Illustration 2 :
The following details relate to an investment proposal of XYZ Ltd.
Investment outlay Rs. 100 lakhs
Lease Rentals are payable at Rs. 180 per Rs.1000
Term of lease 8 years
Cost of capital for the firm is 12%
Find the Present Value of Lease Rentals if
a. Lease Rentals are payable at the end of the year
b. Lease Rentals are payable at the beginning of the year
Solution :
Lease Rentals paid per annum = Rs. 180 × 10000 = Rs. 18 lakhs
a. If Lease Rentals are payable at the year end :
Present Value of Lease Rentals = Rs. 18 lakhs × PV factors for years [ 1-8 ]
= Rs. 18 lakhs × PVIFA (12%, 8)
= Rs. 18 lakhs × 4.9676
= Rs. 89,41,680
b. If Lease Rentals are payable at the begining :
Present Value of Lease Rentals = Rs. 18 lakhs × PV factors for years [ 0-7 ]
= Rs. 18 lakhs × [ 1 +PVIFA (12%, 7) ]
= Rs. 18 lakhs × [ 1 +4.5638 ]
= Rs. 100,14,840
Illustration 3 :
Find out Loan payments per annum for the following :
Cost of Equipment : Rs. 50 lakhs
Borrowing rate : 15%
Term of Loan : 5 years
a. Principal is payable in equal investment over the period of five years
b. Amount of Loan is payable equally over the period of five years
Prepare a table showing principle & interest payments and the total payable over
period of five years.
Solution :
a. If principle is payable in equal installments :
Each installment = Rs. 50 lakhs/5 = Rs. 10 lakhs
Opening Balance Principle Interest Balance
50 Lakhs 10 Lakhs 7.50 Lakhs 40 Lakhs
40 Lakhs 10 Lakhs 6.00 Lakhs 30 Lakhs
30 Lakhs 10 Lakhs 4.50 Lakhs 20 Lakhs
20 Lakhs 10 Lakhs 3.00 Lakhs 10 Lakhs
10 Lakhs 10 Lakhs 1.50 Lakhs Nil
TOTAL 50 Lakhs 22.50 Lakhs
Total Payable : Rs. 50 lakhs + Rs. 22.50 Lakhs = Rs. 72.50 Lakhs
b. If loan is payable in equal installments:
Each installment = Rs.50 Lakhs/PVIFA (15%, 5) = Rs.50 Lakhs/3.3522 = Rs.1491558
Opening Balance Installment Interest Principle Balance
5000000 1491558 750000 741558 4258442
4258442 1491558 638766 852792 3405650
3405650 1491558 510848 980710 2424940
2424940 1491558 363741 1127817 1297123
1297123 1491558 194568 1297123 Nil
TOTAL 7457790 2457923 5000000
Total Payable : Rs. 50 lakhs + Rs. 2457923 lakhs = Rs. 7457923 Lakhs
NET ADVANTAGE OF LEASING - NAL Method
If a firm goes for leasing what it gets and what it foregoes :
What it gets What it spends/foregoes
Pv of Tax Benefit on A PV of Lease rentals C
Lease Rentals By not going for Debt, it foregoes:
Investment Outlay B PV of Interest Tax Shield D
(Not Spent) PV of Depreciation Tax Shield E
PV of Salvage Value F
TOTAL A+B C+D+E+F
If A+B > C+D+E+F, then go for leasing, else Borrowing.
Note: In NAL meyhod we use of debt (and not cost of capital) to find PV of lease rentals as
we are finding the benefit of leasing ‘instead of borrowing’. And the PV of tax-shields are
arrived at by using the opportunity cost of capital. And we also use the PV of lease rentals as
the amount that will be borrowed.
Illustration 4 :
The following details relate to an investment proposals of HI Ltd.
- Investment outlay Rs.180 lakhs
- Net salvage value after 3 years, Rs. 18 lakhs
- Annual rate of Depreciation 40%
HI Ltd. has two alternatives.
Option I: Borrow and buy the equipment @ 17% p.a, Marginal rate of Tax 35%;
Cost of capital of HI Ltd. 12%
Option II: Lease on 3 years full payout basis@ Rs. 444/Rs.1000 payable annually in arrear.
Which option HI Ltd. should choose any and why?
Solution :
Decision Analysis: (Rs.lakhs)
What it gets
1. Investment Outlay : (180.00)
2. Less : PV of Lease rentals (Working Note 1) 176.61
What it spends/foregoes
3. Add : PV of Tax Shield on Lease Rentals (Working Note 2) 67.19
4. Less : PV of tax shields on Depreciation (Working Note 3) 41.01
5. Less : PV of Interest shields on Displaced Debt (Working Note 4) 18.29
6. Less : PV of Salvage value (Working Note 5) 2.81
NAL / NPV (L) (1.53)
Since NAL is negative lease is not economically vaible.
Working Notes :
1. PV of lease rentals = Rs. 180 lakhs × 444/1000 × PVIFA (17,3) = Rs. 79.92 × 2.21
= Rs. 176.61 lakhs
2. PV of Tax shield on lease rentals = Rs. 180 lakhs×444/1000× 0.35×PVIFA (12,3)
= Rs. 27.972 lakhs × 2.402 = Rs. 67.19 Lakhs
3. PV of Tax shield on depreciation = [72 × PVIF (12, 1) +43.2 × PVIF (12,2) +25.92
× PVIF (12,3)] × 0.35 = [72 × 0.893 +43.2 × 0.797 +5.92 ×0.712] × 0.35
= Rs. 41.01 lakhs
Calculation of Depreciation :
Year 1 0.4 * 180 = 72
Year 2 0.4 * (180 - 72) = 43.2
Year 3 0.4 * (180 - 72- 43.2) = 25.92
4. PV of interests Tax shield on Displaced Debt: (assuming that instead of lease, total PV of
the lease rentals has been borrowed)
Displaced debt (PV of lease rentals) Amortization schedule (Rs. lakhs)
Year Loan O/s Interest Capital Installment amount
beginning @ 17% 176.61 + 2.210
1 176.61 30.03 49.89 79.92
2 126.72 21.54 58.38 79.92
3 68.34 11.61 68.34 79.92
Check Total of Capital 176.61
PV of interest Tax shield on Displaced Debt = [30.03 × PVIF (12,1) + 21.54 × PVIF (12,2)
+11.61 × PVIF (12,3)] × 0.35 =[ 30.03 × 0.893 + 21.54 × 0.797 +11.61× 0.712]× 0.35 = Rs.
18.29 lakhs
5. PV of net salvage value = 18 × PVIF (12,3) = 18 × 0.712 = Rs. 12.81 lakhs.
Note : If cost of capital is not given, use borrowing rate i.e. 17 × (1 - 0.35 )=11% approx.
Illustration 5 :
Armada Leasing Company is considering a proposal lease out a school bus. The bus can be
purchased for Rs. 50,0000 and in turn, be leased out at Rs. 125000 per year for 8 years with
payments occuring at the end of each year.
i. Estimate the IRR 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
compounded rate of return, based on thr following assumptions :
1. Tax rate is 40%
2. Straight Line Depreciation
3. Annual expenses of Rs. 50000, and
4. Resale value Rs. 100000 after the turn.
Solution :
i. Finding IRR (without tax effect)
As per above formula we have L× (1 - T) × PVIFA (k %, n years) = PV of Outflow
The only difference being here we need to find k, instead of L.
Therefore 1.25 lacs × (1 - 0) × PVIFA (k%, 8) = 5 lacs
Solving we get PVIFA (k,8) = 4
By interpolating [ See Interpolation method explained in Annexures]
We get IRR = 18.63%
ii. Finding L, given k (without tax effect)
We have L× (1 - T) × PVIFA (k%, n years) = pv of Outflow i.e. 5 lacs
L × (1 - 0) × PVIFA (20%, 8) = 5 lacs
Solving we get L = Rs. 130310.13 p.a
iii. Finding L, with tax, depreciation and other data
Let ‘L’ be the Lease Rental
[(L - expenses - depreciation) (1 - T) + Depreciation] × PVIFA (20%, 8)
+ Salvage value × PVIF (20%, 8) = 5 lacs
By solving the above equation we get,
[(L - 50000 - 50000) (1 - 0.4) + 50000] × 3.837 + 100000 × 0.233 = 5 lacs
L = Rs. 223729.47
Illustration 6 :
The following are the details regrading the machine to be given on lease by X Ltd.
i. Cost of machine to the lessor is Rs. 1,00,000 financed 80% through debt and balance
through equity. Cost of debt before tax amount to 20% and equity 16%.
ii. The lessor is in 35% tax bracket. The rate of depreciation of machinery is 20% according
to diminishing balance method.
iii. The scrap value of machines is Rs. 10,000 at the end of 5th year.
iv. Estimated cost for maintenance and general administration in respect of machine is
Rs.1,000 per annum.
v. The lessee agrees to pay the following:
(a) Annual rent Rs. 36,000 for 5 years. The payment is to be made at the end of
each year.
(b) The security deposit of Rs. 3,000 which is refundabale at the end of lease period
without interest.
(c) Management fees (non-refundable) payable at the inception of lease period is
Rs. 2,500.
You are required to decide whether the lessor should lease the machine using internal rate of
return method.
Solution :
Cost of Capital for Lessor
Source Amount (Rs.) After tax Total cost (Rs.)
Equity 20000 16% 3200
Debt 80000 13% 10400
100000 13600
Average cost of capital = Rs. 100
1 00 000
13 600 ×
, ,
,
= 13.6 %
Computation of Annual tax liability
Years
1 2 3 4 5
Rs. Rs. Rs. Rs. Rs.
Lease revenue 36,000 36,000 36,000 36,000 36,000
Less: Maintenance & Admn. Cost 1,000 1,000 1,000 1,000 1,000
Less: Depreciation 20,000 16,000 12,800 10,240 8,192
Income before tax 15,000 19,000 22,200 24,760 26,808
Less: Income tax @ 35 % 5,250 6,650 7,770 8,666 9,383
Income after tax 9,750 12,350 14,430 16,094 17,425
Computation of Annual Net Cash Inflows
Years
1 2 3 4 5
Rs. Rs. Rs. Rs. Rs.
Lease revenue 36,000 36,000 36,000 36,000 36,000
Add : Sale of machinery (Scrap) - - - - 10,000
Less : Administration cost 1,000 1,000 1,000 1,000 1,000
Less : Refund of deposit - - - - 3,000
Less : Tax liability 5,250 6,650 7,770 8,666 9,383
29,750 28,350 27,230 26,334 32,617
Cash outflow at beginning of year 1
Rs.
Cost of machinery 1,00,000
Less: Management fees 2,500
Security deposit 3,000 5,500
94,500
Computation of Internal Rate of Return
Year Cash Cash Discount Present Discount Present
outflow Inflow factor value factor value
Rs. Rs @ 14% Rs. @ 18% Rs.
0 94,500 - - - - -
1 29,750 0.877 26,091 0.847 25,198
2 28,350 0.769 21,801 0.718 20,355
3 27,230 0.675 18,380 0.609 16,583
4 26,334 0.592 15,590 0.516 13,588
5 32,617 0.519 16,928 0.437 14,254
98,790 89,978
N.P.V 4,290 -4,522
IRR = 4
4 290 4 522
4 290
14 ×
+
+
, ,
,
= 4
8 812
4 290
14 + ×
,
,
= 14 + 1.95
= 15.95
The weighted average cost of capital is 13.6 % while I.R.R from leasing out the asset is
15.95%. Hence, it is beneficial for a company to lease out the machinery.
Break Even Lease Rentals (BELR)
Under this method, the lessee is interested in that quantum of lease rental which will match
the borrowing option. Thus we find the total present value under the borrowing option and
taking that as the benchmark we find the lease rental in the reverse order, keeping in mind
the tax effect and other dat that may be provided, like rentals paid in advance etc. Under this
method the buyer comes to know of the amount he will actually fork out every year under
each option. This helps him to plan his cash flows.
Illustration 7 :
Beta Ltd. 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 the bankers at 15% 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 principle amount of the loan will be paid in five annual equal installments.
b. Interest, lease rental, principle repayment is to be paid on 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% and the after tax cost of capital is 9%
e. The computer will be sold for Rs. 1,700 at the end of the 5th year. The commission on
such sales is 9% on the sale value and the same will be paid.
You are required to compute the annual lease rentals payable by Beta Ltd. which will result
in indifference to the loan option.
Solution :
Computation of present value of total after tax cash flow under loan option:
1. Annual Loan installmment = 50000/5 =Rs. 10000
2. Interested on Loan:
Year 1 2 3 4 5
Principle O/s at the
Beginning of the year 50000 40000 30000 20000 10000
Interest @15% 7500 6000 4500 3000 1500
3. Annual Depreciation on SLM Basis: Rs. 50000/5 = Rs. 10000
4. In flow at the end of year 5
Rs.
Sale Value 1700
Less: Commission at 9% 153
Profit on Sale of Computer 1547 (WDV is Zero)
Less: Tax at 40% 619
Net Inflow 928
5. Computation of net outflow under loan option:
Year 1 2 3 4 5 Total
Principle Repayment 10000 10000 10000 10000 10000 50000
Interest 7500 6000 4500 3000 1500 22500
TOTAL (A) 17500 16000 14500 13000 11500 72500
Less: Tax Saving at 40%
On Depreciation 4000 4000 4000 4000 4000 20000
On interest 3000 2400 1800 1200 600 9000
TOTAL (B) 7000 6400 5800 5200 4600 29000
Net Outflow(A-B) 10500 9600 8700 7800 6900 43500
PV factors @ 9% 0.92 0.84 0.77 0.71 0.65
Present value of Outflow 9660 8064 6699 5538 4485 34446
Less: PV of inflow at the 603
end of 5th Year =928*0.65
PV of Net Outflow 33843
Computation of Annual Lease Rentals :
Steps to calculate Lease Rentals :
Step 1. Let be the lease rental
Step 2. Find L (1-T)
Step 3. Multiply the same with PVIFA (k%, n) where k is the post tax borrowing rate, n is the
number of years
Step 4. Equate this to post tax outflow under borrowing option, to find L
Therefore L × (1 - 0.4) × PV factors for Annuity at 9% for 5 years = PV of Outflow under loan
option i.e L × 0.6 × 3.89 = Rs. 33843 → L = Rs. 14500
(Note: This will result in difference to the loan option i.e. both are required)
Therefore, Annual Lease Rentals payable by Beta Ltd. should be Rs. 14500
Illustration 8 :
Evergreen Ltd. typically writes 5 year leases with rentals payable annually in
arrears. The following information is available about a lease under review.
Equipment cost : Rs. 47 lakh (inclusive of CST @ 10%)
Salvage value : 5% of original cost
After 5 years
Initial Direct cost : Rs. 0.50 lakh (front ended)
Management Fee : Rs 0.75 Lakh (front ended)
The marginal cost of capital to Evergreen Ltd. is 16% and the marginal rate of tax is 46%.
Calculate the break even rental for Evergreen Ltd. assuming a tax relevant depreciation rate
of :
(i) 25%
(ii) 40%
(iii) 100%
Solution :
Define L as the annual break rental for Evergreen:
The components of NPV (L) to Evergreen can be computed as follows:
a. Equipment cost = Rs. 47 lakh
b. PV of lease Payments = L × L × PVIFA (16.5) = 3.274L
c. PV of tax on lease rentals = 0.46 × L × PVIFA (16.5)
= 0.46 × L × 3.274
= 1.506 L
d. PV of tax shield
On Depreciation [25%] = [11.75 × PVIFA (16.5) + 8.81 × PVIFA (16.2)
+ 6.61 × PVIFA (16.3) + 4.96 × PVIFA (16.4)
+ 3.72 × PVIFA (16.5) ] × 0.46
= [(11.75 × 0.862) + (8.81 × 0.743)
+ (6.61 × 0.641) + (4.96 × 0.552)
+ (3.72 × 0.476)] × 0.46
= 25.42 × 0.46
= Rs. 11.69 lakh
On Depreciation [40%] = [18.80 × PVIFA (16.4) + 11.28 × PVIFA (16.2) +
+ 6.77 × PVIFA (16.3) + 4.06 × PVIFA (16.4)
+ 2.44 × PVIFA (16.5) ] × 0.46
= [(18.80 × 0.862) + (11.28 × 0.743)
+(6.77 × 0.641) + (4.06 × 0.552)
+ (2.44 × 0.476)] × 0.46
= 32.32 × 0.46
= Rs. 14.87 lakh
On Depreciation [100%] = 47 × PVIFA (16.1) × 0.46
= 47 × 0.862 × 0.46
= Rs. 18.63 lakh
e. PV of initial direct cost = Rs. 0.5 lakh
f. PV of management fee = Rs. 0.75 lakh
g. Pv of tax shield on initial = 0.5 × 0.46 × PVIF (16,1)
Direct cost = 0.5 × 0.46 × 0.862
= Rs. 0.198 lakh
h. PV of tax on = 0.75 × 0.46 ×PVIFA (16,5)
Management fee = 0.75 × 0.46 × 0.862
= Rs. 0.297 lakh
i. PV of salvage value = 2.35 × PVIFA (16,5)
= 2.35 × 0.476
= Rs. 1.12 lakh
Given a tax relevant depreciation rate of 25% p.a, L can be obtained from the equation.
- 47 + 3.274L - 1.506 + 11.69 - 0.5 +0.75 +0.198 - 0.297 + 1.12 = 0
Solving we get 1.768L = 34.04 i.e. L = Rs. 19.25 lakh
Where the relevant depreciation rate is 40% p.a, L can be obtained from the equa
tion.
- 47 + 3.27L - 1.506L +14.87 - 0.5 +0.75 +0.198 -0.297 +1.12 = 0
Solving we get 1.768L = 30.85 i.e. L= Rs. 17.45 lakh
Where rate of depreciation is 100% L can be obtained from the equation.
- 47 + 3.274L - 1.506L + 18.63 - 0.5 + 0.75 +0.198 - 0.297 +1.12 = 0
Solving we get 1.768L = 27.10 i.e. L = Rs.15.33 lakh
BUY OR LEASE :
Illustration 9 :
A company wishes to acquire an asset costing Rs. 1,00,000. The company has an offer from
a bank to lend @ 18% repayable in 5 years and installments. A leasing company has also
submitted a proposal to the Company to acquire the asset on lease at a yearly rentals of Rs.
280 per Rs. 1000 of the assets value for 5 years payable at year end. The rate of depreciation
of the asset allowable for tax purposes is 20% on W.D.V with no extra shift allowance. The
salvage value of the asset at the end of 5 years period is estimated to be Rs. 1000. Whether the
company should accept the proposal of Bank or leasing company, if the effective tax rate of
the company is 50%.
Solution :
Borrowing Option
1 2 3 4 5 6 7 8
Tax Net Discount
Year Principle Interest Depre- Shield Cash factor = Discounted
@ 18% ciation (3+4)× Flow 18(1-0.5)= Cash flow
20% on 50% (2+3)-5 9% @ 9%
on WDV
1 20000 18000 20000 19000 19000 0.917 17431.19
2 20000 14400 16000 15200 19200 0.842 16160.26
3 20000 10800 12000 11400 19400 0.772 14980.36
4 20000 7200 8000 7600 19600 0.708 13885.13
5 20000 3600 4000 3800 19800 0.650 12868.64
6 - 1000 39000 19500 -20500 0.596 -12223.5
63102.1
Owing to an inflow of Rs. 1000 (salvage value), The terminal depreciation claim
will be Rs. 39000.
Leasing Option
1 2 3 4 5 6
Year Lease Tax shield Net Cash Flow Discount iscounted
Rentals (2) × 50% (2) - 3 factor cash flow
@ 9%
1 28000 14000 14000 0.917 12844.04
2 28000 14000 14000 0.842 11783.52
3 28000 14000 14000 0.772 10810.57
4 28000 14000 14000 0.708 9917.953
5 28000 14000 14000 0.650 9099.039
54455.12
Recommendation: As the NPV of leasing is less, the company should go for leasing
Your company is considering to acquire an sdditional computer to supplement its time share
services to clients. It has two options.
(i) To purchase the computer for Rs. 22 lakhs
(ii) To lease the computer for 3 years from a leasing company for Rs. 5 lakhs as annual least
rent + 10% of gross time share service revenue. The agreement also requires an additional
payment of Rs. 6 lakhs at the end of the third year. Lease rents are payable at year-end and
the computer reverts to the lessor after the contract period.
Illustration 10 :
The company estimates that the computer under review will be worth Rs. 10 lakhs at the end
of the third year. Forecast revenues are:
Year I II III
Amount (Rs. lakhs) 22.5 25 27.5
Annual operation costs excluding depreciation / lease rent of computer are esti mated at
Rs. 9 lakhs with an additional Rs. 1 lakh for start up and training costs at the beginning of
the first year. These costs are to be borne by the lessee. Your com pany will borrow at 16%
interest to finance the acquisition of computer. Repay ment are to be made according to the
following schedule:
Year End I II III
Principle 500 850 850
Interest 352 272 136
The company uses the straight line method of depreciation to depreciate its assets and pays
50% Tax on its income. The management approaches the company secretary for advice.
Which alternative would be recommended and why? [May, 2004]
PV factors for years 1,2,3 for 8% are 0.926, 0.857 & 0.794
PV factors for years 1,2,3 for 10% are 0.862, 0.743 & 0.641
Solution :
Working Notes:
Depreciation = (2200000 - 1000000)/3 = Rs. 400000 p.a
Applicable discount rate for leasing & buying - after tax cost of debt = 16 × (1 - 0.5) = 8%
Operating and training costs are not considered, as they are incurred under both options.
Same logic applied for not taking into account the revenues.
Cost of Leasing :
Years
1 2 3
Lease Rent 500000 500000 500000
10% - Gross Revenue 225000 250000 275000
Lump sum payment - - 600000
Total 725000 750000 1375000
Tax shield 50% 362500 375000 687500
Net cash Outflow 362500 375000 687500
PV Factor 0.926 0.857 0.794
Pv of cash Outflow 335675 321375 545875
Total PV of cash out flow = Rs. 1202925
Cost of Borrowing :
Years
1 2 3
Principle 500000 850000 850000
Interest 352000 272000 136000
Tax shield on Int. (50%) 176000 136000 68000
Tax shield on Depr. (50%) 200000 200000 200000
Salvage value 0 0 (1000000)
Net 476000 786000 (282000)
PV Factor 0.926 0.857 0.794
Pv of Cash Outflow 440776 673602 (223908)
Total PV of Cash Outflow: Rs 890470
Suggestion: Since the present value of net cash outflow of borrowing is less, it is suggested to
purchase the computer instead of leasing it.
Illustration 11 :
Alfa Ltd. is thinking of installing acomputer. Decide whether the computer is to be purchased
outright (through 15% borrowing) or to be acquired on lease rental basis. The rate incometax
may be taken at 40%. The other data available are as under :
Purchase of computer :
Purchase price Rs. 20 lakh
Annual maintenance (to be paid in advance) Rs. 50000 p.a
Expected economic useful life 6 years
Depreciation (for tax purposes) SLM
Salvage value Rs.2 lakhs
Leasing of computer :
Lease charges to be paid in advance Rs. 4.50 lakhs
Maintenance expenses to be borne by lessor. Payment of loan is made in 6 year-end
installments of Rs. 5,28,474 each.
Solution :
Lease Option :
PV of Cash Outflows under Leasing Alternatives [Mmt. in Rs.]
Year end Lease Tax Shield Cash Pvf (9%,n) Total PV
Payment @40% outflows 5%(1-0.40)
after taxes
0 400000 - 400000 1.000 400000
1 - 5 400000 160000 240000 3.890 933600
6 - 160000 (160000) 0.596 (95360)
NPV 1238240
Lease payment = [ Rs. 4,50,000 (lease rent) - Rs. 50,000 (saving in maintenance expenses)] =
Rs. 4,00,000
Purchase Option :
Debt Payment Schedule [Amit. in Rs.]
Year End Loan Loan at the Payment Principle
Installment beginning Interest Principle O/s at the
end
1 528474 2000000 300000 228474 1771526
2 528474 1771526 265729 262745 1508781
3 528474 1508781 226317 302157 1206624
4 528474 1206624 180994 347460 859144
5 528474 859144 128872 399602 459542
6 528474 459542 68932 459542 -
PV of Cash Outflows under Buying Alternative [Amit. in Rs.]
Year Loan Tax advantage @40% Net PVF PV of
End Installment Interest Depreciation Cash (9%,n) Cash flows
Outflow
1 528474 120000 120000 288474 0.917 264531
2 528474 106292 120000 302182 0.842 254437
3 528474 90527 120000 317947 0.772 245455
4 528474 72398 120000 336076 0.708 237942
5 528474 51549 120000 356925 0.650 232001
6 528474 27573 120000 380901 0.596 227017
Total Pv of cash Outflows 1461383
Less: PV of Salvage value (Rs. 200000 × 0.596) 119200
NPV of Cash Outflows under buying alternative 1342183
Since Cash Outflow of Leasing is lower than that of buying, leasing option should be advised.
Illustration 12 :
Welsh Ltd. is faced with a decision to purchase or acquire on lease a mini car. The cost of the
mini car is Rs. 126965. It has a life of 5 years. The mini car can be obtained on lease by paying
equal lease rentals annualy. The leasing company desires a return of 10% on the gross value
of the asset. Welsh limited can also obtain 100% finance from its regular banking channel.
The rate of interest will be 15% p.a and the loan will be paid in five annula installments,
inclusive of interest. The effective tax rate of the company is 40%. For the purpose of taxation
it is to be assumed that the asset will be written off a period of 5 years on straight line basis.
Advise Welsh Limited about the method of acquiring the car.
What should be the annual lease rental to be charged by the leasing company to match the
loan option ?
For your exercise use the following discount factors for five years :
Discount Rate 1 2 3 4 5
10% 0.91 0.83 0.75 0.68 0.62
15% 0.87 0.76 0.66 0.57 0.49
9% 0.92 0.84 0.77 0.71 0.65
Solution :
BUY OPTION :
(a) Annual Loan Repayment : Loan Amount/PVIFA (15%,5) = Rs.126965/3.86 = Rs. 32892
Interest Computation :
Year 0 1 2 3 4
Opening Bal. 126965 94073 75292 53694 28856
Interest 15% 0 14111 11294 8054 4036
Total 126965 108184 86586 61748 32892
Repayment 32892 32892 32892 32892 32892
Closing Bal. 94073 75292 53694 28856 0
Debt Option : Cash Outflows
Year Install Interest Depre Tax Net PVF PV of
ment @ 15% ciation Shield Cash @ 9% Cash
on Int. Outflow Outflows
0 32892 0 0 0 32892 1.00 32892
1 32892 1411 25393 15802 17090 0.92 15723
2 32892 11294 25393 14675 18217 0.84 15302
3 32892 8054 25393 13379 19513 0.77 15025
4 32892 4036 25393 11772 21120 0.71 14995
5 0 0 25393 10157 (10157) 0.65 (6602)
Total Present Value of Cash Outflows: 87335
LEASE OPTION:
Annual Lease rentals = Cost of assets : [1+PVIFA (10%,4)]
[ Note Rentals paid in Advance]
= Rs. 126965 : 4.17 = Rs. 30447
Leasing Alternative :
Year Lease Tax Shield After Tax Cash PV Factors PV of
Payment Outflows at 9% Cash Outflows
0 30447 0 30447 1.00 30447
1 - 4 30447 12179 18268 3.24 59188
5 0 12179 (12179)0.65 (7916)
Total Present Value of Cash Outflows : 81719
Decision : Since PV of Leasing is lower than that of Buying, it is advisable to go for leasing.
(b) Let the Annual Rentals be L
After tax cost of Lease Rentals = 0.60L
PV of Lease Rentals = 0.60L × 4.17 = 2.502L
Equation 2050L = Rs. 87335, we get L as Rs. 34906
Illustration 13 :
A company is thinking of installing a machine. It is to decide whether the machine is to be
purchased outright (through 14% borrowings) or to be acquired on lease rent basis. The firm
is in the 50% tax bracket. The other data available are:
Buying:
Purchase price Rs. 20 lakhs
Expected economic useful life 6 years
Depreciation Straight-line method
Salvage Value Rs. 2 lakhs
Lease Option:
Lease charges (to be paid in adv.) Rs. 4 lakhs
Maintenance Expenses To be borne by the lessor
Payment of Loan 6 year and equal installments of Rs. 5,14,271
Should the company buy or lease ?
Solution :
Buying Option:
Lease Option:
If the firm procures the asset on lease basis, then it will have to pay a lease rental of Rs.
4,00,000 in the beginning of each of 6 years. This means that the first lease rental will be
payable now and the others will be payable in the beginning of next 5 years. These lease
rentals will be tax deductible at the end of each year. So, for the year 0, the net cash
outflow is Rs. 4,00,000. The net cash outflow for years 1, 2, 3, 4 & 5 will be Rs. 4,00,000 - Tax
Shield of Rs. 2,00,000. So, net outflows will be Rs. 2,00,000 only. However, for year 6, there
will not be any outflow but shall be tax shield of Rs. 2,00,000 resulting in net cash inflow.
This may be presented as follows:
Year Cash Flow Tax Shield Net Cash PV Factor PV
(Rs.) (Rs.) Flow (Rs.) (Rs.)
0 -400000 -
-400000 1.000 -400000
1 - 5 -400000 200000 -200000 4.100 -820000
6 200000 +200000 0.666 +133200 -1086800
So, if the firm procures the asset on lease basis, the PV of will be Rs. 10,86,800 which is less
than the PV of outflows in buying option. So, the firm should procure the asset on lease
basis.
Comments (3)
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