverage his tax position, has requested a quote for a
three year lease rentals payable at the end of each year but in a diminishing manner
such that they are in the ratio of 3:2:1. Depreciation can be assumed to be on
straight line basis and Fair Finance’s marginal tax rate is 35%. The target rate of
return for Fair Finance on the transaction is 10%. Calculate the lease rents to be
quoted for the lease for three years. (Nov. 2004)(Nov. 2004)(Nov. 2004)(Nov. 2004)
Answer:Answer:Answer:Answer: Let lease rent of first year = 3x
Year PV of cash inflow
1 [(3x) – (3x – 1,00,00,000)(.35)] x 0.909
2 [(2x) – (2x – 1,00,000,00)(.35)] x 0.826
3 [(x) – (x – 1,00,00,000)(.35)] x 0.751
Total 3.3345x + 87,01,000
- 3,00,00,000 + 3.3345x + 87,01,000 = 0
x = 63,87,464
Lease rent for 1st year : 1,91,62,392
Lease rent for 2nd year : 1,27,74,928
Lease rent for 3rd year : 63,87,464
Q. No. 6 Q. No. 6 Q. No. 6 Q. No. 6 : Armada Leasing Company is considering a proposal to lease out a school
bus. The bus can be purchased for Rs.5,00,000 and , in turn, be leased out at
11
Rs.1,25,000 per year for 8 years with payments occurring at the end of each
year:
(i) Estimate the internal rate of return for the company assuming tax is ignored
(ii) what should be the yearly lease payment charged by the company in order to
earn 20% annual compounded rate of return before expenses and taxes?
(iii) calculate the annual lease rent to be charged so as to amount to 20% after
tax annual compound rate of return, based on the following assumptions: (a)
tax rate 40 % ,Straight line depreciation (b) annual expenses of Rs.50,000 and
(c) resale value of Rs.100000 after the term. (May, 2003)(May, 2003)(May, 2003)(May, 2003)
AnswerAnswerAnswerAnswer
(i) Pay back period = 5.00.000 / 125000 = 4
Approx. IRR = 19 %
NPV at 19 % = (-500000) + (125000 x 3.954 ) = -5750
NPV at 18 % = (-500000) + (125000 x 4.078 ) = 9750
9750
IRR = 18 + ------------------------ x 1 = 18.6290
9750 – (-5750)
(ii) Assumption: lease rent is payable at year end
Annual lease rent: 5,00,000 / 3.837 = 1,30,310
(iii) Assumption: lease rent is payable at year end
Let annual lease rent = x
[(x) – ( 50,000) – (x-50,000-50,000)(.40)] x 3.837
+ (100000) x (0.233) - 5,00,000 = 0
x = 2,23,730
Q. No. 7:Q. No. 7:Q. No. 7:Q. No. 7: ABC Ltd. is considering a proposal to acquire a machine costing
Rs.1,10,000 payable Rs.10,000 down and balance payable in 10 annual equal
installments at the end of each year inclusive of interest chargeable at 15%.
Another option before it is to acquire the asset on a lease rental of Rs.15,000 per
annum payable at the end of each year for 10 years. The following information is
available :
(i) Terminal scrap value of Rs.20,000 is realizable , if the asset is purchased.
(ii) the company provides 10% depreciation on straight line on the original cost
(iii) Income rate is 50%
You are required to compute and analyze cash flows and to advise as to which
option is better. (May, 2005)(May, 2005)(May, 2005)(May, 2005)
12
AnswerAnswerAnswerAnswer
Purchase option : Annual installment : 100000 /5.0188 = 19925
Amount Due Principal Interest
1,10,000
Down payment -10000 10000 Nil
Balance Due 1,00,000
I Installment -4925 4925 15000
Balance Due 95,075
II Installment -5,664 5664 14261
Balance Due 89,411
III installment -6,513 6513 13412
Balance Due 82,898
IV installment -7,490 7490 12435
Balance Due 75,408
V installment -8,614 8614 11,311
Balance Due 66,794
VI Installment -9,906 9906 10019
Balance Due 56,888
VII installment -11,392 11,392 8533
Balance Due 45,496
VIII installment -13,101 13,101 6,824
Balance Due 32,395
IX Installment -15,066 15066 4859
Balance Due 17,329
X Installment -17,329 17329 2596
Balance Due nil
PV of tax savings on interest and depreciation
Year Int. and
depreciation
Tax saving on int.
and Depreciation
PVF PV
1 26000 13000 .930 12090
2 25261 12631 .865 10926
3 24412 12206 .805 9826
4 23435 11718 .748 8765
5 22311 11156 .696 7765
6 21019 10510 .647 6800
7 19533 9767 .602 5880
8 17824 8912 .560 4991
9 15859 7930 .521 4132
10 13596 6798 .484 3290
13
Total 6.858 74465
NPV of purchase proposal:
Period PV
Payment to Bank 0 -10,000
----do------- 1-10 -19925 x 6.858
Tax saving on
depreciation and interest
+74465
Sale of scrap net of tax 10 +10,000 x 0.484
NPV of cost under purchase proposal -67,341
NPV of cost under lease = -7,500 x 6.858 -51,435
Lease is recommended.
Q. No. 8:Q. No. 8:Q. No. 8:Q. No. 8: ABC Ltd sells computer services to its clients. The company has recently
completed a feasibility study and decided to acquire an additional computer, the
details of which are as follows:
(i) The purchase price of the computer is Rs.2,30,000; maintenance, property taxes
and insurance will be Rs.20,000 per year. The additional expenses to operate the
computer are estimated to be Rs.80,000. If the computer is rented from the owner,
the annual rent will be Rs.85,000, plus 5% of the annual billings. The rent is due on
the last day of each year.
(ii) Due to competitive conditions, the company feels that it will be necessary to
replace the computer at the end of three years with a more advanced model. Its
resale value is estimated at Rs.1,10,000.
(iii) Tax rate 50%. Depreciation method: straight line.
(iv) The annual billing will be Rs.2,20,000 in the first year and Rs.2,60,000 annually
for next two years
(v) if the computer is purchased, the company will borrow to finance the purchase
from a bank with interest at 16% p.a. the interest will be paid regularly and the
principal will be returned in lump sum at the end of year 3.
Should the company purchase the computer or lease it? Assume (i) cost of capital as
12%, (ii) straight line depreciation (iii) Salvage value Rs.1,10,000 and evaluate the
proposal from the point of view of lessor also. (Nov. 2007)(Nov. 2007)(Nov. 2007)(Nov. 2007)
AnswerAnswerAnswerAnswer
Assumptions:
(i) The lessor’s cost of capital is 12%.
(ii) (a)The maintenance, property taxes and insurance Rs. 20,000 per year
and (b) operating expenses of Rs, 80,000 per year will be born by ABC
Ltd in case of lease as well as purchase.
Decision from lessee point of view (Rs.’000)
14
DCF analysis of Lease Proposal
Year 1 Year 2 Year 3 Total
Payment to lessor 85 + 11 85 + 13 85+13
Tax savings 48 49 49
Net cash outflow 48 49 49
PV 0.926 x48 0,857 x 49 0.794 x 49 125.35
Year 1 Year 2 Year 3 Total
Payment to bank 36.80 36.80 266.80
Tax saving on dep.& int. 38.40 38.40 38.40
Sale of scrap - - 110
Net cash flow +1.60 +1.60 -118.40
PV +1.60 x 0.926 +1.60 x 0.857 -118.40 x 0.794 91.16
Buying is recommended on account of its lower net present value of cost.
Analysis of the proposal from lessor point of view Analysis of the proposal from lessor point of view Analysis of the proposal from lessor point of view Analysis of the proposal from lessor point of view :
Working note (Rs.Thousands)
Year Lease rent +
revenue share
Depreciation Tax Cash flow
1 96 40 28 68
2 98 40 29 69
3 98 40 29 69
NPV (Rs.’000) = - 230 + 68.(0.893) + 69.(0.797) +179.(0.712) = 13.165
Lease proposal is profitable from the lessor point of view.
Q. No. 9:Q. No. 9:Q. No. 9:Q. No. 9: Agrani Ltd. is in the business of manufacturing bearings. Some more
product lines are being planned to be added to the existing system. The machinery
required may be bought or may be taken on lease. The cost of machine is
Rs.40,00,000 having a useful life of 5 years with the salvage value of Rs.8,00,000.
The full purchase value of machine can be financed by 20 per cent loan repayable in
five equal installments falling due at the end of each year. Alternatively, the machine
can be procured on a 5 years lease, year-end lease rentals being Rs. 12,00,000 per
annum. The company follows the written down value method of depreciation at the
rate of 25 per cent. Company’s tax rate is 35 per cent and cost of capital is 14 per
cent:
(i) Advise the company which option it should choose – lease or borrow.
(ii) Assess the proposal from the lessor’s point of view examining whether leasing
the machine is financially viable at 14 per cent cost of capital (Detailed working
notes should be given. Calculations can be rounded off to Rs. lakhs. ((((Nov. 2002Nov. 2002Nov. 2002Nov. 2002))))
15
Working note :Working note :Working note :Working note :
AnswerAnswerAnswerAnswer
Loan installment = ( 40,00,000 ) / ( 2.991 ) = 13,37,345
Calculation of interest and tax savings of interest: Calculation of interest and tax savings of interest: Calculation of interest and tax savings of interest: Calculation of interest and tax savings of interest:
Amount due Principal Interest Tax saving of interest
Total borrowing
I Payment
II Payment
III Payment
IV Payment
V payment
40,00,000
5,37,345
34,62,655
6,44,814
28,17,841
7,73,777
20,44,064
9,28,532
11,15,532
11,15,532
5,37,345
6,44,814
7,73,777
9,28,532
11,15,532
8,00,000
6,92,531
5,63,568
4,08,813
2,21,813
2,80,000
2,42,386
1,97,249
1,43,085
77,635
YEAR DEP/STCL WDV
1 10,00,000 30,00,000
2 7, 50,000 22,50,000
3 5,62,500 16,87,500
4 4,21,875 12,65,625
5 4,65,625 (STCL)
Assumption: In future year 5, the company shall have sufficient amount of STCG to
take tax advantage, by way of set off, of STCL arising in that year.
Tax savings on Depreciation / STCL :Tax savings on Depreciation / STCL :Tax savings on Depreciation / STCL :Tax savings on Depreciation / STCL :
Year 1: 3,50,000 Year 2: 2,62,500
Year 3:1,96,875 Year 4: 1,47,656
Year 5: 1,62,969
Year Loan
installment
Tax savings on Interest
& Depreciation / STCL
CF
1 1337345 630000 707345
2 1337345 504886 832459
3 1337345 394124 943221
4 1337345 290741 1046604
5 1337345 240604 1096741
DCF analysis at 13%
Year PV of cash inflow
1 -(707345 x 0.885)
2 -(832459 x 0.783)
3 – (943221 x .693)
16
4 –(1046604 x 0.613)
5 - (1096741 x 0.543)
5 +(800000 x 0.543) Sale of scrap
Total -27,34,165
(iii) DCF analysis of proposal of giving the asset on lease :
Period Particulars PV of cash flow
1-5 Lease rent net of tax +[12,00,000 x 0.65(3.432)]
1 Tax savings on Depreciation +[(350000 x 0.877)
2 ------do------------ +(262500 x 0.769)
3 ------do------------ +(196875x0.675)
4 ------do------------- +(147656x0.592)
5 Tax savings on STCL + (162969x.519)]
5 Sale of scrap +[800000 x 0.519]
0 Cost of machine -40,00,000
Total -94142
The machine not to be given on lease.
LEASE V/S HIRE PURCHASELEASE V/S HIRE PURCHASELEASE V/S HIRE PURCHASELEASE V/S HIRE PURCHASE
Q. No. 10: Q. No. 10: Q. No. 10: Q. No. 10: Company X needs a machine which if purchased outright will cost
Rs.10Lakhs. A Hire purchase and Leasing company has offered two alternatives as
below:
Hire purchase :Hire purchase :Hire purchase :Hire purchase : Rs.2,50,000 down payment, 3 annual installments of
Rs.4,00,000 each payable at year end.
Lease : Lease : Lease : Lease : Rs.20,000 initial fees payable on signing the agreement. 3 annual year-end
installments of Rs.4,32,000 each.
Straight line depreciation. Salvage value zero. Tax rate is 30%. Advise the company
as to which alternative implies least cost.
AnswerAnswerAnswerAnswer
Hire PurchaseHire PurchaseHire PurchaseHire Purchase
Total payment under hire purchase 2,50,000 + 4,00,000x3 =14,50,000
Cash price 10, 00,000
Total interest 4,50,000
INTEREST IN VARIOUS INSTALMENTS:
I 2,25,000, II 1,50,000, III 75,000.
Period Down payment/installment Tax savings Net cash flow
0 - 2,50,000 - -2,50,000
1 -4,00,000 +67,500 -3,32,500
2 -4,00,000 +45,000 -3,55,000
17
3 -4,00,000 +22,500 -3,77,500
Statement showing incremental cash flows on account of hire purchase
PERIOD HP Outright purchase Incremental CFs
0 -250000 -1000000 +750000
1 -332500 - -332500
2 -355000 - -355000
3 -377500 - -377500
Average CF = (332500 + 355000 + 377500) / 3 = 355000
Fake pay back period = 750000 / 355000 = 2.11 App. Cost of HP = 20 %
NPV at 20 %.
PERIIOD PVF/A CASHFLOW PV
0 1 +7,50,000 750000
1 0.833 -3,32,500 -2,76,973
2 0.694 -3,55,000 -2,46,370
3 0.579 -3,77,500 -2,18,573
NPV +8,085
As NPV is positive, the other rate may be lower say, 18%
NPV at 18 %.
PERIIOD PVF/A CASHFLOW PV
0 1 +7,50,000 7,50,000
1 0.847 -3,32,500 -2,81,628
2 0.718 -3,55,000 -2,54,890
3 0.609 -3,77,500 -2,29,898
NPV -16,415
Cost of Hire Purchase:
Lower rate NPV
= Lower rate + ————————————————— × Diff. in rates
Lower rate NPV – Higher rate NPV
-16415
18
= 18 + ----------------- x 2 = 19.34%
-16415 - 8085
LeaseLeaseLeaseLease
Period payments/ Tax savings NET CASH FLOW
0 - 20000 - -20,000
1 -432000 +1,35,600 -2,96,400
2 -432000 +1,29,600 -3,02,400
3 -432000 +1,29,600 -3,02,400
Statement showing incremental cash flows on account of lease
PERIO
D
lease Outright
purchase
Incremental CFs
0 -20000 -1000000 +980000
1 -296400 +100000 -396400
2 -302400 +100000 -402400
3 -302400 +100000 -402400
Average CF = (3,96,400 +4,02,400 +4,02,400 / 3 = 4,00,400
Fake pay back period = 980000 /400400 = 2.45
App. Cost of Lease = 11 %
NPV at 11%
PERIIOD PVF/A CASHFLOW PV
0 1 +9,80,000 +9,80,000
1 0.901 -3,96,400 -3,57,156
2 0.812 -4,02,400 - 3,26,749
3 0.731 -4,02,400 - 294,154
NPV +1,941
As NPV is positive, the other rate may be taken at lower level, say 10%
NPV at 10%
PERIIOD PVF/A CASHFLOW PV
0 1 +9,80,000 +9,80,000
1 0.909 -3,96,400 -360328
2 0.826 -4,02,400 -332382
3 0.751 -4,02,400 -302202
NPV -14,912
Cost of lease:
19
Lower rate NPV
= Lower rate + ——————————————------- × Diff. in rates
Lower rate NPV – Higher rate NPV
-14,912
= 10 + ----------------- x 1 = 10.88 %
-14912 - 1941
Lease is recommended as its cost is lower than that of HP.
MONTHLY LEASE INSTALMENTSMONTHLY LEASE INSTALMENTSMONTHLY LEASE INSTALMENTSMONTHLY LEASE INSTALMENTS
Q. No. 11Q. No. 11Q. No. 11Q. No. 11: Kunti Ltd requires a machine costing Rs.5,00,000. It has received four
lease proposals from different leasing companies.
I : I : I : I : Vasudev Ltd has offered to lease out the machine for a period of 120 months, the
lease rent payable at the end of the month as per the following schedule :
First 36 months Rs.32 per month per Rs.1,000 of the machine cost
Next 24 months Rs.28 per month per Rs.1,000 of the machine cost
Next 60 months Rs.10 per month per Rs.1,000 of the machine cost.
Vasudev Ltd has offered to sell the machine to Kunti Ltd for Rs.1000 after 10 years.
II : II : II : II : Parthsarthy Ltd has offered to lease out the machine for a period of 96 months,
the lease rent payable at the end of the month as per the following schedule :
First 36 months Rs.40 per month per Rs.1,000 of the machine cost
Next 24 months Rs.28 per month per Rs.1,000 of the machine cost
Next 36 months Rs.10 per month per Rs.1,000 of the machine cost.
The lessor will abandon the machine after the expiry of the lease period.
III : III : III : III : Under the offer from Devaki Nandan Ltd., Kunti Ltd has to make a security
deposit of Rs.1,00,000 and pay the lease rent at the end of the months as follows:
First 36 months Rs.30 per month per Rs.1,000 of the machine cost
Next 24 months Rs.28 per month per Rs.1,000 of the machine cost
Next 24 months Rs.10 per month per Rs.1,000 of the machine cost.
After 84 months, the ownership of the machine will be transferred to Kunti Ltd
against the security deposit. Kunti Ltd shall be able to use the machine for further 3
years and after that its scrap value will be nil.
Assume (i) the cost of capital of Kunti Ltd being 12% p.a.(ii) Depreciation rate for tax
purposes : 15% and (iii) Tax rate applicable to Kunti Ltd is 35%. Advise. Present
value factors at 12% p.a.
Year Monthly discounting factor Year end discounting factor
1 0.940 0.893
2 0.839 0.797
3 ? 0.712
4 ? 0.636
5 ? 0.567
20
6 ? 0.507
7 ? 0.452
8 ? 0.404
9 ? 0.361
10 ? 0.322
AnswerAnswerAnswerAnswer
General assumptions:
(a) The machine is required for 10 years
(b) After 10 Years its value will be zero
Alternative specific assumptions & notes
Alternative I WE shall be paying lease rent for 10 years , we shall not purchase
machine after 10 years as it shall have no value [ see our general assumption (b)]
Alternative II We shall be paying lease rent for 8 years, we shall be using the
machine for 10 years i.e. for 2 years ( year 9th and 10th ) we shall be using the
machine without paying lease rent .
Alternative III No depreciation or tax saving on initial deposit under Income Tax
Act, 1961. Depreciation on this amount will be allowed under WDV method after 7
years when the ownership will be transferred to us.
It is assumed that the machine will be discarded in the beginning of 11th year.
A note on monthly discounting factor:A note on monthly discounting factor:A note on monthly discounting factor:A note on monthly discounting factor:
Monthly discounting factors given in the question represent PV of Cash flow of 1/12
rupee at the end of each month. In other words, these factors represent average of
PVFs calculated on monthly basis.
For example:
Monthly discounting factor for year 1:
1/12[(1/1.01) + (1/1.02) +………+ (1/1.12)] = 0.940
Monthly discounting factor for year PVF
3 0.750
4 0.669
5 0.598
6 0.534
7 0.477
Working note III Alternative
Year Depreciation Tax savings
1 15,000 5,250
2 12,750 4,463
3 10,838 3,793
DCF Analysis of I Proposal
21
YEAR PV OF “LEASE RENT LESS TAX SAVINGS”
1 (-1,92,000 X 0.940) + (0.893 X 67,200) = -1,20,470
2 (-1,92,000 X 0.839) + (0.797 X 67,200) = -1,07,530
3 (-1,92,000 X 0.750) + (0.712 X 67,200) = - 96,154
4 (-1,68,000 X 0.669) + (0.636 X 58,800) = - 74,995
5 (-1,68,000 X 0.598) + (0.567 X 58,800) = - 67,124
6 ( -60,000 X 0.534) + (0.507 X 21,000) = - 21,393
7 ( -60,000 X 0.477) + (0.452 X 21,000) = - 19,128
8 ( -60,000 X 0.426) + (0.404 X 21,000) = - 17,076
9 ( -60,000 X 0.380) + (0.361 X 21,000) = - 15,219
10 ( -60,000 X 0.340) + (0.322 X 21,000) = - 13,638
NPV OF COST 5,52,727
DCF Analysis of II Proposal
YEAR PV OF “LEASE RENT LESS TAX SAVINGS”
1 (-2,40,000 X 0.940) + (0.893 X 84,000) = -1,50,588
2 (-2,40,000 X 0.839) + (0.797 X 84,000) = -1,34,412
3 (-2,40,000 X 0.750) + (0.712 X 84,000) = -1,20,192
4 (-1,68,000 X 0.669) + (0.636 X 58,800) = - 74,995
5 (-1,68,000 X 0.598) + (0.567 X 58,800) = - 67,124
6 ( -60,000 X 0.534) + (0.507 X 21,000) = - 21,393
7 ( -60,000 X 0.477) + (0.452 X 21,000) = -19,128
8 ( -60,000 X 0.426) + (0.404 X 21,000) = -17,076
NPV OF COST 6,04,908
DCF Analysis of III Proposal
PERIOD PARTICULARS PV
0 SECUIRTY DEPOSIT -1,00,000
PV OF “LEASE RENT LESS TAX SAVINGS”
1 (-1,80,000 X 0.940) + (0.893 X 63,000) = -1,12,941
2 (-1,80,000 X 0.839) + (0.797 X 63,000) = -1,00,809
3 (-1,80,000 X 0.750) + (0.712 X 63,000) = - 90,144
4 (-1,68,000 X 0.669) + (0.636 X 58,800) = - 74,995
5 (-1,68,000 X 0.598) + (0.567 X 58,800) = - 67,124
6 ( -60,000 X 0.534) + (0.507 X 21,000) = - 21,393
7 ( -60,000 X 0.477) + (0.452 X 21,000) = - 19,128
Tax Savings on Depreciation
8 15,000 x 0.35 x 0.404 +2,121
9 12,750 x 0.35 x 0.361 +1,611
10 10,838 x 0.35 x 0.322 +1,221
NPV of Cost 5,81,581
On account of the least cost, I Proposal is recommended.
CALCULATION OF COST OF THE MACHINECALCULATION OF COST OF THE MACHINECALCULATION OF COST OF THE MACHINECALCULATION OF COST OF THE MACHINE
22
Q. No. 12 Q. No. 12 Q. No. 12 Q. No. 12 M/s Gama & Co. is planning of installing a power saving machine and
are considering buying or leasing alternative. The machine is subject to straight-
line method of depreciation. Gama & Co. can raise debt at 14% payable in five
equal annual installments of Rs. 1,78,858 each, at the beginning of the year. In
case of leasing, the company would be required to pay an annual end of year rent
of 25% of the cost of machine for 5 years. The Company is in 40% tax bracket.
The salvage value is estimated at Rs. 24,998 at the end of 5 years.
Evaluate the two alternatives and advise the company by considering after tax
cost of debt concept under both alternatives.
P.V. factors 0.9225, 0.8510, 0.7851, 0.7242, and 0.6681 respectively for 1 to 5
years. (12 Marks) (June 2009)(June 2009)(June 2009)(June 2009)
AnswerAnswerAnswerAnswer :
Let the cost of machine = x
x /(1+ 2.9137) = 1,78858
x = 699998
Calculation of interest and tax savings of interest : Calculation of interest and tax savings of interest : Calculation of interest and tax savings of interest : Calculation of interest and tax savings of interest :
Amount due Principal Interest
Total borrowing
I Payment
II Payment
III Payment
IV Payment
V payment
6,99,998
1,78,858
5,21,140
1,05,898
4,15,242
1,20,724
2,94,518
1,37,625
1,56,893
1,56,893
1,78,858
1,05,898
1,20,724
1,37,625
1,56,893
Nil
7,2960
58,134
41,233
21,965
Annual depreciation = (6,99,998 – 24,998)/5 = 1,35,000
TEACHING NOTE TEACHING NOTE TEACHING NOTE TEACHING NOTE : may not be given in the exam: Under section 43(b) of the
Income tax Act, 1961, the deduction of interest will be allowed on accrual basis
(as interest is being paid before the date of submission of Income Tax return)
Year Dep. + int. Tax savings PV
1 135000+72960 83,184 76,737
2 135000 +58,134 77.254 65,743
23
3 135000 +41,233 70,493 55,344
4 135000 +21,965 62,786 45,470
5 135000 54,000 36,077
Total 2,79,371
DCF Analysis of purchase proposal
PERIIOD PVF/A CASHFLOW PV
Bank payments 0-4 4,2828 1,78,858 Annually -7,66,013
Scrap 5 0.6681 24,998 + 16,701
Tax savings +2,79,371
NPV OF COST 4,69,941
DCF ANALYSIS OF LEASDCF ANALYSIS OF LEASDCF ANALYSIS OF LEASDCF ANALYSIS OF LEASE PROPOSAL E PROPOSAL E PROPOSAL E PROPOSAL
PERIIOD PVF/A CASHFLOW PV
Lease rent
less tax
savings
1-5 3.9509 1,05,000Annually -4,14,845
NPV OF COST 4,14,845
Lease is recommended on account of its lower net present value of cost.
Q. NO. 13 Q. NO. 13 Q. NO. 13 Q. NO. 13 The following data re furnished by he SIGMA leasing Ltd.(SLL).
Investment Rs.99L
Lease period 3 years
Residual value Nil
Pre tax required rate of return 22%
The SLL seeks your advice in determining the annual lease rental under the
following rental structures:
(i) Equated (ii) Stepped (annual increase of 12%) (iii) Ballooned (annual rental of
Rs.15L for year 1 and 2) (iv) Deferred (deferment period 1 year).
You are required to compute the annual rental under four structures.
Answer (i) Answer (i) Answer (i) Answer (i)
Let annual lease rent = x
-99L + x(2.042)= 0
x = 48.48L
Annual lease rent : Rs.48.48L
(ii) Let annual lease rent for period = x
24
-99L + x(0.820) + x(0.672)(1.12) + x(0.551)(1.12)2 = 0
-99L = 2.264x
x = 43.72L
(iii) Let lease rent for 3rd year = x
-99L + 15L(1.492) + x(0.551) = 0
x = lease rent for 3rd year = 139.06L
(iv) Let annual lease rent for 2nd and 3rd year = x
-99L +x(1.223) =0
x= Annual lease rent 80.95L
CROSS – BORDER LEASE
CrossCrossCrossCross----border leasingborder leasingborder leasingborder leasing is a lease arrangement where lessor and lessee are based
in different countries. It is a means of international financing the equipments
requiring huge funds like aircrafts, transport equipments, marine equipments, and
telecommunication equipments etc which have predictable revenue streams.
(Such leases are also referred as Big Ticket Leases). In developing countries,
the local resources may not be available for such financing. The financing is in
the form of debt i.e. the lessor gets the return at fixed rate. It is a safer way of
debt financing as it is easier for a lessor to repossess the leased equipment
following a default by the lessee because the lessor is the owner and not mere
secured lender.
Q. No. 1Q. No. 1Q. No. 1Q. No. 14444 An Indian company is in need of a super computer, operating life of
the super computer being 5 years. Scrap value at the end of the life is estimated
to be nil. It can be purchased for $ 1.50 million with the help of 10% p.a. finance
available in rupees. Alternatively it can be acquired on the basis of lease, annual
lease rent being $ 325000, payable in the beginning of each year for 5 years.
Tax rate : 40%. Depreciation rate: 25% WDV. Interest rates in USA and in India
are 4% and 8% respectively. The spot rate is 1$ = Rs.40.
AnswerAnswerAnswerAnswer
Working note (1)
Using IRPT;
1 year forward rate: 1$ = 41.54
2 years forward rate : 1$ = 43.14
3 years forward rate : 1$ = 44.80
4 years forward rate : 1$ = 46.52
Working note (2)
Period Lease rent (Rs.)c Tax Savings
0 325000x40.00 = 130.00 Lakhs Nil
25
1 325000x41.54 = 135.00 Lakhs 52.00 Lakhs
2 325000x43.14 = 140.20 Lakhs 54.00 Lakhs
3 325000x44.80 = 145.60 Lakhs 56.08 Lakhs
4 325000x46.52 = 151.19 Lakhs 58.24 Lakhs
5 Nil 60.48 Lakhs
Working note (3)
1.50m x 40
Bank installment = ------------ = 143.8849 Lakhs
1 + 3.17
Calculation of interest
Amount due Principal Interest
Total borrowing
I Payment
II Payment
III Payment
IV Payment
V payment
600 Lakhs
143.8849 L
456.1151 L
98,2734 L
357.8417 L
108.1007 L
249.7410 L
118.9100 L
130.8302 L
130.8302 L
Nil
143,8849 L
98.2734 L
108.1007 L
118.9100 L
130.8302 L
Nil
45.6115 L
35.7842 L
24.9741
13.0547
Working note (3)
Assumption : The machine will be discarded in the beginning of 6th year.
Year Dep. Dep. + int. Tax savings PV
1 150 L 195.6115 L 78.2446 L 73.7847 L
2 112.50 L 148.2842 L 59.3137 L 52.7892 L
3 84.375 L 109.3491 L 43.7396 L 36.7413 L
4 63.281 L 76.3357 L 30.5343 L 24.1832 L
5 47.461 L 47.4610 L 18.9844 L 14.1813 L
Total 201.6797 L
MAIN ANSWER : DCF ANMAIN ANSWER : DCF ANMAIN ANSWER : DCF ANMAIN ANSWER : DCF ANALYSIS OF PURCHASE PALYSIS OF PURCHASE PALYSIS OF PURCHASE PALYSIS OF PURCHASE PROPOSAL ROPOSAL ROPOSAL ROPOSAL
PERIIOD PVF/A CASHFLOW PV
Bank payments 0-4 4.465 -143.8849 L - 642.4461 L
26
Tax savings +201.6797 L
NPV OF COST - 440.7664 L
DCF ANALYSIS OF LEASDCF ANALYSIS OF LEASDCF ANALYSIS OF LEASDCF ANALYSIS OF LEASE PROPOSAL E PROPOSAL E PROPOSAL E PROPOSAL
PERIIOD PVF/A CASHFLOW PV
Lease rent 0 1 - 130.00 L - 130.00 L
Tax savings 1 0.943 + 52 L + 49.036 L
Lease rent 1 0.943 - 135,00 L -127.305 L
Tax savings 2 0.890 + 54 L + 48.06 L
Lease rent 2 0.890 - 140.20 L -124.778 L
Tax savings 3 0.840 + 56.08 L + 47.1072 L
Lease rent 3 0.840 - 145.60 L -122.304 L
Tax savings 4 0.792 + 58.24 L +46.1261 L
Lease rent 4 0.792 -151.19 L -119.7425 L
Tax savings 5 0.747 + 60.48 L + 45.1786 L
- 388.6216 L
Lease is recommended on account of its lower net present value of cost
Q. No. 15Q. No. 15Q. No. 15Q. No. 15 A Japanese leasing company is to quote lease rent for 5 aircrafts
required by an Indian company. The operating life of the aircrafts may be
assumed to be 5 years, at the end of which it can be disposed off at 10% of its
cost in US market. The cost of each aircraft is $ 10m. The Japanese tax system
allows sum of digit method depreciation to the lessor. Assume income tax rate in
Japan is 25%. Find the annual lease rent, in yens, to be charged so as to provide
4% post return to the lessor. Assume that the lease rent if payable in the
beginning of each year. The spot rate: 1 $ = 120 Yens. Assume that the USD is
expected to depreciate against Yen by 2% p.a.
AnsAnsAnsAnswer (Calculations on the basis of one airwer (Calculations on the basis of one airwer (Calculations on the basis of one airwer (Calculations on the basis of one air----craft)craft)craft)craft)
Working note (1) 5 years forward rate: 1$ = 120 (0.98)5 Yens = 108.4705 Yens
Working note (2) Calculation of Depreciation:
Cost: 1200 million Yens
Sale of scrap: 108.4705 Million Yens
Depreciable amount: 1091.5295 Million Yens
Year Depreciation PV of Tax savings on Dep.
27
1 1091.5295 x(5/15) = 363.8432m Yens 363.8432 x 0.25 x 0.962
2 1091.5295 x(4/15) = 291.0745m Yens 291.0745 x 0.25 x 0.925
3 1091.5295 x(3/15) = 218.3059m Yens 218.3059 x 0.25 x 0.889
4 1091.5295 x(2/15) = 145.5373m Yens 145.5373 x 0.25 x 0.885
5 1091.5295 x(1/15) = 72.7686m Yens 72.7686 x 0.25 x 0.822
Total 250.4878m Yens
PV of sale of scrap = 108.4705 Million Yens x 0.822 = 89.1628 m Yens
Main Answer:
The lessor wants a return of 4%. Hence NPV at 4% should be zero.
Let annual lease rent = y
PV of lease receipts: y +3.63y = 4,63y
0 = -investment +
PV of lease rent – PV of tax on lease rent +
PV of tax savings on Depreciation + PV of sale of scrap
0 = -1200 + 4.63y – 0.25y (4.452) + 250.4878 + 89.1628
-3.517y = -860.3494
y = 244.6259m Yens
Annual lease rent for five aircrafts = 1223.1295 m Yens
Q. No. 1Q. No. 1Q. No. 1Q. No. 16666 Five aircrafts are required by an Indian company. The operating life of
the aircraft may be assumed to be 4 years, at the end of which it can be disposed
off at 10% of its cost in US market. The cost of each aircraft is $ 10m. The
Indian company can raise the required funds in US market at 6% p.a., the
principal to be payable in four equal annual installments. The pre-tax cost of
debt for the Indian company is 10%, Depreciation rate for tax purpose to be 30%
WDV, tax rate 30%. Alternatively, the Indian company can acquire the aircrafts
on lease from a Japanese company, the leasing company requiring a pre tax 7%
return. Assume that the lease rent is payable at the end of each year. The spot
rate: 1 $ = 120 Yens = Rs.40. Assume no change in foreign exchange rates.
AnswerAnswerAnswerAnswer
Working note (1)
Repayment (Rs.
Million)
Interest Rs.
Million
Tax savings on
interest Rs. Million
(12.50+3.00)x40 = 620 120 36
(12.50+2.25)x40 = 590 90 27
(12.50+1.50)x40 = 560 60 18
(12.50+0.75)x40 = 530 30 9
Working note (2)
Calculation of tax savings on Dep./STCL (Rs. Million)
Year Depreciation/STCL WDV Tax Savings on Dep./ STCL
28
1 600 Dep. 1400 180
2 420 Dep. 980 126
3 294 Dep. 686 88
4 486 STCL 146
It is assumed that future year 4, the company shall have sufficient
amount of Short Term Capital Gain to set off the STCL of Rs.486m.
Working note (3)
Period Cash flows ( Loan repayment –tax savings) (Rs. Million)
1 -620 + 36 + 180 = -404
2 -590 + 27 + 126 = -437
3 -560 + 18 + 88 = -454
4 -530 + 9 + 146 = -375
4 Sale of scrap 200
Working note (4)
Annual lease rent =[(Rs.2000m) – (Rs.200x0.762)] /3.387 = Rs.545.50m
Annual lease rent (net of tax) = Rs.381.85m
Main answer :
Net present value of cost (lease proposal):-381.85x3.387=-Rs.1293.32m
DCF analysis of purchase proposal
‘Purchase’ is recommended on account of its lower net present value of cost
Q 17Q 17Q 17Q 17: : : : 21st Century Leasing company Ltd, an Indian company, has been
approached by a Singapore company for structuring a lease for a Computer
system costing Rs.10,00,000 for a period of six years after which its scrap value
would be Rs.1,00,000. Depreciation : straight line.
The lessor’s required rate of return is 10% post tax. Tax rate applicable to the
lessor is 30%.
The lessor has to incur SGD 1,000 in the beginning of each year for maintenance
of the computer for which the contract has to be given to a Singapore based
Period PVF CF PV
1 0.935 -404 -377.74
2 0.873 -437 -381.50
3 0.816 -454 -370.46
4 0.762 -375 -285.75
4 0.762 +200 +152.40
NPV of cost -1,308.59
29
Computer Maintenance firm. The lessee proposes to pay the lease rental in SGDs
in the beginning of each year.
Calculate annual lease rent assuming 1 SGD = Rs.25.
Ignore the cost of carrying the supercomputer to Singapore and its scrap back to
India.
Answer Answer Answer Answer
Working note:Working note:Working note:Working note:
Year Depreciation Maintenance Depreciation
+Maintenance
Tax
savings
CF (Maintenance
minus tax
savings)
1 1,50,000 25,000 1,75,000 52500 +27500
2 1,50,000 25,000 1,75,000 52500 +27500
3 1,50,000 25,000 1,75,000 52500 +27500
4 1,50,000 25,000 1,75,000 52500 +27500
5 1,50,000 25,000 1,75,000 52500 +27500
6 1,50,000 25,000 1,75,000 52500 +27500
Let annual lease rent = Rs.y
0 = -10,00,000 + {y.(1 +3.791)} –[ 25,000)(1+3.791)]
– {y -25000 – 150000][0.30].(4.355) + 1,00,000(0.564)
0 = -10,00,000 + 4.791y – 119775 – 1.3065y +2,28,638 + 56400
3.4845y = 834737
y = Rs.2,39,557 = 9582SGD
Annual lease rent (receivable in the beginning of the year) = SGD 9582
EXTREXTREXTREXTRA PRACTICE ( MUST DO )A PRACTICE ( MUST DO )A PRACTICE ( MUST DO )A PRACTICE ( MUST DO )
QQQQ. NO. 18 . NO. 18 . NO. 18 . NO. 18 M/s ABC Ltd is to acquire a personal computer with modem and
printer. Its price is Rs.60,000. ABC can borrow Rs. 60,000 from a bank at 12%
p.a. to finance the purchase. The principal sum is to be repaid in five equal year-
end installments. ABC Ltd can also have the computer on lease for 5 years.
The firm seeks your advise to know the maximum lease rent payable at each
year end. Consider the following additional information:
(a) Interest on loan is payable at each year end.
(b) The full cost of the computer will be written off over the effective life of
computer on a straight line basis and the same will be allowed for tax
purposes.
30
(c) The computer will be sold for Rs.1,500 at the end of the fifth year. The
commission on such sales is 8 per cent on the sale value and the same will be
paid. (d) The company’s effective tax rate is 30 per cent and the cost of capital is 11%.
Suggest the maximum annual lease rental payable by ABC Limited . Discount factors:
( at 11%) 0.901, 0.812, 0.731, 0.659, 0.593. ((((Nov. 2009Nov. 2009Nov. 2009Nov. 2009))))
Borrow Rs.60,000 from bank
Period Loan
repayment
Interest Tax Saving on Interest &
Depreciation
Cash outflow
1 12000 7200 5760 13440
2 12000 5760 5328 12432
3 12000 4320 4896 11424
4 12000 2880 4464 10416
5 12000 1440 4032 9408
Period 5 : sale of scrap net of com. and tax = 1500x.92x0.70 = Rs.966
Present value of cost under purchase proposal:
Period PV of cost
1 13440x 0.901
2 12432x 0.812
3 11424x0.731
4 10416x 0.659
5 9408x 0.593
5 -966x 0.593
42470
Let equal. Lease rent (annual) =X
(0.70X)(3.696) = 42470 X =
Hence annual lease rent ( Maximum) = Rs.16,415
Q. No.1Q. No.1Q. No.1Q. No.19 9 9 9 Sundaram Ltd. discounts its cash flows at 16% and is in the tax bracket
of 35%. For the acquisition of a machinery worth Rs.10,00,000, it has two options
– either to acquire the asset by taking a bank loan @ 15% p.a. repayable in 5
yearly installments of Rs.2,00,000 each plus interest or to lease the asset at
yearly rentals of Rs.3,34,000 for five (5) years.
In both the cases, the instalment is payable at the end of the year. Depreciation
is to be applied at the rate of 15% using ‘written down value’ (WDV) method. You
are required to advise which of the financing options is to be exercised and why.
Year 1 2 3 4 5
P.V factor @16% 0.862 0.743 0.641 0.552 0.476
(14 Marks) ) (JUNE 2009(JUNE 2009(JUNE 2009(JUNE 2009)
31
Answer Answer Answer Answer
Borrow Rs.10,00,000 from bank
Period Loan
repayment
Interest Dep. Tax Saving on
Interest &
Depreciation
Cash
outflow
1 2,00,000 1,50,000 1,50,000 1,05,000 2,45,000
2 2,00,000 1,20,000 1,27,500 86,625 2,33,375
3 2,00,000 90,000 1,08,375 69,431 2,20,566
4 2,00,000 60,000 92,119 53,242 2,06,758
5 2,00,000 30,000 78,301 37,905 1,92,095
Assumption : the machine will be discarded in the beginning of 6th year.
% 0.862 0.743 0.641 0.552 0.476
Present value of cost under purchase proposal:
Period PV of cost
1 2,45,000x0.862
2 2,33,375x0.743
3 2,20,566x0.641
4 2,06,758x0.552
5 1,92,095x0.476
Total 7,31,538
Present value of cost under lease alternative : 334000 x 0.65 x 3.274 :
= Rs. 710785
Lease may be preferred as the present value of cost is lower under this
alternative.
Q. No.Q. No.Q. No.Q. No. 20202020 Classic Finance, a leasing company, has been approached by A
prospective customer intending to acquire a machine whose cash down price is
Rs.6.00 Crores. The customer , in order to leverage his tax position, has
requested to quote three year lease rentals payable at year end but in a
diminishing manner in the ratio of 3:2:1. Depreciation can be assumed to be on
WDV basis at 25% and marginal tax rate of Classic Ltd is 35%. The target rate of
32
return for Classic Finance on the transaction is 10%. You are required to
calculate the lease rents to be quoted for the lease. (Nov.2009)(Nov.2009)(Nov.2009)(Nov.2009)
Answer:Answer:Answer:Answer:
Assumption: Assumption: Assumption: Assumption: Life of the machine is 3 years. The machine will be discarded discarded discarded discarded in the
beginning of the 4th year.
Working note
Year Depreciation
1 1.50 Crores
2 1.125 Crores
3 0.84375 Crores
Present value of cash in flows :
Year Lease
Rent
Tax CF PV
1 3x (3x – 1.50 Cr.)(0.35) =
1.05x – 0.525Cr.
1.95x +
0.525 Cr.
(1.95x+0.525Cr.)X
0909
2 2x (2x – 1.50 Cr.)(0.35) =
0.70x – 0.525
1.30x +
0.525Cr.
(1.30x + 0.525Cr.) X
0.826
3 x (x – 1.50 Cr.)(0.35) =
0.35x – 0.525
0.65x +
0.525 Cr
(0.65x + 0.525 Cr) X
0.751
Total 1.30515 Cr +3.3345x
As the required return is 10%, the NPV at 10% should be zero.
0 = -6.00 Crores +1.30515 Cr +3.3345x
x = 1,40,79,622
Year Lease Rent
1 4,22,38,866
2 281,59,244
33
3 14079622
Q. No. Q. No. Q. No. Q. No. 21212121 XYZ Ltd requires an equipment costing Rs.10,00,000: the same will be
utilized over a period of five years. It has two financing options in this regard:
(i) Arrangement of a Loan of Rs. 10,00,000 at an interest of 13% p.a.; the loan
being repayable in five equal year end installments; the equipment can be sold at
the end of fifth year for Rs. 1,00,000.
(ii) leasing the equipment for a period of five years at an yearly rental of Rs.
3,30,000 payable at year end.
The rate of depreciation is 15% on WDV basis, tax rate 35% and discount rate is
12%. Advise the XYZ Ltd that which of the financing options is to be exercised
and why? (Nov. 2008Nov. 2008Nov. 2008Nov. 2008))))
Answer
Working note :
Loan installment = ( 10,00,000 ) / ( 3.517 ) = 2,84,333
Calculation of interest and tax savings of interest: Calculation of interest and tax savings of interest: Calculation of interest and tax savings of interest: Calculation of interest and tax savings of interest:
Amount due Principal Interest Tax saving of
interest
Total borrowing
I Payment
II Payment
III Payment
IV Payment
V payment
10,00,000
1,54,333
8,45,667
1,74,396
6,71,271
1,97,068
4,74,203
2,22,687
2,51,516
2,51,516
NIL
1,54,333
1,74,396
1,97,068
2,22,687
251,516
1,30,000
1,09,937
87,265
61,646
32,817
45,500
38,478
30,543
21,576
11,486
YEAR Dep./STCL WDV Tax saving on Dep./STCL
1 1,50,000 Dep. 8,50,000 52500
34
2 1,27,500 Dep. 7,22,500 44625
3 1,08,375 Dep. 6,14,125 37931
4 92,119 Dep. 5,22,006 32242
5 4,22,006 STCL 1,47,702
No WDV depreciation is allowed in the year the asset is sold (when there is no
asset in the Block)
Assumption: In future year 5, the company shall have sufficient amount of STCG
to take tax advantage, by way of set off, of STCL arising in that year.
Year Loan installment Tax savings on Interest &
Depreciation / STCL
CF
1 2,84,333 52500 + 45500 = 98,000 1,86,333
2 2,84,333 44625 + 38478 = 83,103 2,01,230
3 2,84,333 37931 + 30,543 = 68,474 2,15,859
4 2,84,333 32242 +21,576 = 53,818 2,30,515
5 2,84,333 1,47,702 + 11,486 = 1,59,188 1,25,145
DCF analysis at 12%
Year PV of cash flow
1 -1,86,333 x 0.893
2 -2,01,230 x 0.797
3 -2,15,859 x 0.712
4 -2,30,515 x 0.636
5 -1,25,145 x 0.567
5 +1,00,000 x 0.567
Total - 6,41,332
PV of cost under purchase proposal : 6,41,332
PV of cost under lease ; 3,30,000 x 0.65 x 3.605 = 7,73,273
Purchase option (borrowing ) is recommended because of lower amount of cost. Q. No. Q. No. Q. No. Q. No. 22222222: Mahalaxmi Lease Finance Ltd (MLFL) has been approached by a customer
for structuring the lease of a machine. The cost of the machine is Rs.5,00,000. Its
primary life is 5 years. Depreciation rate for tax purposes is 25%. Tax rate
applicable to MLFL is 35%. Calculate the annual lease rent assuming that the lease
rent is payable in the beginning of the year and that the MLFL’s target post tax rate
of return is 9% p.
Answer Answer Answer Answer Note : As per the question, 5 years is the primary lease period. We are not given any
information about secondary lease period. Hence, we ignore the lease rent, tax on
lease rent and tax savings on depreciation for the secondary period.
35
Year Dep. WDV Tax savings PV
1 1,25,000 3,75,000 43,750 40119
2 93,750 2,81,250 32,813 27629
3 70,313 2,10,938 24,609 18998
4 52,734 1,58,204 18,457 13068
5 39,551 1,18.653 13,843 8998
Total 108812
Let annual lease rent = Rs.y
0 = - 5,00,000 + y.(1+ 3.24) + 1,08,812 - 0.35.y.(3.89)
-2.8785y = - 3,91,188.
y= 1,35,900
Annual lease rent receivable in the beginning of the year = Rs.1,35,900
Q. No. 23Q. No. 23Q. No. 23Q. No. 23:::: Mahalaxmi Lease Finance Ltd (MLFL) has been approached by a customer
for structuring the lease of a machine. The cost of the machine is Rs.5,00,000. Its life
is 8 years, scrap value after full life Rs.20,000. Depreciation is allowed for tax
purposes by straight line method. Tax rate applicable to MLFL is 30% for first 4
years and after that it is expected to go up 33%. Calculate the annual lease rent
assuming that the lease rent is payable at the end of the year and that the MLFL’s
target rate of return is 8% p.a.
Answer Answer Answer Answer
Let annual lease rent = y
-5,00,000 + (y)(0.70)( 3.312) + (y)(0.67)( 2.435) + 60,000.(0.30).((3.312) +
(60,000).(0.33).(2.435) + 20,000(0.54) = 0
-3.94985y = -3,81,371
Y = 96,553
Annual lease rent = Rs.96,553
EXTRA PRACTICE QUESTIONS EXTRA PRACTICE QUESTIONS EXTRA PRACTICE QUESTIONS EXTRA PRACTICE QUESTIONS (OPTIONAL)(OPTIONAL)(OPTIONAL)(OPTIONAL)
Q. No.2Q. No.2Q. No.2Q. No.24444: Mahalaxmi Lease Finance Ltd (MLFL) has been approached by a customer
for structuring the lease of a machine. The cost of the machine is Rs.5,00,000. Its
primary life is 5 years. The machine is to be fully written off for tax purposes over
its primary life. Tax rate applicable to MLFL is 35%. Calculate the annual lease rent
assuming that the lease rent is payable in the beginning of the year. The risk free
rate of return is 10% post tax but MLFL wish to mark up this rate by 2 percentage
points to provide premium for the risk in this proposal. Calculate the annual lease
rent.
Let Annual lease rent = y
0 = -5,00,000 + y.(1+ 3.037 ) - ( y – 1,00,000)(0.35)(3.605)
0 = -5,00,000 + 4.037y -1.26175y +126175
- 2.77525 y = - 3,73,825
36
y = 1,34,700
Annual lease rent = 1,34,700.
Q. No. 25Q. No. 25Q. No. 25Q. No. 25: : : : ABC Company has decided to acquire a Rs.5,00,000 Pulp control device
that has a useful life of 10 years. A subsidy of Rs.50,000 is at the time the device is
acquired and placed into the service. Straight line Deprecation, with no salvage
value. Tax rate 50%.If the acquisition is financed with lease, lease payments of
Rs.55000 would be required at the beginning of each year. The company can also
borrow at 10% repayable in 10 equal installments. Debt payments would be due at
the beginning of each year. What is the present value of cash flow for each of these
financing alternatives, using after tax cost of debt? Which alternative is preferable?
(May, 2006)(May, 2006)(May, 2006)(May, 2006)
AnswAnswAnswAnswer er er er
Loan installment ( including interest ) = 4,50,000/(1+5.759) = 66,578
Calculation of interest and tax savings of interest : Calculation of interest and tax savings of interest : Calculation of interest and tax savings of interest : Calculation of interest and tax savings of interest :
Amount due Principal Interest PV of Tax saving of int.
Total
borrowing
I Payment
II Payment
III Payment
IV Payment
V payment
VI payment
VII payment
VIII payment
IX payment
4,50,000
-66758
383422
-28236
3,55,186
-31059
324127
-34165
289962
-37582
252380
-41,340
211040
- 45474
165566
-50021
115545
-55023
60522
-60522
66758
28236
31059
34165
37582
41340
45474
50021
55023
60522
-
38342
35,519
32413
28996
25238
21104
16557
11555
6056
-
19171 x 0.952
17760 x 0907
16207 x 0.864
14498 x 0.823
12619 x 0.784
10552 x 0.746
8279 x 0.711
5778 x 0.677
3028 x 0.645
Total 89810
PV of tax savings on Dep = 22500 x 7.722 = 173745
DCF Analysis of Borrowing AlternativeDCF Analysis of Borrowing AlternativeDCF Analysis of Borrowing AlternativeDCF Analysis of Borrowing Alternative
Period PVF/A CF PV
Payment to Bank 0-9 8.108 -66578 each year -539814
Tax Savings on Dep. 1-10 +173745
Tax savings on interest 1-10 + 89810
Net present value of cost 276259
37
DCF Analysis of Lease AlternativeDCF Analysis of Lease AlternativeDCF Analysis of Lease AlternativeDCF Analysis of Lease Alternative
Period PVF/A CF PV
Lease payment 0-9 8.108 -55000 each year -445940
Tax savings on lease rent 1-10 7.722 + 27500 each year +212355
Net present value of cost 233585
Lease is recommended
Q. No. Q. No. Q. No. Q. No. 26262626: : : : The company is planning to acquire a machine costing Rs.5,00,000.
Effective life of the machine is 5 years. The company is considering two options.
One is to purchase the machine lease and the other is to borrows Rs.5,00,000 from
the bank at 10% p.a. the principal amount of loan will be paid in 5 equal installments
to be paid annually. The machine will be sold at Rs.50,000 at the end of 5th year.
Following further information are given :
(i) Principal, interest and lease rentals are payable at year end
(ii) The machine will be fully depreciated over its effective life.
(iii) Tax rate 30% and after tax cost of capital is 8%.
Compute the lease rentals payable which will make the firm indifferent to loan option. ( May 2007)( May 2007)( May 2007)( May 2007) AnswerAnswerAnswerAnswer
NoteNoteNoteNote:We assume that the sentence “The machine will be fully depreciated over its
useful life” conveys that the full cost of the machine will be depreciated over its
useful life. The full cost can be written off only under straight life method. Hence
annual depreciation = 5,00,000/5 = 1,00,000.
Statement showing annual cash flowsStatement showing annual cash flowsStatement showing annual cash flowsStatement showing annual cash flows
Years → 1 2 3 4 5
Principal & Int. -1,50,000 -
1,40,000
-1,30,000 -1,20,000 -1,10,000
Tax savings on
Depreciation & interest
+45,000 +42,000 +39,000 +36,000 +33,000
Scrap net of tax +35,000
CASH flows -1,05,000 -98,000 -91,000 -84,000 -42,000
DCF ANALYSIS OF BORROWING ALTERNATIVE
Period PVF CF PV
Cash Flows 1 0.935 -105000 -98,175
Cash Flows 2 0.873 -98000 -85,554
Cash Flows 3 0.816 -91000 -74256
Cash Flows 4 0.763 -84000 -64092
Cash Flows 5 0.713 -42000 -29946
Present value of net cost -3,52,023
Let annual lease ( payable at year end) = x
0.70x ( 4.1)= 352023 x = 1,22,656.
Annual lease rent matching with loan option (payable at year end) = 1,22,656.
38
Q. No. 27Q. No. 27Q. No. 27Q. No. 27: : : : ABC leasing Ltd has been approached by a client to write a five years
lease on an asset costing Rs. 10,00,000 and having estimated salvage value of Rs.
1,00,000 thereafter. The company’s after tax required rate of return is 10% and its
tax rate is 50%.
Depreciation 33 1/3 % on WDV method. Annual Lease rent ? ((((May 2006)May 2006)May 2006)May 2006)
AnswerAnswerAnswerAnswer
Calculation of tax savings on Depreciation and STCL
Year Depreciation/ STCL WDV Tax savings on
depreciation/
STCL
PV of Tax savings
1 3,33,333 6,66,667 1,66,667 1,66,667 x 0.909
2 2,22,222 4,44,445 1,11,111 1,11,111 x 0.826
3 1,48,148 2,96,297 74,074 74,074 x 0.751
4 98,766 1,97,531 49,383 49,383 x 0.683
5 97,531(STCL) 48767 48,767 x 0.621
Total Rs.3,62,920
• It is assumed that in the future year five, ABC Ltd will have sufficient amount
of STCG to set off the short term capital loss of Rs.97,531.
• Under Income Tax Act, 1961, depreciation is not allowed in year the asset is
sold. Hence, Deprecation for future year fiver has not been considered.
• It is assumed that the lease rent is received in the beginning of the year.
• For 10% post tax return, NPV at 10% should be zero.
Let annual lease rent = Rs.y
0 = -10,00,000 + y.(1+ 3.17) – 0.50y.(3.791)+ 1,00,000(0.621)+ 3,62,920
-y(2.2745) = -5,74,980
y = 2,52,794
Annual lease rent ( receivable in the beginning of the year) = Rs.2,52,794
Q. No. 28Q. No. 28Q. No. 28Q. No. 28: : : : Your company is considering to acquire an additional computer to
supplement its time-share computer services to its clients. It has two options :
(i) to purchase the computer for Rs. 22 lakhs.
(ii) to lease the computer for three years from a leasing company for Rs. 5 lakh as
annual lease rent plus 10% gross time share service revenue. The agreement
also requires an additional payment of Rs. 6 Lakhs at the end of 3rd year.
Lease rents are payable at the year-end, and computer reverts to the lessor
after the contract period.
The company estimates that the computer under review will be worth Rs. 10 lakhs
at the end of 3rd year.
Forecast Revenue :
39
Year 1 2 3
Amount (Rs. Lakhs) 22.50 25 27.50
Annual operating costs excluding depreciation/lease rent of computer are estimated
at Rs. 9 Lakhs with additional Rs. 1 lakhs for start up and training costs at the
beginning of the first year. These costs are to be borne by the lessee.
Your company will borrow at 16% interest to finance the acquisition of the computer.
Repayments are to be made according to the following schedule (Rs.’000)
Year end : 1 2 3
Principal 500 850 850
Interest 352 272 136
The company uses straight line method to depreciate its assets and pays 50% tax
on its income. The management approaches you to advice. Which alternative is
recommended and why? (May 2004)(May 2004)(May 2004)(May 2004)
Answer :Answer :Answer :Answer :
Year 1 Year 2 Year 3 Total
Payment to lessor 5 + 2.25 5 + 2.50 5+2.75+6
Tax savings 3.625 3.75 6.875
Net cash outflow 3.625 3.75 6.875
PV 3.35675 3.21375 5.45875 12.02925
Year 1 Year 2 Year 3 Total
Payment to bank 8.52 11.22 9.86
Tax saving on dep.& int. 3.76 3.36 2.68
Sale of scrap 10
Net cash out flow 4.76 7.86 -2.82
PV 4.40776 6.73602 -2.23908 8.9047
Purchase is recommended.Purchase is recommended.Purchase is recommended.Purchase is recommended.
Q. No.29Q. No.29Q. No.29Q. No.29: : : : Engineers Ltd requires a machine which be either bought or taken on
lease. The cost of machine is Rs.20,00,000, useful life 5 years, salvage value
Rs.4,00,000 (consider short term capital loss/gain for the income tax). The purchase
value of the machine can be financed by bank loan at 20% interest repayable in five
equal annual installments falling due at year end. Alternatively, the machine can be
procured on a 5 years lease, year-end rentals being Rs.6,00,000 per annum. The
company follows WDV method of depreciation at the rate of 25%. Tax rate is 35%.
Cost of capital 14%.
(i) Advise the company which option it should choose – lease or borrow.
(ii) Assess the proposal from the lessor’s point of view examining whether leasing
machine is financially viable at 14 % cost of capital. (Nov. 2005)(Nov. 2005)(Nov. 2005)(Nov. 2005)
40
AnswerAnswerAnswerAnswer
Loan installment = ( 20,00,000 ) / ( 2.991 ) = 6,68,673
Calculation of interest and tax savings of Calculation of interest and tax savings of Calculation of interest and tax savings of Calculation of interest and tax savings of interest: interest: interest: interest:
Amount due Principal Interest Tax saving of interest
Total borrowing
I Payment
II Payment
III Payment
IV Payment
V payment
20,00,000
2,68,673
17,31,327
3,22,408
14,08,919
3,86,889
10,22,030
4,67,267
5,57,763
5,57,763
2,68,673
3,22,408
3,86.889
4,64,267
5,57,763
4,00,000
3,46,265
2,81,784
2,04,406
1,10,910
1,40,000
1,21,193
98,624
71,542
38,819
YEAR DEP/STCL WDV
1 5,00,000 15,00,000
2 3,75,000 11,25,000
3 2,81,250 8,43,750
4 210938 6,32,812
5 2,32,812(STCL)
Assumption: In future year 5, the company shall have sufficient amount of STCG to
take tax advantage, by way of set off, of STCL arising in that year.
Tax savings on Depreciation / STCL :Tax savings on Depreciation / STCL :Tax savings on Depreciation / STCL :Tax savings on Depreciation / STCL :
Year 1: 1,75,000
Year 2: 1,31,250
Year 3: 98438
Year 4: 73,828
Year 5: 81484
Ye
ar
Loan installment Tax savings on Interest
& Depreciation/STCL
CF
1 6,68,673 3,15,000 3,53,673
2 6,68,673 2,52,443 4,16,230
3 6,68,673 1,97,062 4,71,611
4 6,68,673 1,45,370 5,23,303
5 6,68,673 1,20,303 5,48,370
41
DCF analysis at 13%
Year PV of cash inflow
1 -3,53,673 x.885
2 -(4,16,230 x ).783
3 – (4,71,611x .693)
4 –(523303x 0.613)
5 - (548370 x 0.543)
5 +(400000 x 0.543) Sale of scrap
Total -13,67,085
DCF analysis of lease proposal = - 3,90,000 x 3.517 = - 13,71,630
Purchase through borrowing is recommended.
(ii)DCF analysis of proposal of giving the asset on lease :
Period Particulars PV of cash flow
1-5 Lease rent net of tax +[6,00,000 x 0.65(3.432)]
1 Tax savings on Depreciation +[(1,75,000 x 0.877)
2 ------do------------ +[1,31,250 x 0.769)
3 ------do------------ +(98438x0.675)
4 ------do------------- +(73828x0.592)
5 Tax savings o n STCL + (81484 x.519)]
5 Sale of scrap +[400000 x 0.519]
0 Cost of machine -20,00,000
Total - 47072
The machine not be given on lease.
Q. No. 30Q. No. 30Q. No. 30Q. No. 30:::: Brij Kishore Ltd requires a machine, the details as follows: Cost
Rs.5,00,000; Life 5 years; Salvage value on completion of life Rs.1,00,000;
Depreciation for tax purpose WDV method: 25%.
The purchase of the machine can be financed through a loan of
Rs.5,00,000 repayable in five equal year-end installments.
The loan carries interest at the rate of 10% p.a.
Alternatively, the machine can be acquired on lease basis, the year-end lease rent
would be Rs.275 per Rs.1000 of the cost of the machine. Assume tax rate to be 40%.
Advise.
42
Answer Answer Answer Answer
Working Note No. 1
Bank installment = 5,00,000/3.791 = 1,31,891
Amount Due Principal Interest
I
II
III
IV
V
5,00,000
-81,891
4,18,109
-90,079
3,28,030
-99,088
2,28,942
-1,08,997
1,19,945
-1,19,945
nil
81,891
90,079
99,088
1,08,997
1,19,945
50000
41812
32803
22894
11946
Working note No. 2 :Working note No. 2 :Working note No. 2 :Working note No. 2 :
Depreciation/
STCL
WDV Depreciation/S
TCL + Interest
Tax savings
1 125000 Dep. 375000 1,75,000 70,000
2 93750 Dep. 281250 1,35,562 54,225
3 70313 Dep. 210938 1,03,116 41,246
4 52734 Dep. 158204 75,628 30,251
5 58204 STCL Nil 70,150 28,060
DCF analysis of Purchase proposal
Period PVF/A CF PV
Payment to Bank 1-5 4.212 -131891 Annually -5,55,525
Tax Savings 1 0.943 +70,000 +66,010
____do----- 2 0.890 +54,225 +48,260
----do---- 3 0.840 +41,246 +34,647
----do--- 4 0.792 +30,251 +23,959
----do--- 5 0.747 +28,060 +20,961
Sale of scrap 5 0.747 +1,00,000 +74,700
NPV of cost of purchase proposal 2,86,988
DCF analysis of Lease Proposal
Period PVF/A CF PV
Lease rent net of tax 1-5 4.212 -82,500 Annually -347490
NPV of cost of lease proposal 3,47,490
43
Purchase proposal is recommended.
Q. No.Q. No.Q. No.Q. No. 31313131:::: PQR Ltd. is evaluating a proposal to acquire new equipment. The new
equipment would cost Rs. 3.5 million and was expected to generated cash inflows of
Rs. 4,70,000 a year for nine years. After that point, the equipment would be obsolete
and have no significant salvage value. The company’s weighted average cost of
capital is 16%.
The management of the PQR Ltd. seemed to be convinced with the merits of the
investment but was not sure about the best way to finance it. PQR Ltd. could raise
the money by issuing a secured eight-year note at an interest rate of 12%. However,
PQR Ltd. had huge tax-loss carry forwards from a disastrous foray into foreign
exchange options. As a result, the company was unlikely to be in a position of tax-
paying for many years. The CEO of PQR Ltd. thought it better to lease the equipment
than to buy it. The proposals for lease have been obtained from MGM Leasing Ltd.
and Zeta Leasing Ltd. The terms of the lease are as under:
MGM Leasing Ltd. Zeta Leasing Ltd.
Lease period offered 9 years 7 years
Number of lease rental payments
with initial lease payment due on
entering the lease contract
10 8
Annual lease rental Rs. 5,44,300 Rs. 6,19,400
Lease terms equivalent to
borrowing cost (Claim of lessor)
11.5% p.a. 11.41% p.a.
Leasing terms proposal coverage Entire
Rs. 3.5 million cost
of equipment
Entire
Rs. 3.5 million cost
of equipment
Required:
(i) Calculate the NPV to PQR Ltd. of the two lease proposals.
(ii) Does the new equipment have a positive NPV with (i) ordinary financing,
(ii) lease financing?
(Ada(Ada(Ada(Adapted : PE II Nov. 2004) pted : PE II Nov. 2004) pted : PE II Nov. 2004) pted : PE II Nov. 2004)
AnswerAnswerAnswerAnswer
(i)
Net Present value of cost under lease from MGM = Rs.5,44,300(1+5.328)
= Rs. 34,44,330
Net Present value of cost under lease from Zeta = Rs.6,19,400(1+4.564)
= Rs. 34,46,342
(ii)
NPV of cost with ordinary financing : - 35,00,000 + 4,70.000 (4.607)
= - 13.34,710
NPV of cost with lease financing : - 34,44,330 + 4,70,000(4.607)
44
= - 12,79,040
The equipment does not have a positive NPV in either of the two cases.
Q. No.Q. No.Q. No.Q. No. 32323232:::: Alfa Ltd desires to acquire a diesel generating set costing Rs.20 Lakh
which will be used for a period of 5 years. It is considering two alternatives (i)
taking the generating set on lease or (ii) purchasing the asset outright by raising
loan. The company has been offered a lease contract with a lease payment of
Rs.5.2 Lakh per annum for five years payable in advance. The company’s banker
requires the loan to be repaid@ 12% p.a. in 5 equal installments, each installment
being due at the beginning of the each year. Tax relevant depreciation is 20%
p.a. WDV. At the end of 5th year the generator can be sold at Rs.2,00,000.
Marginal tax rate of Alfa Ltd is 30% and its post tax cost of capital is 10%.
Determine (i) The net advantage of leasing to Alfa Ltd and recommend whether
leasing is financially viable (ii) Break even lease rental. (May 2010)(May 2010)(May 2010)(May 2010)
AnswerAnswerAnswerAnswer (i)(i)(i)(i)
NoteNoteNoteNote: The question is silent on the point whether the 5 equal installments
would be inclusive interest or plus interest. It is assumed that the loan will be
repaid in 5 equal installments inclusive of interest. This assumption places loan
on an equivalent basis with lease.
Annual Bank installment : (20,00,000) / (1+ 3.037) = 4,95,417Annual Bank installment : (20,00,000) / (1+ 3.037) = 4,95,417Annual Bank installment : (20,00,000) / (1+ 3.037) = 4,95,417Annual Bank installment : (20,00,000) / (1+ 3.037) = 4,95,417
Amount due Principal Interest
Total borrowing
I Payment
II Payment
III Payment
IV Payment
V payment
20,00,000
4,95,417
15,04,583
3,14,867
11,89,716
3,52,650
8,37,066
3,94,969
4,42,097
4,42,097
nil
4,95,417
3,14,867
3,52,650
3,94,969
4,42,097
1,80,550
1,42,767
1,00,448
53,320
Year Dep./STCL Dep. + int. Tax savings PV @
8.40%
1 4,00,000 Dep. 5,80,550 1,74,165 1,60,667
2 3,20,000 Dep. 4,62,767 1,38,830 1,18,148
3 2,56,000 Dep. 3,56,448 1,06,934 83,951
4 2,04,800 Dep. 2,58,120 77,436 56,918
45
5 6,20,000 STCL 6,20,000 STCL 1,86,000 1,24,270
Total 5,43,954
NOTES ;NOTES ;NOTES ;NOTES ;
(I) NO WDV DEPRECIATION IS ALLOWED IN THE YEAR IN WHICH THE
ASSET IS SOLD.[SECTION 32(1) OF INCOME TAX ACT, 1961]
(II) It is assumed that in future year five the company shall have sufficient
amount of short term capital gain to set off the short term capital loss of
Rs.6,20,000 arising in that year.(STCL CANN’T BE SET OFF AGAINST
BUSINESS INCOME)
(III) Interest included II installment would be allowed as deduction against
taxable income of I year [Section 43(B) of Income Tax Act, 1961] and so
on.
(IV) A lease versus buy analysis is performed when the decision is made to
acquire an asset. “It is not a capital expenditure decision. It is financing
decision. Whether nor not to acquire the asset is not part of typical lease
analysis – in a lease analysis we are simply concerned with whether to
obtain the use of the asset through lease or by purchase.5” Rather we can
say the analysis does not aim to decide lease or purchase (as the
purchase has already been decided); it is to decided whether lease or
borrow. The cash flows of this analysis are more like debt service cash
flows than operating cash flows6. Hence the appropriate discount rate is
the after tax cost of debt.
DCF Analysis of purchase proposal
PERIIOD PVF/A CASHFLOW PV
Bank payments 0-4 4.283 -4,95,417
ANNUALLY
-21,21,871
Tax savings 1-5 3.951 +5,43,954
NPV OF COST 15,77,917
DCF Analysis of lease proposal PV = PV of lease payments – PV of tax savings.
= 5.20L x 4.283 - 1.56L x 3.951 = 22.2716oL – 6.16356L = 16.10804L
Purchase is recommended.
5 Financial Management – Brigham and Ehrhardt.
6 There is almost no uncertainty in debt –service like cash flows as the cash flows are governed by
the contracts. The operating cash flows are estimated ones, these are not contractual, hence these
are uncertain.
46
Q. No.33: Q. No.33: Q. No.33: Q. No.33: P Ltd had decided to acquire a machine costing Rs,50 Lakhs through
leasing. Quotations from 2 leasing companies have been obtained which are
summarized below :
Quote A Quote B
Lease term 3 years 4 years
Initial lease rent Rs.5.00 Lakhs Rs.1.00 Lakh
Annual lease rent
payable in arrear
Rs,21.06 Lakhs
Rs.19.66 Lakhs
P Ltd evaluates investment proposals at 10% cost of capital and its effective rate
is 30%. Terminal payment in both the cases is negligible and may be ignored.
Make calculations and show which quote is beneficial to P Ltd. Present value
factors at 10% rate for years 1-4 are respectively 0.91, 0.83, 0.75 and 0.66.
Considerations may be rounded off to 2 decimals in Lakhs.
Answer Answer Answer Answer
DCF Analysis of each of two proposals regarding Lease
Rs. Lakhs
Quote A Quote B
Period PVF/A CF PV CF PV
Initial lease rent 0 1 -5.00 -5.00 -1.00 -1.00
Tax savings on
Initial lease rent
1
0.91
+1.50
1.37
+0.30
+0.27
Annual lease rent
less tax savings
1-3
2.49
-14.74
-36.71
-13.76
-34.26
---do--- 4 0.68 -13.76 -9.36
NPV -40.34 -44.35
A B
Equalized Annual cost 40.34L/2.49 =Rs.16.20L 44.35L/3.17 = Rs.13.99L
Quote B is recommended.
Alternatively, we may assume that in both the cases we shall be using the
machine for equal period, say 4 years. In one case, we have to pay only for three
years; in the fourth year we can use the machine free of lease rent cost i.e.
without any payment of lease rent. In the second case, we shall use the machine
for four years and we shall be paying the lease rent for four years. In this case,
the answer will be as follows:
47
DCF Analysis of each of two proposals regarding Lease
Rs. Lakhs
Quote A Quote B
Period PVF/A CF PV CF PV
Initial lease rent 0 1 -5.00 -5.00 -1.00 -1.00
Tax savings on
Initial lease rent
1
0.91
+1.50
1.37
+0.30
+0.27
Annual lease rent
less tax savings
1-3
2.49
-14.74
-36.71
-13.76
-34.26
---do--- 4 0.68 -13.76 -9.36
NPV -40.34 -44.35
Quote A is recommended on account of lower absolute amount of NPV.
THEORETICAL ASPECTSTHEORETICAL ASPECTSTHEORETICAL ASPECTSTHEORETICAL ASPECTS
Q.No.34Q.No.34Q.No.34Q.No.34: : : : What are the characteristic features of Financial and operating lease? (Nov. (Nov. (Nov. (Nov.
2006)2006)2006)2006)
Answer Answer Answer Answer
A leaseleaseleaselease is a contract conveying from one person (the lessor) to another person (the
lessee) the right to use and control some article of property over the span of the
lease term, without conveying ownership, in exchange for some consideration
(usually a periodic payment.). Leasing is a viable financing alternative to buying with
a loan. Leasing may allow the enterprise to conserve cash. It also allows to avoid
buying equipment which may not be required for long. Companies routinely use
leasing for some of their financing. Airlines lease their airplanes. Car-rental
companies lease their fleets of rental vehicles. Most companies lease some or all of
their office, warehousing, and retailing space.
Basic types of leases:Basic types of leases:Basic types of leases:Basic types of leases:
Finance Finance Finance Finance leases. leases. leases. leases. In this case, the lessor transfers substantially all the risks and
reward of the leased asset to the lessee. Generally this type of lease satisfies one or
more of following conditions:
1. lessee acquires title by the end of lease period
2. option to purchase at bargain price
3. lease period covers major portion of useful life
4. present value of rental payments equals or exceeds asset's fair market value.
5. lease contract is generally non-cancelable.
48
Operating leases: Operating leases: Operating leases: Operating leases: A lease which is not finance lease is known as operating lease.
Features of operating lease:
(i) The lease does not cover the major portion of useful life.
(ii) Lease is generally cancelable.
(iii) Risk of Obsolescence is born by the lesser.
(iv) Generally the cost of maintenance and repair are born by the lessor.
Q..No.35Q..No.35Q..No.35Q..No.35:::: What are the advantages of lease financing?
Answer:Answer:Answer:Answer:
� It offers fixed rate financing. The lessee has pay lease rent at the same rate
periodically.
� There is less upfront cash outlay. The lessee does not need to make large cash
payments for the purchase of needed equipment.
� Leasing better utilizes equipment. Lessee leases and pays for equipment only
for the time it is needed.
� Lessee has an option to buy equipment at end of lease term. ( only in case of
finance lease )
� Upgrading. As new equipment becomes available the lessee can upgrade to the
latest models each time the lease ends. One of the reasons for the popularity of
leasing is the steady stream of new and improved technology.
� There are a variety of ways in which a lease can be structured. This provides
greater flexibility so that the lease is structured to best accommodate the
individual cash flow requirements of a specific business. For example, there
may be balloon payments, step up or step down payments, deferred payments
or even seasonal payments.
� Generally, it is easier to obtain lease financing than loans from commercial
lenders.
� It offers potential tax benefits depending on how the lease is structured.
Q. No. 36Q. No. 36Q. No. 36Q. No. 36 : : : : Many companies calculate the internal rate of return of the incremental
after-tax cash flows from financial leases. What problems do you think this may give
rise to? To what rate should the IRR be compared? Discuss. ( May, 2001)( May, 2001)( May, 2001)( May, 2001)
Answer: Answer: Answer: Answer:
Calculation of cost of lease by IRR is one of the methods of evaluation of Lease vs.
buy proposals. Under this method, five steps are there
(i) Find cash flows under lease proposal
(ii) Find cash flows under buy proposal ( Here we make an assumption that we do
not have to borrow funds i.e. we have funds to buy the asset and there is no cost of
these funds, we shall be withdrawing this assumption under 5th step.
(iii) Find incremental cash flows i.e. “cash flows of lease minus cash flows of buy”
(iv) Find IRR i.e. cost of lease on the basis of incremental cash flows.
49
(v) We withdraw the assumption we have made under step (ii). We find cost of
borrowed funds for buying the asset. Compare this cost of borrowed funds with the
cost of lease (calculated under step iv). If cost of lease is more than cost of
borrowed funds, buying is recommended. In otherwise situation, lease is
recommended.
Problems which may arise in this method:Problems which may arise in this method:Problems which may arise in this method:Problems which may arise in this method:
(i) IRR may me indeterminate (This may happen if more than one sign reversal
in cash flows is there.)
(ii) Multiple IRRs may be there (This may happen if more than one sign reversal
in cash flows is there.)
(iii) Generally the cash outflows calculated under step (iii) are negative. The
method assumes that funds required for these cash outflows will be
arranged at a cost equal to cost of lease by IRR method.
(iv) Life of the asset may not be equal to the period for which lease is to be
taken. This may complicate the decision.
Q. No.37: Q. No.37: Q. No.37: Q. No.37: Write a short note on Cross Border Lease. (Nov. 2008Nov. 2008Nov. 2008Nov. 2008)
AnswerAnswerAnswerAnswer
CrossCrossCrossCross----border leasingborder leasingborder leasingborder leasing is a lease arrangement where lessor and lessee are based
in different countries. It is a means of international financing the equipments
requiring huge funds like aircrafts, transport equipments, marine equipments, and
telecommunication equipments etc which have predictable revenue streams.
(Such leases are also referred as Big Ticket Leases). In developing countries,
the local resources may not be available for such financing. The financing is in
the form of debt i.e. the lessor gets the return at fixed rate. It is a safer way of
debt financing as it is easier for a lessor to repossess the leased equipment
following a default by the lessee because the lessor is the owner and not mere
secured lender.
In India, the cross border lease agreements have been entered for acquiring
aircrafts, marine equipments and the containers. The acquisition of these items
requires huge amount of foreign currency funds which are not available at
competitive rates in India. The foreign lessors feel secure here because of the
long history of fair, mature and independent judiciary. The courts have upheld
the rights of lessors of taking repossession of the leased assets in case of
defaults by the lessees.
The main attraction of cross border lease is “Cross-border tax arbitrage”
meaning the “profiting” from differences in the tax systems of two countries.
Suppose in the country of the lessor, depreciation on the leased asset is allowed
to the lessor and in country of the lessee the same is allowed to the lessee, this
means that both the lessor and the lessee can claim depreciation deduction. (In
India, the depreciation deduction of tax purposes is allowed to the lessor). (Cross
50
border tax arbitrage is disappearing fast as most of the countries allow
depreciation to the lessors and not to the lessees). The liberal depreciation
allowance in country of the lessor makes the lease tax efficient for the lessor
and as a result the lessor offers attractive terms for the lease. Sometimes, the
double taxation avoidance agreements between the two counties make the
cross-border lease an attractive deal.
Japan, as lessor, is ahead of all the countries of the world in the field of cross-
border lease. (The reason is low interest rate prevailing in Japan)
The lessee faces the foreign exchange risk in such arrangements (as compared
to domestic lease). The main risk from the lessor point of view is political risk.
RBI has specifically permitted such cross border lease arrangements in which
Indian companies are lessees. Such arrangements are covered under External
Commercial Borrowings.
51