BBA VISION
Lease Financing (ইজারা অর্ায়ন)
থ
Definition: Lease is a contract between a lessor; the
owner of the assets and a lessee the user of the assets.
Lessor = যিযন সম্পদটির মাযিক অর্যাত
থ
যিযন সম্পদটি ভাড়া যদবেন ।
Lessee = যিযন সম্পদটি ভাড়া যনবেন । অর্াৎ
থ যিযন ভাড়া পযরব াধ করবেন ।
সাধারণত একটি সম্পদ আমরা দুভাবে েযেহার করবত পাযর ।
১। সম্পদটি ক্রয় অর্ো
২। সম্পদটি ভাড়া যনবয়
Lease হবিা একটি চুক্তি যি চুক্তিবত ভাড়ার মাধযবম একটি সম্পদ, সম্পবদর মাযিবকর
কাছ যর্বক েযেহার করার অনুমযত যনয়া হয় ।
Truck = 10,00,000 Tk
a. Buying 10,00,000 Loan kore
interest
b. Lease 5 year 3 lac per year Lease Rental
Which option will be better for you…?
Lease ebong Buying (Loan) ei duitar present value ber korte hobe….
Buying Option:
Loan = Installment
Present Value of Future Installment (Loan)
Lease:
Lease Rental
Rental Installment
Present Value of Future Lease Rental Installment (Lease)
Lease এর অংক করার যনয়মােযিিঃ
১। Loan এর যকক্তি যের করবত হবে ।
২। Interest এেং Principal Amount যের করবত হবে ।
অর্াৎ
থ Loan Amortization Schedule করবত হবে ।
৩। Present Value যের করবত হবে ।
৪।
Loan Payment/Installment যের করার সূত্রােযি
𝟏−
𝑷𝑽𝑨 = 𝑨 × {
𝟏−
𝑷𝑽𝑨 = 𝑨 × {
𝟏
(𝟏+𝒊)𝒏
𝒊
𝟏
(𝟏+𝒊)𝒏
𝒊
}
(Ending অর্ো, যকছু েিা না র্াকবি)
} (1+i) (Beginning or paid in advance েিা র্াকবি)
এখাবন,
𝑷𝑽𝑨 = Present Value of Annuity, Lease payment, Installment. অর্াৎ
থ সম্পদটির
মূিয ।
A = Annuity, Lease payment/Loan Payment Installment. অর্াৎ
থ যিবজর ভাড়ামূিয
ো যকক্তি ।
i = interest rate (সুবদর হার)
n = Lease period.
SV= Salvage Value = ভগ্নােব ষ মূিয (Scrap Value, Residual Value)
3 িা খরবচর উপর আমরা সাধারণত Tax Saving পাই
1.
2.
3.
Interest Cost
Depreciation Cost
Maintenance
Problem-01:
N Car Ltd. () with a decision to acquire on lease a mini car. The cost of mini car is Tk. 150000.it has a life
of 5 years. The leasing company desire a return of 10% on the gross value of the asset. Find out lease
rental installment if--i)
to be paid at the beginning of each year.
ii)
To be paid at the end of each year.
Solution: Req-i:
𝟏
{𝟏−(𝟏+𝒊)𝒏 } (𝟏+𝒊)
We know, PVA = A [
⇒ 150000= A [
⇒ 150000 = A [
⇒ 150000 = A [
]
𝒊
{𝟏−
𝟏
}(𝟏.𝟏𝟎)
(𝟏.𝟏𝟎)𝟓
𝟎.𝟏𝟎
𝒉𝒆𝒓𝒆, 𝑷𝑽𝑨 = 𝟏𝟓𝟎𝟎𝟎𝟎, 𝒊 = 𝟎. 𝟏𝟎
]
n=5
(𝟏−𝟎.𝟔𝟐𝟎𝟗)(𝟏.𝟏𝟎)
𝟎.𝟏𝟎
𝟎.𝟑𝟕𝟗𝟏×𝟏.𝟏𝟎
𝟎.𝟏𝟎
𝟎.𝟒𝟏𝟕𝟎𝟏
]
]
⇒ 150000 = A ( 𝟎.𝟏𝟎 )
⇒ 150000 = A ×4.1701
𝟏𝟓𝟎𝟎𝟎𝟎
⇒ A = 𝟒.𝟏𝟕𝟎𝟏 𝒔𝒐, 𝑨 = 𝑻𝒌. 𝟑𝟓𝟗𝟕𝟎
𝟏
𝟏−(𝟏+𝒊)𝒏
Req-ii: we know, PVA = A[
⇒150000= A[
𝒊
𝟏−
⇒ 150000= A [
]
𝟏
(𝟏.𝟏𝟎)𝟓
𝟎.𝟏𝟎
𝒉𝒆𝒓𝒆, 𝑷𝑽𝑨 = 𝟏𝟓𝟎𝟎𝟎𝟎, 𝒊 =. 𝟏𝟎, 𝒏 = 𝟓 𝒚𝒆𝒂𝒓𝒔
]
𝟏−𝟎.𝟔𝟐𝟎𝟗
𝟎.𝟏𝟎
𝟎.𝟑𝟕𝟗𝟏
]
⇒ 150000 = A ( 𝟎.𝟏𝟎 )
⇒ 150000 = A×3.791
𝟏𝟓𝟎𝟎𝟎𝟎
⇒ A= 𝟑.𝟕𝟗𝟏
So, A= Tk. 39567
Problem-02:
A Company is thinking to purchase a machine for Tk. 12500. The company can borrow Tk.
12500 at an interest rate of 12% to be repaid in 5 equal installment or it can take the machine
for an annual lease payment of Tk. 3000 for 5 years. Under income Tax Act, the company pay
tax @ 40%, straight line basis of depreciation is allowed. Which alternative should the
company accept?
Present Value of Loan Installment
Present Value of Lease Rental Installment
Borrow and buying option:
Calculation of Installment:
Here Given,
𝑷𝑽𝑨 = 12500
i = 12% or .12
n=5
A=?
We know,
𝑷𝑽𝑨 = 𝑨 × {
𝟏−
> 12500 = 𝑨 × {
𝟏
(𝟏+𝒊)𝒏
𝒊
𝟏−
}
𝟏
(𝟏+.𝟏𝟐)𝟓
.𝟏𝟐
𝟏−.𝟓𝟔𝟕𝟒𝟐𝟔
> 12500= 𝑨 × {
.𝟏𝟐
.𝟒𝟑𝟐𝟓𝟕𝟑
> 12500 = 𝑨 × {
.𝟏𝟐
}
}
}
> 12500 = 𝑨 × 𝟑. 𝟔𝟎𝟒𝟕𝟕
∴ A = 3468 Tk
Table for Calculation of Interest:
Year
Beginning
Loan
Total
Installment
Interest @12%
Principal
Installment
Ending Loan
1
2
3
4=2*12%
5=3-4
6=2-5
1
12500
1500
1968
10532
2
10532
3468
3468
1264
2204
8328
3
8328
3468
999
2463
5853
4
5853
3468
703
2768
3088
5
3088
3468
380
3088
0
4=(3-2)
Table for Calculation PV of Buying
1
2
3
4
5=3+4
6=5×40%
7=2-6
8
9=7×8
Year
ALP
Int.
Dep.
Total
Tax@40%
NCF
DF@7.20%
PV
1
1500
1600
1868
.933
1743
1264
2500
2500
4000
2
3468
3468
3764
1506
1962
.870
1707
3
3468
999
2500
3499
1400
2068
.812
1679
4
3468
703
2500
3203
1281
2187
.757
1656
5
3468
380
2500
2880
1152
2316
.706
1635
TPV
8420
DF =
𝟏−
𝟏
(𝟏+𝒊)𝒏
𝒊
(Equal NCF)
𝟏
𝟏
DF = (𝟏+𝒊)𝒏 = (𝟏+.𝟎𝟕𝟐)𝟐 (Unequal NCF)
Depreciation =
𝑪𝒐𝒔𝒕−𝑺𝑽
𝑳𝒊𝒇𝒆
=
𝟏𝟐𝟓𝟎𝟎
𝟓
= 2500
Discount Factor after tax= Interest rate (1-tr) × 100
= .12(1-.40) × 100
= 7.2%
Lease Option:
Table for Calculation PV of Lease:
1
2
3
4=2-3
5
Year
ALP
Tax@40%
NCF
DF@7.2%
1-5
3000
1200
1800
4.078
Comment: The Company should accept lease option because it’s PV is lower than other.
6=4×5
PV
7340
Problem-03:
Mehrin is to decide whether a computer is to be purchased through 12% borrowing or to
acquire on lease rent basis. The price of the computer is 300000. It’s annual maintenance cost
Tk. 25000 per year and expected life is 5 years. Tax rate is 40% and straight line method of
depreciation is allowable. The salvage value of the computer is Tk. 50000. In case of leasing,
annual lease rental is Tk. 100000 for 5 equal annual be borne by lessee. If the installation is
given beginning of the year for both buy and lease option, which alternative is the best for
Mehrin ?
Borrow and buying option:
Calculation of Installment:
Here Given,
𝑷𝑽𝑨 = 300000
i = 12% or .12
n=5
A=?
We know,
𝑷𝑽𝑨 = 𝑨 × {
𝟏−
𝟏
(𝟏+𝒊)𝒏
𝒊
} (1+i)
> 300000 = 𝑨 × {
𝟏−
𝟏
(𝟏+.𝟏𝟐)𝟓
.𝟏𝟑
𝟏−.𝟓𝟔𝟕𝟒𝟐𝟔
> 300000 = 𝑨 × {
.𝟏𝟐
.𝟒𝟑𝟐𝟓𝟕𝟑
> 300000 = 𝑨 × {
.𝟏𝟐
} (1+.12)
} × 𝟏. 𝟏𝟐
} × 𝟏. 𝟏𝟐
> 300000 = 𝑨 × 𝟑. 𝟔𝟎𝟒𝟕𝟕 × 𝟏. 𝟏𝟐
> 300000 = 𝑨 × 𝟒. 𝟎𝟑𝟕𝟑
∴ A = 74306 Tk
Table for Calculation Interest:
0
1
2
3
4
Beginning
Loan
300000
225694
178471
125582
66346
Year
Dep
Interest
Maintenance. Cost
Total Cost
Tax@40%
1
50000
27083
25000
102083
40833
2
3
4
5
50000
50000
50000
50000
21417
15070
7962
25000
25000
25000
25000
96417
90070
82962
75000
38567
36028
33185
30000
Year
Depreciation =
𝟑𝟎𝟎𝟎𝟎𝟎−𝟓𝟎𝟎𝟎𝟎
𝟓
Installment
Interest@12%
74306
74306
74306
74306
74306
0
27083
21417
15070
7962
Principal
Installment
74306
47223
52889
59236
66344
Ending Loan
225694
178471
125582
66346
0
= 50000
Table for calculation of tax saving:
Table for Calculation PV of Buying
1
2
3
4
5
7=(4-5)
8
9=7×8
Year
ALP
MC
TCF
Tax
NCF
DF@7.20%
PV
0
74306
74306
1.00
74306
1
74306
25000
99306
40833
58473
.933
54555
2
74306
25000
99306
38565
60739
.870
52843
3
74306
25000
99306
36028
63278
.812
51382
4
74306
25000
99306
33185
66121
.752
49723
5
0
25000
25000
30000
(5000)
.706
(3530)
(50000)
.706
(35300)
5
74306
TPV
243979
Discount Factor after tax= Interest rate (1-tr) × 100
= .12(1-.40) × 100
= 7.2%
Note: If there is any salvage value in question, it will be adjusted in NCF at negative figure in last year.
Lease option:
PV Of lease
Year
ALR
0
100000
1-4
100000
5
MC
25000
25000
TCF
75000
75000
0
Tax
30000
30000
NCF
75000
45000
(30000)
DF
1.00
3.3719
.706
TPV
PV
75000
151736
(1180)
205556
The firm should select the lease. Because its pv is lower.
Problem-04
Tahmina is thinking of acquiring a car. For that purpose she is to decide whether
car is to be purchased through 12% borrowing or to acquire on lease rent basis.
The car price is Tk 600000. Its annual maintenance cost is tk 25000 per year and
expected life is 5 years. It is assumed that the straight line method of
depreciation is applicable. Tax rate is 35%. The salvage value 100000. In case of
leasing, the lease rental is tk 200000 for 5 equal annual installments (to be in
advance) and maintenance expenses to be borne by lessor. Which alternative is
to selected by Tahmina.
Borrowing and buying option:
Calculation of Installment:
Here Given,
𝑷𝑽𝑨 = 600000
i = 12% or .12
n=5
A=?
We know,
𝟏
(𝟏+𝒊)𝒏
𝟏−
𝑷𝑽𝑨 = 𝑨 × {
𝒊
}
> 600000 = 𝑨 × {
𝟏
(𝟏+.𝟏𝟐)𝟓
𝟏−
.𝟏𝟑
> 600000 = 𝑨 × {
𝟏−.𝟓𝟔𝟕𝟒𝟐𝟔
> 600000 = 𝑨 × {
.𝟒𝟑𝟐𝟓𝟕𝟑
.𝟏𝟐
.𝟏𝟐
}
}
}
> 600000 = 𝑨 × 𝟑. 𝟔𝟎𝟒𝟕𝟕
∴ A = 166436 Tk
Table for Calculation Interest:
Beginning
Loan
2
600000
505564
399796
281336
148660
Year
1
1
2
3
4
5
Depreciation =
𝟔𝟎𝟎𝟎𝟎𝟎−𝟏𝟎𝟎𝟎𝟎𝟎
𝟓
Installment
Interest@12%
3
166436
166436
166436
166436
166436
4=2*12%
72000
60668
47976
33760
17776
Principal
Installment
5=3-4
94436
105768
118460
132676
148660
Ending
Loan
6=2-5
505564
399796
281336
148660
0
= 100000
Table for calculation of tax saving
Year
Dep
Interest
Mainten. Cost
Total Cost
Tax@35%
1
100000
72000
25000
197000
68950
2
100000
60668
25000
185668
64984
3
100000
47976
25000
172976
60542
4
100000
33760
25000
158760
55566
5
100000
17776
25000
142776
49972
DF =
DF =
𝟏
(𝟏+𝒊)𝒏
𝟏−
𝒊
𝟏
(𝟏+𝒊)𝒏
=
(Equal NCF)
𝟏
(𝟏+.𝟎𝟕𝟖)𝟐
(Unequal NCF)
Table for Calculation PV of Buying
1
2
3
4
5
6=(4-5)
7
8=6×7
Year
ALP
MC
TCF
Tax
Saving
NCF
DF@7.80%
PV
1
166446
25000
191446
68950
122496
0.928
113676
2
166446
25000
191446
64984
126462
0.861
108884
3
166446
25000
191446
60542
130904
0.798
104461
4
166446
25000
191446
55566
135880
0.74
100551
5
166446
25000
191446
49972
141474
0.686
97051
SV
-100000
0.686
-68600
TPV
456024
5
Discount Factor after tax= Interest rate (1-tr) × 100
= .12(1-.35) × 100
= 7.8%
Lease option:
PV Of lease
Year
ALR
MC
TCF
Tax@35%
NCF
DF@7.80%
PV
1
2
3
4=2-3
5=4*35%
6=4-5
7
8=6*7
0
200000
200000
1
200000
0-4
200000
25000
175000
61250
113750
3.3269
378435
5
0
25000
-25000
-8750
-16250
0.687
-11164
TPV
567271
200000
The firm should select the Borrowing option. Because its pv is lower.
Problem-05:
Rajib Chemical Ltd is considering the acquisition of machine costing Tk. 1600000. The
machine has an economic life of 5 years. The company can purchase the machine by
borrowing at an annual interest rate of 13 percent. The loan should be repaid in 5 years in
equal installment at the end of each year. Govt. provides 5% tax credit for purchasing new
industrial machines. Under the lease alternative, a rental of Tk. 435000 should be paid
annually (at the beginning) for five years. This includes a maintenance cost of Tk. 20000 per
year to borne by lessor. The company charge depreciation on straight line method. The
estimated salvage value of the machine is Tk. 100000. Tax rate is 30% and WACC is 14% for
the firm.
Requirement:
1. If the loan is taken for purchasing the machine, what would be the equal annual
installment?
2. Which alternative is best for the company ? Lease or Buying ?
Req-1:
Here Given,
𝑷𝑽𝑨 = 1600000
i = 13% or .13
n=5
A=?
We know,
𝟏
(𝟏+𝒊)𝒏
𝟏−
𝑷𝑽𝑨 = 𝑨 × {
𝒊
}
𝟏
(𝟏+.𝟏𝟑)𝟓
𝟏−
> 1600000 = 𝑨 × {
.𝟏𝟑
}
> 1600000 = 𝑨 × {
𝟏−.𝟓𝟒𝟐𝟕𝟓𝟗𝟗
> 1600000 = 𝑨 × {
.𝟒𝟓𝟕𝟐𝟒𝟎𝟎𝟎𝟔𝟒
.𝟏𝟑
.𝟏𝟑
}
}
> 1600000 = 𝑨 × 𝟑. 𝟓𝟏𝟕𝟐𝟑
∴ A = 454903 Tk
Req-2:
Table for Calculation Interest:
Year
1
1
2
3
Beginning
Loan
2
1600000
1353097
1074096
Installment
Interest@13%
3
454903
454903
454903
4=2×13%
208000
175902
139632
Principal
Installment
5=(3-4)
246903
279001
315271
Ending
Loan
6=(2-5)
1353097
1074096
758825
4
5
758825
402569
454903
454903
98647
52334
356256
402569
402569
0
Calculation table for tax saving:
Year
1
2
3
4
5
Dep
300000
300000
300000
300000
300000
Depreciation =
Interest
208000
175902
139632
98647
52334
𝟏𝟔𝟎𝟎𝟎𝟎𝟎−𝟏𝟎𝟎𝟎𝟎𝟎
𝟓
Total Cost Tax@30%
508000
152400
475902
142771
439632
131890
398647
119594
352334
105700
= 𝟑𝟎𝟎𝟎𝟎𝟎
Table for Calculation PV of Buying
1
2
Year
ALP
1
2
3
4
5
5
454903
454903
454903
454903
454903
4
5
6=(4+5)
Tax
Int. Tax Total
Saving Saving Saving
152400 80000 232400
142771
142771
131890
131890
119594
119594
105700
105700
SV
7(2-6)
8
9=7×8
NCF
DF@14%
PV
222503
312132
323013
335309
249203
(100000)
.911
.829
.755
.688
.627
.627
TPV
202700
258757
243875
230693
156250
(62700)
1029575
Int. Tax Saving = (1600000×5%)= 80000
Lease option:
PV Of lease
Tax@30%
Year
ALR
MC
TCF
0
435000
435000
1-4
435000
20000 415000 124500
5
20000 (20000) (6000)
NCF
DF@14%
435000
290000
(14000)
1.00
3.1836
.626
TPV
PV
435000
923244
(8764)
1349480
The firm should select the buying option. Because its pv is
lower.
Problem-06:
GEC Ltd. needs to acquire a machine costing Tk. 700000. The company follows straight
line method of depreciation. The salvage value of the machine is estimated Tk. 50000
at the end of 5 years. The lease rent is Tk. 150000 per year to be paid in advance each
year for 5 years. GEC Ltd. Can rise debt 14% and tax rate is 40%. Should the company
lease or buy the machine?
Solution: Leasing Option:
Year
Lease rent
Tax saving
NCO
PV at 8.4%
PV of NCO
40%
0
150000
-150000
1.000
150000
1-4
150000
60000
90000
3.2828
295452
5
-60000
-60000
0.6681
40086
Total
405366
PV
Buying option:
Workings:
𝐶𝑜𝑠𝑡−𝑆𝑎𝑙𝑣𝑎𝑔𝑒 𝑉𝑎𝑙𝑢𝑒
Depreciation =
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐿𝑖𝑓𝑒
𝟕𝟎𝟎𝟎𝟎𝟎−50000
650000
=
=
= 130000
𝟓
5
Cost of debt/ Interest expenses =14%
After tax cost of capital = 0.14 (1-.4) = 0.084
Loan amortization schedule:
Year Principal
Installment
Interest
1
700000
203912
98000
2
594088
203912
83172
3
473348
203912
66269
4
335705
203912
46999
5
178792
203912
25120
Installment Calculation:
𝑃𝑉×𝑖
A=
1 𝑛
=
Prin. Paid
105912
120740
137643
156913
178792
Rest Prin.
594088
473348
335705
178792
---
1−(1+𝑖)
700000×.14
1
5
1−(1+.14)
98000
=
0.4806
=Tk. 203912
Year
Payment
Dep.
×interest
Tax
NCO
PV
PV
factor at
8.4%
1
203192
2
203192
3
203192
4
203192
5
203192
SV
(50000)
Total PV of NCO
228000
213172
196269
176999
155120
91200
85269
78508
70800
62048
112712
118643
125404
132112
141864
(50000)
0.9225
0.8510
0.7850
0.7242
0.6681
0.6681
103977
100965
98442
95676
94779
(33405)
460434
Calculation of PV of NCO
Comment: Since PV of cash outflow in leasing option is lower than that of buying
option. Leasing option should be selected.
Problem-07:
Xenon Company is faced with a decision to purchase or acquire an equipment. The cost of
the equipment is Tk. 250000. It has a life of 5 years. The equipment can be obtained on lease
by paying in advance equal lease rental annually. The leasing Company desires a return of
10%. Xenon Co. can also buy the equipment by taking loan from DBBL with 15% interest. The
loan is to be paid in 5 equal installments at the end of each year. Corporate tax rate is 40%
the company follows straight line depreciation system. Should it lease or buy the equipment?
Solution: Leasing Option:
We know,
𝟏
𝟏−(𝟏+𝒊)𝒏
𝑷𝑽𝑨 = 𝑨 × {
𝒊
} (𝟏 + 𝒊)
> 250000 = 𝑨 × {
𝟏
(𝟏+.𝟏𝟎)𝟓
𝟏−
.𝟏𝟎
} (𝟏+. 𝟏𝟎)
> 250000 = 𝑨 × 𝟑. 𝟕𝟗𝟎𝟕 × 𝟏. 𝟏𝟎
> 250000 = 𝑨 × 𝟒. 𝟏𝟔𝟗𝟖𝟕
∴ A = 59966 Tk
Cost of capital = .15(1-.4) = .09
Year-end
Lease Rent
1
0
1-4
5
2
59966
59966
----
PV of cash outflows:
Tax Shield
After tax
40%
cash outflow
(L)× (0.4)
3=2×0.40
4
--59966
23986
35980
23986
(23986)
PV factor 9%
Total (PV)
5
1.00
3.24
0.65
Total
6=4×5
59966
116575
(15591)
160950
Buying option:
Loan Installment =
𝑃𝑉
𝑃𝑉𝐼𝐹𝐴 𝑎𝑡 15%
250000
=
3.352
250000
= 74582
= 50000
Loan amortization Schedule:
Year
Principal
Installment
Interest
Principal paid
1
2
3
4= 2×0.15
5=3-4
1
250000
74582
37500
37082
2
212918
74582
31938
42644
3
170274
74582
25541
49041
4
121233
74582
18185
56397
5
64830
74582
9746
64836
Calculation of PV:
Year Loan
Int+ Dep.
Tax Shield
Net Cash
PV factor
PV
Install
Outflow
1
2
3
4= 3×0.40
5=2-4
6
7= 5×6
1
74582
87500
35000
39582
0.917
36296
2
74582
81938
32775
41807
0.842
35201
3
74582
75541
30216
44366
0.772
34250
4
74582
68185
27274
47308
0.708
33494
5
74582
59746
23898
50684
0.650
32945
Total
172186
Comment: Since the PV of cash outflow in leasing option is lower than that of buying
option, lease should take lease.
Depreciation =
5
Problem-08:
XYZ limited wants to lease a computer system for the purpose of color matching. The
system will cost Tk. 30 lakh and has a 5 years of life time. The applicable written-down
depreciation is 25%. The annual rental is payable at the end of year for 5 years, will be
Tk. 8,40,000. The lessor will maintain the computer system which will be Tk. 50,000 per
year. At the end of its useful life, the system can be sold for 50% of its written down value.
The company’s borrowing rate is 14% and tax rate is 35%. Should the system be leased?
Show your calculations.
Solution: Buying Option:
1
PVA = A[
1−(1+𝑖)𝑛
𝑖
]
⇒ 30,00,000= A[
1−
1
(1+.14)5
0.14
A = Tk. 875000
]
Loan Amortization Schedule:
Year
Principle
Install
1
2
3
1
3000000
875000
2
2545000
875000
3
2026300
875000
4
1434982
875000
5
760880
875000
Interest
4=2×0.14
420000
356300
283682
200897
114120
Princ. Paid
5=3-4
455000
518700
591318
674102
760880
Princ. Due
6=2-5
2545000
2026300
1434982
760880
0
Depreciation: 1st year = 3000000×25%= 750000
2nd year = (3000000-750000)×.25= 2250000×.25= 562500
3rd year= (2250000-562500)×.25 = 1687500×.25 = 421875
4th year= (1687500-421875)×.25 = 1265625×.25 = 316406
5th year = (1265625-316406)×.25= 949219×.25 = 237305
Written down price = 949219-237305=711914
Salvage Value = 711914÷2
= 355957
After tax cost of debt = .14(1-.35) = .14×.65 = 0.091
Calculation of PV of Buying Option:
Year
ALP
In + Dep
Tax saving NCF
35%
PV Factor
9.1%
PV
1
1
2
3
4
5
5
2
875000
875000
875000
875000
875000
SV
3
1170000
918800
705557
517303
351425
4=3×0.35
409500
321580
246945
181056
122999
6
0.916
0.840
0.770
0.706
0.647
0.647
7=5×6
426398
468873
483602
489924
486545
(230304)
2125038
5=2-4
465500
553420
628055
693944
752001
(355957)
Total Present Value
Leasing Option:
Year
ALR
Tax
35%
saving- NCF
1
1-5
2
840000
3=2×0.35
294000
4=2-3
546000
PV Factor 9.1% PV
5
3.879
6=4×5
2117934
Comment: Since the PV in leasing option is lower, leasing option should be selected.
Note: Maintenance cost is not included in lease rent.
Problem-09
Mehrin is decide whether a computer is to be purchased through 12% borrowing or to be
acquired on lease rent basis. The price of the computer is tk. 300000. It’s annual maintenance
cost Tk. 25000 per year and expected life is 5 years. Tax rate is 40% and straight line method of
depreciation is allowable. The salvage value of the computer is Tk. 50000. In case of leasing,
annual lease rental is Tk. 100000 for 5 equal annual installment including maintenance cost Tk.
25000 and maintenance cost to be borne by lessor. If the installment is given at beginning of the
year for both lease and buy option, which alternative is best for Mehrin?
Solution: Buying Option:
(i)
Lease Installment:
𝟏
{𝟏−(𝟏+𝒊)𝒏 } (𝟏+𝒊)
PVA= = A [
⇒ 300000=
⇒300000 =
⇒300000 =
]
𝒊
𝑨{𝟏−
𝟏
}(𝟏+.𝟏𝟐)
(𝟏+.𝟏𝟐)𝟓
𝟎.𝟏𝟐
𝑨{𝟏−𝟎.𝟓𝟔𝟕𝟒𝟐𝟕}×(𝟏.𝟏𝟐)
𝟎.𝟏𝟐
𝑨×𝟎.𝟒𝟑𝟐𝟓𝟕𝟑×𝟏.𝟏𝟐
𝟎.𝟏𝟐
⇒ A ×0.48448 = 36000
𝟑𝟔𝟎𝟎𝟎
⇒ A = 𝟎.𝟒𝟖𝟒𝟒𝟖 So, A= Tk. 74306
(ii) Depreciation =
𝑪𝒐𝒔𝒕−𝑺𝒂𝒍𝒗𝒂𝒈𝒆 𝑽𝒂𝒍𝒖𝒆
𝑼𝒔𝒆𝒇𝒖𝒍 𝒍𝒊𝒇𝒆
𝟑𝟎𝟎𝟎𝟎𝟎−𝟓𝟎𝟎𝟎𝟎
=
𝟓
= Tk. 50000
(iii) Kd= Cost of debt(1-TR)
= 12%(1-0.40)
= 12%× 0.60
= 7.2%
(iv) Loan Amortization Schedule
Year
Loan at
Installment
beginning
1
2
3
0
300000
74306
1
225694
74306
2
178471
74306
3
125582
74306
4
66346
74306
Calculation of PV of Net Cash Outflow:
interest@
12%
4
27083
21417
15070
7960
Principal
Payment
5=3-4
74306
47223
52889
59236
66346
Loan at the
ending
6= 2-5
225694
178471
125582
66346
0
Ye
ar
Install
ment
Dep.
tk
Main.
cost
Itn. tk
Total
tax ex.
Tax
save
NCO
1
2
3
4
5
74306
99306
99306
99306
99306
---50000
50000
50000
50000
50000
---25000
25000
25000
25000
25000
---27083
21417
15070
7960
7=6×4
0%
---40833
38567
36028
33184
30000
8=1-7
0
1
2
3
4
5
sv
6=3+4
+5
---102083
96417
90070
82960
75000
PVIF
@7.20
%
9
74306
58478
60739
63278
66122
(30000)
(50000)
1.000
0.933
0.870
0.812
.757
0.706
0.706
PV
10=8×
9
74306
54555
52843
51382
50054
(21180
0)
(35300
)
Total
226660
Leasing Option:
Calculation of PV of lease:
Year
1
0
1-4
5
Total
Installment Mainten.
cost
2
3
100000
25000
100000
25000
Total
Tax 40%
4=2-3
75000
75000
30000
5
---30000
(30000)
NCF
6=4-5
75000
45000
(30000)
PVIF @
7.20%
7
1.00
3.3719
0.706
PV
8=6×7
75000
151736
(21180)
205556
𝟏
*PVIFA (1-4) =
𝟏−(𝟏+𝒓)𝒏
𝟏−
=
𝒓
𝟏
(𝟏+𝟎.𝟎𝟕𝟐)𝟒
𝟎.𝟎𝟕𝟐
= 𝑻𝒌. 𝟑. 𝟑𝟕𝟏𝟗
Problem-10
Mr. Rahman is thinking of acquiring a car. For that purpose she is to decide whether the car is to be
purchased through 12% borrowing or to be acquired on lease rent basis.
The price of the car is Tk. 700000. Its annual maintenance cost is Tk. 45000 per year and expected life
is 5 years. It is assumed that the straight line method of depreciation is allowable under income Tax Act
and tax rate is 35%. The salvage value of the car is Tk. 100000.
In case of leasing, the lease rental Is Tk. 300000 for 5 equal annual installment (to be paid in advance)
and maintenance expenses to be borne by lessor.
Which alternative is to be selected by Mr. Rahman?
Solution: loan option:
1
PVA = A {1 − (1+𝑟)𝑛 }
𝑖
1
Or, 700000= A{1 − (1.12)5 }
0.12
Or, 700000= A(3.60478)
700000
Or, A= 3.60478
So, A = Tk. 194187
Table 1- Loan Amortization Schedule:
Year
Principal
Installment
Interest 12%
Principal
Principal
Paid
Due
1
2
3
4= 2×12%
5= 3-4
6= 2-5
1
700000
194187
84000
110187
589813
2
589813
194187
70778
123409
466404
3
466404
194187
55968
138219
328185
4
328185
194187
39382
154805
173380
5
173380
194187
20807
173380
0
Total annual payment= Annual Loan Installment + Annual Maintenance Cost
= Tk. 194187+Tk. 45000 = Tk. 239187
Annual Depreciation:
=
=
𝐴𝑠𝑠𝑒𝑡 𝑐𝑜𝑠𝑡−𝑆𝑎𝑙𝑣𝑎𝑔𝑒 𝑉𝑎𝑙𝑢𝑒
𝐴𝑠𝑠𝑒𝑡 𝑙𝑖𝑓𝑒
700000−100000
5
600000
5
= 𝑇𝑘. 120000
After tax Cost of Debt, ki= kd(1-t) = 12% (1-0.35) = 7.85 or 8%
Table-02: PV of NCO at Buying Option:
Year Total
Interest Maint
payment
cost
1
1
2
3
4
5
2
239187
239187
239187
239187
239187
3
84000
70778
55968
39382
20807
4
45000
45000
45000
45000
45000
Dep.
Total
taxable
exp.
5
120000
120000
120000
120000
120000
6=3+4+5
249000
235778
220968
204382
185807
Tax shield
@35%
NCO
PV
factor
@
8%
9
0.926
0.857
0.794
0.735
0.681
7=6×35% 8=2-7
87150
152037
82522
156665
77339
161848
71534
167653
65032
174155
Total PV of NCO
Less: PV of SV (100000×0.681)
Net PV of NCO
PV of
NCO
10=8×9
140786
134262
128507
123225
118600
645380
(68100)
577280
Leasing Option: Beginning of the year:
Annual Net Lease Rent Payment
= Annual Lease Payment – Annual Maintenance Cost
= 300000-45000 = Tk. 255000
Table- 3: PV of NCO at leasing option:
Table for calculation PV of cash outflow (after tax) under lease option.
End of
the
year
1
0
1-4
5
Lease rent
Tax saving @
35%
NCO
2
255000
255000
---
3
--89250
89250
4=2-3
255000
165750
(89250)
PV factor at
8%
PV of NCO
5
6=4×5
255000
548964
(60779)
743185
1.000
3.312
0.681
Total PV
=
Net advantage at Borrowing and Buying Option= 743185-577280 = tk. 165905
Decision: Borrowing and Buying Alternative should certainly be selected by Mr. Rahman.
Problem-11:
Maliha is thinking of acquiring a computer for that purpose she is to decide whether the computer is
to be purchased through 12% borrowing or to be acquired on lease rent basis. The price of the
computer is Tk. 60000. Its annual maintenance cost Tk. 2500 per year and expected life is 5 years. It is
assumed that the straight line method of depreciation is allowable under income tax act and tax rate is
40%. The salvage value of the computer is Tk. 10000.In case of leasing, the lease rentals is Tk. 20000
for 5 equal installment and maintenance expenses to be borne by lessor. Which alternative is least for
Maliha.
1
Solution: PVA = A {1 − (1+𝑟)𝑛 }
𝑖
1
Or, 60000= A{1 − (1.12)5 }
0.12
Or, 60000= A(3.605)
60000
Or, A= 3.605
So, A = Tk. 16644
Table 1- Loan Amortization Schedule:
Year
Principal
Installment
Interest 12%
1
2
3
4= 2×12%
1
60000
16644
7200
2
50556
16644
6067
3
39978
16644
4797
4
28131
16644
3377
5
14863
16644
*1781
Note: in the last year interest is to be adjusted.
Principal
Paid
5= 3-4
9444
10557
11846
13268
14863
Principal
Due
6= 2-5
50556
39978
28131
14863
0
Total annual payment= Annual Loan Installment + Annual Maintenance Cost
= Tk. 16644+Tk. 2500 = Tk. 14144
Annual Depreciation:
=
𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡−𝑆𝑎𝑙𝑣𝑎𝑔𝑒 𝑉𝑎𝑙𝑢𝑒
𝑈𝑠𝑒𝑓𝑢𝑙 𝑙𝑖𝑓𝑒
60000−10000
5
= 𝑇𝑘. 10000
After tax Cost of Debt, ki= kd(1-t) = 12% (1-0.40) = 7.2%
Table-02: calculation of PV of cash outflow (NCO) at buying option:
Year Total
Interest Maint Dep.
payment
cost
1
1
2
3
4
5
2
19144
19144
19144
19144
19144
3
7200
6067
4797
3377
1781
Leasing Option:
Net Lease Rent Payment
4
2500
2500
2500
2500
2500
5
10000
10000
10000
10000
10000
Total
taxable
exp.
6=3+4+5
19700
18567
17297
15877
14281
Tax shield
@40%
NCO
PV
factor
@
7%
9
0.935
0.873
0.816
0.763
0.713
7=6×35% 8=2-7
7880
11264
7427
11717
6919
12225
6351
12793
5712
13432
Total PV of NCO
Less: PV of SV (100000×0.713)
Net PV of NCO
PV of
NCO
10=8×9
10532
10229
9976
9761
9577
50075
(7130)
42945
= 20000-2500 = Tk. 17500
1 Calculation of PV of Net cost of lease:
Year
Installment
Tax saving
1
1
2
3
2
17500
17500
17500
3
7000
7000
7000
Net cost of
lease
4=2-3
10500
10500
10500
PV factor @
7%
5
0.935
0.873
0.816
PV
6= 4×5
9878
9167
8568
Homework Try yourself
Problem-12
ABC Co. needs to require a new machine costing Tk. 5,00,000. There are two alternatives way of financing:
a. To take loan from AB Bank @ 16% interest payable at the end of each year in equal installment for four
years.
b. To take lease from union capital for four years with an annual payment of Tk. 2,20,000 to be paid at the
end of each year. Which offer the company should accept ?
Assume Tax rate is 35% and SLM of depreciation is applicable.
Problem-13
Maxim Company is planning to acquire an equipment that’s value is Tk. 15,00,000. IDLC is willing to lease
the equipment to Maxim for four years period at Tk. 5,20,000 periodic rental payment at the end of each
year. Maxim can borrow Tk. 15,00,000 from Spartan Bank Ltd. at 14% for four years period. The corporate
tax rate is 40%. The company uses SLM of depreciation with no salvage value. Evaluate which alternative will
be best for Maxim company ?
Problem-14
[NU. BBA (Hon's) – 2012, 16]
A company needs to acquire an equipment that will cost Tk. 3,35,220. The company has two alternatives to finance
the equipment:
(a) To take lease from United Leasing Company ILC for 5 years with an annual lease payment of Tk. 1,20,000 to be
paid at the end of each period.
(b) To take loan from Janata Bank/Jamuna Bank at 15% interest p.a. repayable annually at the end of each of the 5
years in equal installments. The equipment will be depreciated on straight line basis.
Corporate tax rate is 40%.
Which offer the company should accept?
Problem-15
[NU. BBA (Hon's) – 2017]
A company needs to acquire an equipment that will cost Tk. 4,00,000. The company has two alternatives to finance
the equipment:
(a) To take lease from a leasing company for 5 years with an annual lease payment of 1,25,000 to be paid at the
beginning of each period.
(b) To take loan form AB Bank at 14% interest per annum repayable annually at the end of each of the 5 years in equal
instalment. The salvage value of the equipment is Tk. 20,000 and the equipment will be depreciated on straight
line basis.
Corporate tax rate is 40%.
Which offer the company should accept?