1. Project cost is Rs. 30,000 and the cash inflows are Rs. 10,000 p.a, the life of
the project is 5 years. Calculate the pay-back period.
PBP = Initial cash outflow/Annual cash inflow
PBP = Rs.30,000 / Rs. 10,000
= 3 years[
2. Determine the pay-back period which requires a cash outlay of Rs.10,000
and generates cash inflows of Rs.3,000,Rs.4,000, Rs.3,000 and Rs.2,000 in
the first, second, third and fourth year respectively. Calculate PBP.
Year
Cash Inflow
Cumulative Cash Inflow
1.
3,000
3,000
2.
4,000
7,000
3.
3,000
10,000
4
2,000
12,000
PBP = 3 years
3. Determine the pay-back period which requires a cash outlay of Rs.10,000
and generates cash inflows of Rs.2,000,Rs.4,000, Rs.3,000 and Rs.2,000 in
the first, second, third and fourth year respectively.
Year
Cash Inflow
Cumulative Cash Inflow
1.
2,000
2,000
2.
4,000
6,000
3.
3,000
9,000
4
2,000
11,000
PBP = year before full recovery of the Investment +( Number of months in
year/the inflow in the beginning of the year ) X amount required for the
recovering of the investment
PBP = 3 years + (12 months /2,000)X1,000
PBP = 3 Years + 6 months
PBP = 3 years and 6 months
4. A large sized chemical company is considering investing in a project that
costs Rs. 4,00,000. The estimated salvage value is zero. Tax rate is 55%.
The company uses straight line depreciation and the proposed project has
cash flows before tax and depreciation (CFBT) as follows
Year
CFBT
1
1,00,000
2
1,00,000
3
1,50,000
4
1,50,000
5
2,50,000
Calculate PBP
Depreciation p.a = (Investment – Salvage value of the Investment) / Life of the
project
Depreciation p.a = (4,00,000 – 0) / 5 years
Depreciation p.a = 80,000
Year
CFBD&T
Dep
CFAD&BT
Tax = 55%
CFAD&T
CIF
(CFAD&T
+ Dep)
1
1,00,000
80,000
20,000
11,000
9,000
89,000
2
1,00,000
80,000
20,000
11,000
9,000
89,000
3
1,50,000
80,000
70,000
38,500
31,500
1,11,500
4
1,50,000
80,000
70,000
38,500
31,500
1,11,500
5
2,50,000
80,000
1,70,000
93,500
76,500
1,56,500
Year
CIF
Cumulative
(CFAD&T
CIF
+ Dep)
1
89,000
89,000
2
89,000
1,78,000
3
1,11,500
2,89,500
4
1,11,500
4,01,000
5
1,56,500
5,57,500
PBP = year before full recovery of the Investment +( Number of months in
year/the inflow in the beginning of the year ) X amount required for the
recovering of the investment
PBP = 3 years + (365 days/1,11,500) X 1,10,500
PBP = 3 years + 362 days/30 days
PBP = 3 years + 11 months and 27
5. A company is considering an investment proposal to purchase a machine
costing Rs.2,50,000. The machine has a life expectancy of 5 years and Rs.
10,000 is a salvage value. The company’s tax rate is 40%. The firm uses
straight line method for providing depreciation. The estimated cash flows
before tax and depreciation from the machine are as follows:
Year
1
Cash flow before tax and depreciation
60,000
2
70,000
3
90,000
4
1,00,000
5
1,60,000 (including scrap value)
Calculate: Pay-back period
Depreciation for p.a = (Initial Investment – Scrap Value of the Machine) /
Expected life of the Machine
Depreciation p.a = (2,50,000 – 10,000) / 5
Depreciation = Rs.48,000
Year
CFBD&T
Dep
CFAD&BT
Tax = 40%
CFAD&T
CIF
(CFAD&T
+ Dep)
1
60,000
48,000
12,000
4,800
7,200
55,200
2
70,000
48,000
22,000
8,800
13,200
61,200
3
90,000
48,000
42,000
16,800
25,200
73,200
4
1,00,000
48,000
52,000
20,800
31,200
79,200
5
1,60,000
48,000
1,12,000
44,800
67,200
1,15,200
Year
CIF
Cumulative
(CFAD&T
cash inflow
+ Dep)
1
55,200
55,200
2
61,200
1,16,400
3
73,200
1,89,600
4
79,200
2,68,800
5
1,15,200
3,84,000
PBP = year before full recovery of the Investment +( Number of months in
year/the inflow in the beginning of the year ) X amount required for the
recovering of the investment
PBP = 3 + ( 365 days/79,200)X 60,400
PBP = 3 + 279 days
PBP = 3 years 9 months 9 days
6. The Alpha Company Ltd. Is considering the purchase of a new machine. Two
alternative machine ( A and B) have been suggested each costing Rs.4,00,000. Life
time of the machine is 5 years. Earnings before tax and after depreciation are
expected to be as follows:
Year
Cash flow before tax and after
depreciation
Machine A
Machine B
100,000
1,20,000
1
2
1,20,000
1,60,000
3
1,60,000
2,00,000
4
2,40,000
1,20,000
5
1,60,000
80,000
State which alternative is suitable under PBP method.
For Machine A
Year
1
2
3
4
5
CFBT &AD
1,00,000
1,20,000
1,60,000
2,40,000
1,60,000
Tax @ 50%
50,000
60,000
80,000
1,20,000
80,000
Year
CF AT &BD
1
2
3
4
5
1,30,000
1,40,000
1,60,000
2,00,000
1,60,000
Cumulative
Cash flow
1,30,000
2,70,000
4,30,000
6,30,000
7,90,000
CFAT&D
50,000
60,000
80,000
1,20,000
80,000
Dep
80,000
80,000
80,000
80,000
80,000
CF AT &BD
1,30,000
1,40,000
1,60,000
2,00,000
1,60,000
PBP = year before full recovery of the Investment +( Number of months in
year/the inflow in the beginning of the year ) X amount required for the
recovering of the investment
PBP = 2 + (365 days/1,60,000)X1,30,000
PBP = 2 years + 296 days
PBP = 2 years + 9 months 26 days
For Machine B
Year
1
2
3
4
5
CFBT &AD
1,20,000
1,60,000
2,00,000
1,20,000
80,000
Tax @ 50%
60,000
80,000
1,00,000
60,000
40,000
Year
CF AT &BD
1
2
3
4
5
1,40,000
1,60,000
1,80,000
1,40,000
1,20,000
Cumulative
Cash flow
1,40,000
3,00,000
4,80,000
6,20,000
7,40,000
CFAT&D
60,000
80,000
100,000
60,000
40,000
Dep
80,000
80,000
80,000
80,000
80,000
CF AT &BD
1,40,000
1,60,000
1,80,000
1,40,000
1,20,000
PBP = year before full recovery of the Investment +( Number of months in
year/the inflow in the beginning of the year ) X amount required for the
recovering of the investment
PBP = 2 year + (365 days / 1,80,000)X 1,00,000
PBP = 2 years + 203 days
PBP = 2 years + 6 months + 23 days
Machine B can be selected
7. From the following information calculate the PBP of the two projects and
suggest which of the two projects should be accepted assuming a discount rate of
10%.
Particulars
Initial Investment
Estimated Life
Scrap Value
Year
1
2
3
4
5
Project X
Project Y
Rs.20,000
Rs.30,000
5 yrs
5 years
Rs.1000
Rs.2,000
Profit after depreciation and taxes are as follows:
5,000
20,000
10,000
10,000
10,000
5,000
3,000
3,000
2,000
2,000
State which alternative is suitable under PBP method.
Year
CFAD&T Dep
1
2
3
4
5
5,000
10,000
10,000
3,000
2,000
3,800
3,800
3,800
3,800
3,800
CFAT&BS Discount
factor
10%
8,800
0.909
13,800
0.826
13,800
0.751
6,800
0.683
5,800
0.621
PV of
Future
CI
8,000
11,399
10,362
4,644
3,602
Cumulative
PV of
Future
CI
23,270
12,886
7,961
5,874
4,720
Cumulative
8,000
19,399
29,761
34,405
38,007
Dep = 20,000-1000/5 years
Dep = 3,800
PBP = 2 years + (365 days / 10,362)X 601
PBP = 2 Years + 21 days
For Project Y
Year
CFAD&T Dep
1
2
3
4
5
20,000
10,000
5,000
3,000
2,0000
5,600
5,600
5,600
5,600
5,600
CFAT&BS Discount
factor
10%
25,600
0.909
15,600
0.826
10,600
0.751
8,600
0.683
7,600
0.621
Dep = 30,000 – 2,000 / 5
Dep = 5,600
PBP = 1 year + (365 days /12,886)X 6,730
PBP = 1 year + 191 days
23,270
36,156
44,117
49,991
54,711
PBP = 1 year + 6 months + 11 days
5. X company is examining two mutually exclusive proposals for the new capital
investment. The data on the proposals are as follows:
Particulars
Net Cash outlay
Salvage Value
Estimated Life
Depreciation
Income Tax
Cost of Capital (present Value)
Year
Proposal A
Proposal B
Rs.40,000
Rs.50,000
Nil
Nil
4 Years
5 years
Straight Line Method Straight Line Method
50%
50%
10%
10%
Earnings before depreciation and taxes
I Year
II Year
III Year
IV Year
V Year
12,000
14,000
16,000
22,000
-
14,000
16,000
18,000
22,000
20,000
You are asked to advise which proposal would be financially preferable under
PBP.
Dep = Initial Investment – Salvage value / Life
Dep = 40,000 – 0/4 years = Rs.10,000
For B
Dep = 50,000 – 0 / 5 years = Rs.10,000
For Proposal A
Year
1.
2.
3.
CFB
D&T
12,000
14,000
16,000
Dep
CFAD
&BT
10,000 2,000
10,000 4,000
10,000 6,000
Tax =
50%
1,000
2,000
3,000
CFAD
&T
1,000
2,000
3,000
CFBD
&AT
11,000
12,000
13,000
PV
10%
0.909
0.826
0.751
PV of CI
Cumulative
9,999
9,912
9,763
9,999
19,911
29,674
4.
22,000 10,000 12,000 6,000
6,000
16,000 0.683
10,928
40,602
CFBD
&AT
12,000
13,000
14,000
16,000
15,000
PV of CI
Cumulative
10,908
10,738
10,514
10,928
9,315
10,908
21,646
32,160
43,088
52,403
PBP = 3 Years+( 365 days /10,928)X 10,326
PBP = 3 Years + 345 days
PBP = 3 years + 11 months + 15 days
For Proposal B
Year
1.
2.
3.
4.
5.
CFB
D&T
14,000
16,000
18,000
22,000
20,000
Dep
10,000
10,000
10,000
10,000
10,000
CFAD
&BT
4,000
6,000
8,000
12,000
10,000
Tax =
50%
2,000
3,000
4,000
6,000
5,000
CFAD
&T
2,000
3,000
4,000
6,000
5,000
PV
10%
0.909
0.826
0.751
0.683
0.621
PBP = 4 years + (365 days /9,315 ) X 6,912
PBP = 4 years + 271 days
PBP = 4 years + 9 months + one day
Net Present value method
NPV = difference between present value of cash outflow and present value of
future cash inflow
9. Initial investment is Rs. 30,000. Life time of the machine is 5 years. The cash
inflow for next five years is Rs.10,000 p.a. Discount factor is 10%. Calculate the
NPV.
Year
1.
2
3
4
5
Cash inflow
10,000
10,000
10,000
10,000
10,000
Discount factor
10%
0.909
0.826
0.751
0.683
0.621
Total
present
value of future
cash inflow
Less Investment
NPV
Present value of
future cash inflow
9090
8260
7510
6830
6210
37,900
30,000
7,900
10. X company is examining two mutually exclusive proposals for the new capital
investment. The data on the proposals are as follows:
Particulars
Net Cash outlay
Salvage Value
Estimated Life
Depreciation
Income Tax
Cost of Capital (present Value)
Year
I Year
II Year
III Year
IV Year
V Year
Proposal A
Proposal B
Rs.40,000
Rs.50,000
Nil
Nil
4 Years
5 years
Straight Line Method Straight Line Method
50%
50%
10%
10%
Earnings before depreciation and taxes
12,000
14,000
16,000
22,000
-
14,000
16,000
18,000
22,000
20,000
You are asked to advise which proposal would be financially preferable under
NPV method.
Dep = Initial Investment – Salvage value / Life
Dep = 40,000 – 0/4 years = Rs.10,000
For B
Dep = 50,000 – 0 / 5 years = Rs.10,000
For Proposal A
Year
1.
2.
3.
4.
CFB
D&T
12,000
14,000
16,000
22,000
Dep
10,000
10,000
10,000
10,000
CFAD
&BT
2,000
4,000
6,000
12,000
Tax =
50%
1,000
2,000
3,000
6,000
CFAD
&T
1,000
2,000
3,000
6,000
CFBD PV
&AT
10%
11,000 0.909
12,000 0.826
13,000 0.751
16,000 0.683
Total present
value of Future
cash inflow
Less
Investment
NPV
PV of CI
9,999
9,912
9,763
10,928
40,602
40,000
602
For Proposal B
Year
1.
2.
3.
4.
5.
CFB
D&T
14,000
16,000
18,000
22,000
20,000
Dep
10,000
10,000
10,000
10,000
10,000
CFAD
&BT
4,000
6,000
8,000
12,000
10,000
Tax =
50%
2,000
3,000
4,000
6,000
5,000
CFAD
&T
2,000
3,000
4,000
6,000
5,000
CFBD PV
&AT
10%
12,000 0.909
13,000 0.826
14,000 0.751
16,000 0.683
15,000 0.621
Total present
value of future
cash inflow
Less
Investment
NPV
PV of CI
10,908
10,738
10,514
10,928
9,315
52,403
50,000
2,403
Decision since the proposal B is gives 2,403 , the B can be accepted.
11. From the following information calculate the NPV of the two projects and
suggest which of the two projects should be accepted assuming a discount rate of
10%.
Particulars
Initial Investment
Estimated Life
Scrap Value
Year
1
2
3
4
5
Project X
Project Y
Rs.20,000
Rs.30,000
5 yrs
5 years
Rs.1000
Rs.2,000
Profit after depreciation and taxes are as follows:
5,000
20,000
10,000
10,000
10,000
5,000
3,000
3,000
2,000
2,000
Year
CFAD&T
Dep
1
2
3
4
5
5
5,000
10,000
10,000
3,000
2,000
scrap
3,800
3,800
3,800
3,800
3,800
CFAT&BS
Discount
factor 10%
8,800
0.909
13,800
0.826
13,800
0.751
6,800
0.683
5,800
0.621
1,000
0.621
Total present value of future
cash inflow
Less Investment
NPV
PV
of
Future CI
8,000
11,399
10,362
4,644
3,602
621
38,628
20,000
18,628