Techniques of Capital Budgeting Part 1 solved questions with solutions
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Techniques of Capital Budgeting numerical with solutions
1. RBL Ltd. is considering
purchasing a machinery to increase its production capacity to meet demand of
its products. It is evaluating three machines. The relevant details including
estimated yearly expenditure and sales are given below: Corporate Income Tax
rate is 30 %.
|
|
Machine I |
Machine II |
Machine III |
|
Initial Investment |
30,00,000 |
30,00,000 |
30,00,000 |
|
Projected sales p.a. |
50,00,000 |
40,00,000 |
45,00,000 |
|
Projected Cost |
|
|
|
|
Direct Material |
4,00,000 |
5,00,000 |
4,80,000 |
|
Direct Wages |
5,00,000 |
3,00,000 |
3,60,000 |
|
Factory Overhead |
6,00,000 |
5,00,000 |
5,80,000 |
|
Administration overhead |
2,00,000 |
1,00,000 |
1,50,000 |
|
Selling and Distribution Overhead |
1,00,000 |
1,00,000 |
1,00,000 |
The economic life of Machine 1 is 4 years,
while it is 5 years for the machine II and 6 years for machine III. The scrap
values are Rs. 4,00,000, Rs. 5,00,000, and Rs. 6,00,000 respectively. Using
Payback method, find out the best alternative out of three machines you will
recommend to company.
Solution
|
|
Machine I |
Machine II |
Machine III |
|
Initial Investment (1) |
30,00,000 |
30,00,000 |
30,00,000 |
|
Projected sales p.a. (2) |
50,00,000 |
40,00,000 |
45,00,000 |
|
Projected Cost |
|
|
|
|
Direct Material |
4,00,000 |
5,00,000 |
4,80,000 |
|
Direct Wages |
5,00,000 |
3,00,000 |
3,60,000 |
|
Factory Overhead |
6,00,000 |
5,00,000 |
5,80,000 |
|
Administration overhead |
2,00,000 |
1,00,000 |
1,50,000 |
|
Selling and Distribution Overhead |
1,00,000 |
1,00,000 |
1,00,000 |
|
Total Cost (3) |
18,00,000 |
15,00,000 |
16,70,000 |
|
EBDT (2-3) |
32,00,000 |
25,00,000 |
28,30,000 |
|
Less: Depreciation |
(6,50,000) |
(5,00,000) |
(4,00,000) |
|
EBT |
25,50,000 |
20,00,000 |
24,30,000 |
|
Less tax @ 30 % |
(7,65,000) |
(6,00,000) |
(7,29,000) |
|
PAT |
17,85,000 |
14,00,000 |
17,01,000 |
|
Add: Depreciation |
6,50,000 |
5,00,000 |
4,00,000 |
|
Cash inflow (4) |
24,35,000 |
19,00,000 |
21,01,000 |
|
Payback period (1÷4) |
1.23 years |
1.58 years |
1.43 years |
Since Machine I has lowest payback, hence company should
invest in machine I.
Note: When annual cash inflows are equal
Payback Period =
Initial Investment / Annual cash inflow
Depreciation = Initial investment / cost of machine – scrap
value / Estimated life
Depreciation on Machinery I = (Rs.30,00,000 – Rs. 4,00,000)
/ 4 = Rs.6,50,000
Depreciation on Machinery II = (Rs.30,00,000 – Rs. 5,00,000)
/ 5 = Rs. 5,00,000
Depreciation on Machinery III = (Rs.30,00,000 – Rs.
6,00,000) / 6 = Rs. 4,00,000
2. RBL Academy Ltd. Wants to replace
one of its machines in its plant. First option available to company is
Installation of equipment "King" having cost of Rs. 7,50,000 with an
expectation of cash inflow of Rs. 2,00,000 p.a. for next 6 years. Second is to
Install equipment "Queen" having cost of Rs. 5,00,000 which is
expected to generate a cash inflow of Rs. 1,80,000 per annum for next 4 years.
Which equipment should be preferred under (a) Payback period (b) Internal Rate
of Return?
Solution
Since annual cash inflows are equal;
Payback period for Equipment “King” = Initial investment or cost
of equipment ÷ annual cash inflow
= Rs. 7,50,000 / 2,00,000 = 3.75 years.
Payback period for Equipment “Queen” = Initial investment or
cost of equipment ÷ annual cash inflow
= Rs. 5,00,000 / 1,80,000 = 2.78 years.
From Payback Period method, equipment “Queen” is better.
Internal Rate of
Return method (IRR)
Since cash annual cash inflows are equal for both equipment;
Equipment “King”-
Initial outflow or investment = Rs. 7,50,000
Annual cash inflow = Rs.2,00,000
Calculating PVAF using Payback period method
PVAFr,6 =
Rs. 7,50,000 / Rs.2,00,000 = 3.75
Looking at present value annuity factor table, the value
nearest to 3.75 in the year 6 in interest rate column is 15 % (3.784) and 16 %
(3.685).
Using interpolation formula
IRR = Lower discount
rate
+
= 15% +
15 % +[ (3.784 – 3.75) / (3.784 – 3.685)]
×
(16 % - 15%) = 15.34 %
Equipment “Queen”-
Initial outflow or investment = Rs. 5,00,000
Annual cash inflow = Rs.1,80,000
PVAFr,6 =
Rs. 5,00,000 / Rs.1,80,000 = 2.778
Looking at present value annuity factor table, the value
nearest to 2.778 in the year 4 in interest rate column is 16 % (2.798) and 17 %
(2.743).
Using interpolation formula
IRR = Lower discount
rate
+
= 16% +
16 % +[ (2.798 – 2.778) / (2.798 –
2.743)] × (17 % - 16%) = 16.36 %
Since IRR of Equipment “Queen” has higher IRR so equipment “Queen”
should be preferred.
3. Machine A costs 1,80,000 payable
immediately. Machine B costs Rs. 2,00,000 half payable immediately and half
payable in one year's time. The cash receipts expected are as follows:
|
Year at end |
Machine A |
Machine B |
|
1 |
40,000 |
---------- |
|
2 |
60,000 |
80,000 |
|
3 |
70,000 |
1,00,000 |
|
4 |
50,000 |
1,20,000 |
|
5 |
50,000 |
----------- |
At 8 % opportunity cost, which
machine should be selected on the basis of NPV?
Solution
|
Year |
Machine
A |
Machine
B |
||||
|
|
Cash Flow |
PVF0.08 |
PV = Cash Flow × PVF0.08 |
Cash Flow |
PVF0.08 |
PV= Cash Flow × PVF0.08 |
|
0 |
(1,80,000) |
1.000 |
(1,80,000) |
(1,00,000) |
1.000 |
(1,00,000) |
|
1 |
40,000 |
0.926 |
37,040 |
(1,00,000) |
0.926 |
(92,600) |
|
2 |
60,000 |
0.857 |
51,420 |
80,000 |
0.857 |
68,560 |
|
3 |
70,000 |
0.794 |
55,580 |
1,00,000 |
0.794 |
79,400 |
|
4 |
50,000 |
0.735 |
36,750 |
1,20,000 |
0.735 |
88,200 |
|
5 |
50,000 |
0.681 |
34,050 |
----------- |
0.681 |
-------- |
|
|
NPV |
34,840 |
NPV434 | 43,560 | ||
NPV = PV of Cash
inflow – PV of Cash outflow
NPV of Machine B is
higher than Machine A. Hence, Machine B should be selected.
4. A company is considering a new
project for which requires a Capital outlay of Rs. 5,00,000 and depreciation is
to be allowed at 20 % on SLM basis. Forecasted annual earnings before charging
depreciation is as follows:
|
Year |
Earnings (Rs.) |
|
1 |
2,50,000 |
|
2 |
2,50,000 |
|
3 |
1,00,000 |
|
4 |
1,20,000 |
|
5 |
80,000 |
|
Total |
8,00,000 |
Evaluate the project using (a)
Payback method. (b) Rate of return on original investment.
Solution
Payback Period
|
Year |
Rs. |
Cumulative |
|
1 |
2,50,000 |
2,50,000 |
|
2 |
2,50,000 |
5,00,000 |
|
3 |
1,00,000 |
6,00,000 |
|
4 |
1,20,000 |
7,20,000 |
|
5 |
80,000 |
8,00,000 |
|
Total |
8,00,000 |
|
Payback period = 2 years (Money invested or Capital outlay
of Rs. 2,00,000 has been recovered in 2 years.)
Rate of return onoriginal investment
|
Year |
Earnings (Rs.) |
Less: Depreciation |
Net Earnings |
|
1 |
2,50,000 |
(1,00,000) |
1,50,000 |
|
2 |
2,50,000 |
(1,00,000) |
1,50,000 |
|
3 |
1,00,000 |
(1,00,000) |
0 |
|
4 |
1,20,000 |
(1,00,000) |
20,000 |
|
5 |
80,000 |
(1,00,000) |
(20,000) |
|
Total |
|
|
3,00,000 |
Average income = Total net income / no. of years =
Rs.3,00,000 / 5 = Rs. 60,000
Rate of return on original investment = (Average income ÷
original investment) × 100
= (Rs. 60,000 ÷ Rs.5,00,000) × 100 = 12 %.
5. RBL Academy is considering a project with an initial
outflow of Rs. 1,20,000 with following cash inflow:
|
Year |
Cash inflow |
|
1 |
32,000 |
|
2 |
28,000 |
|
3 |
30,000 |
|
4 |
30,000 |
|
5 |
29,000 |
|
Total |
1,49,000 |
Comment on the project considering
cost of capital to be 7% using internal rate of return method.
Solution
Calculation of
Internal rate of return
Cash outflow = Rs.1,20,000
Average cash inflow = Total cash inflow / number of years =
Rs. 1,49,000 / 5 = Rs. 29,800
Approximate payback period = Cash outflow / average cash
inflow
= Rs. 1,20,000 /Rs.29,800 = 4.0268
In PVAF table, value near to 4.0268 in year 5 is 4.1002 at 7
% and 3.9927 at 15%.
|
Year |
Cash inflow |
PVF at 7% |
PVF at 8% |
PV at 7% = Cash inflow × PVF at 7% |
PV at 8% = Cash inflow × PVF at 8% |
|
0 |
(1,20,000) |
1 |
1 |
(1,20,000) |
(1,20,000) |
|
1 |
32,000 |
0.9346 |
0.9259 |
29907.2 |
29628.8 |
|
2 |
28,000 |
0.8734 |
0.8573 |
24455.2 |
24004.4 |
|
3 |
30,000 |
0.8163 |
0.7938 |
24489 |
23814 |
|
4 |
30,000 |
0.7629 |
0.735 |
22887 |
22050 |
|
5 |
29,000 |
0.713 |
0.6806 |
20677 |
19737.4 |
|
Total of PV of cash inflow |
122415.4 |
119234.6 |
|||
|
NPV= Total of PV of cash
inflow – PV of cash outflow |
2415 |
(765.4) |
|||
IRR = Lower discount rate + [NPV at lower rate / (NPV at
lower rate – NPV at higher rate) × (Difference between two rates)]
= 7% + [2415/2415-(-765.4) × (8% - 7%)]
= 7% + [(2415/3180.4) × 1 %]
7% + 0.7593% = 7.7593 %
Since cost of capital is 7% and IRR is 7.7593%. Hence
project should be included.
6. RBL Academy Ltd. is considering
two mutually exclusive projects. The after-tax cash flows of these projects are
as follows:
|
Year |
Project A Cash flow (Rs.) |
Project B Cash flow (Rs.) |
|
0 |
(1,00,000) |
(1,00,000) |
|
1 |
30,000 |
|
|
2 |
30,000 |
|
|
3 |
30,000 |
|
|
4 |
30,000 |
|
|
5 |
30,000 |
1,82,500 |
Opportunity cost of capital for
these projects is 10 %. Calculate
a. NPV and IRR of each project.
b. Is there any conflict in ranking
of projects? Which project should be accepted?
Solution
NPV of Project A = PV of cash inflow – PV of cash outflow
= Rs. 30,000 × PVAF0.1, 5 – Rs.1,00,000
(Since there is equal cash flow, hence PVAF has been taken)
= (Rs. 30,000 × 3.7908) – Rs.1,00,000
= Rs. 1,13,724 – Rs.1,00,000 = Rs.13,724
NPV of Project B = PV of cash inflow – PV of cash outflow
= Rs. 1,90,000 × PVF0.1, 5 – Rs.1,00,000
= (Rs. 1,82,500 × 0.6209) – Rs.1,00,000 = Rs.13,314
Calculation of
Internal rate of return
Project A
Initial outflow or investment = Rs. 1,00,000
Annual cash inflow = Rs.30,000
Calculating PVAF using Payback period method
PVAFr,5 = Rs. 1,00,000 / Rs.30,000 = 3.333
Looking at present value annuity factor table, the value
nearest to 3.333 in the year 5 in interest rate column is 15 % (3.352) and 16 %
(3.274).
We can calculate IRR using both methods
Method 1: Using
interpolation formula
= 15 % +[ (3.352– 3.333) / (3.352– 3.274)] × (16 % - 15%) = 15.34 % = 15.24
Method 2 : Using NPVfor IRR calculation
NPV @ 15 % = PV of cash inflow – PV of cash outflow
= Rs.30,000 × 3.352 – Rs. 1,00,000 = Rs. 560
NPV @ 16% = Rs.30,000 × 3.274 – Rs. 1,00,000 =
(Rs.1,780)
IRR = Lower discount rate + [NPV at lower rate / (NPV at
lower rate – NPV at higher rate) × (Difference between two rates)]
= 15 % + [(560/560 + 1780) × 1) = 15.24%
Project B:
In this case, there is only one cash inflow in the year 5.
We can use Trial and error method. In PVF table, at year 5, we need to find an
interest rate whose value when multiplied by cash inflow gives positive return
and other which gives negative return and difference between two rates is 1.
Looking into PVF table at year 5, 12 % (0.567)and 13 %
(0.543)will be considered.
NPV at 12 % = PV of cash inflow – PV of cash outflow
= (Rs. 1,82,500 × 0.567) – Rs.1,00,000 = Rs. 3,477.5
NPV at 12 % = =( Rs. 1,82,500 × 0.543) – Rs.1,00,000 = (Rs. 902.5)
IRR = Lower discount rate + [NPV at lower rate / (NPV at
lower rate – NPV at higher rate) × (Difference between two rates)]
= 12 % + [ (3,477.5/ 3,477.5 + 902.5)] × 1
= 12.79 %
According to NPV method and IRR method, Project A is better.
There is no difference in ranking A. Difference in ranking of projects arises
because of difference in patterns of inflows. However, in this case from both
methods, Project A is better than project B, hence, Project A should be opted.
7. A firm whose cost of capital is
10% is considering two mutually exclusive projects X and Y, The after-tax cash
flows of these projects are as follows:
|
Year |
Project X (Rs.) |
Project Y (Rs.) |
|
0 |
(1,00,000) |
(1,00,000) |
|
1 |
15,000 |
45,000 |
|
2 |
18,000 |
45,000 |
|
3 |
30,000 |
22,000 |
|
4 |
45,000 |
10,000 |
|
5 |
60,000 |
10,000 |
|
|
|
|
Compute the Net Present Value at 10%,
Profitability Index, and Internal Rate of Return for the two projects.
Solution
Calculation of NPV
& IRR
|
Year |
Project X (Rs.) |
Project Y (Rs.) |
PVF @ 10 % |
PV of X = PVF × cash flow |
PV of Y = PVF × cash flow |
|
0 |
(1,00,000) |
(1,00,000) |
1 |
(1,00,000) |
(1,00,000) |
|
1 |
15,000 |
45,000 |
0.909 |
13,635 |
40,905 |
|
2 |
18,000 |
45,000 |
0.826 |
14,868 |
37,170 |
|
3 |
30,000 |
22,000 |
0.751 |
22,530 |
16,522 |
|
4 |
45,000 |
10,000 |
0.683 |
30,735 |
6,830 |
|
5 |
60,000 |
10,000 |
0.621 |
37,260 |
6,210 |
|
Total of cash inflows |
1,68,000 |
|
|
|
|
|
Total of PV of cash inflows |
1,19,028 |
1,07,637 |
|||
|
PV of cash outflow |
(1,00,000) |
(1,00,000) |
|||
|
NPV = Total of PV of cash inflows - PV of cash outflow |
19,028 |
7,637 |
|||
|
Profitability index = PV of cash inflows / PV of cash outflow |
1.19028 |
1.07637 |
|||
Project X
Calculating PVAF using Payback period method
Payback value = Initial cash outflow / average cash inflow
Project X average cash inflow = Rs. 1,68,000 / 5 = Rs.
33,600
Payback value (PVAFr,5) = Rs. 1,00,000 / Rs.33,600
= 2.976
The PVAF table indicates that for Project X, the PV Factor
closest to 2.976 against 5 years is 2.991 at 20% and In the case of Project X,
since Cash inflow in the initial years are considerably smaller than the
average cash flows, the IRR is likely to be much smaller than 19%. So, Project
X may be tried at 15% and 16% .
|
Year |
Project X (Rs.) |
PVF @ 16 % |
PVF @ 15 % |
PV of cash inflow @ 15 % |
PV of cash inflow @ 16 % |
|
0 |
(1,00,000) |
1 |
1 |
(1,00,000) |
(1,00,000) |
|
1 |
15,000 |
0.87 |
0.862 |
13050 |
12930 |
|
2 |
18,000 |
0.756 |
0.743 |
13608 |
13374 |
|
3 |
30,000 |
0.658 |
0.641 |
19740 |
19230 |
|
4 |
45,000 |
0.572 |
0.552 |
25740 |
24840 |
|
5 |
60,000 |
0.497 |
0.476 |
29820 |
28560 |
|
Total of PV of cash inflows |
101958 |
98934 |
|||
|
NPV |
1,958 |
(1,066) |
|||
IRR = Lower discount rate + [NPV at lower rate / (NPV at
lower rate – NPV at higher rate) × (Difference between two rates)]
= 15 % + [ (1,958/ 1,958 + 1,066) × 1] = 15.65%
Project Y
Calculating PVAF using Payback period method
Payback value = Initial cash outflow / average cash inflow
Project Y average cash inflow = Rs.1,32,000/5 = Rs.26,400
Payback value (PVAFr,5) = Rs. 1,00,000 / Rs.26,400
= 3.788
Looking at present value annuity factor table, the value
nearest to 3.788 in the year 5 in interest rate column for Project Y, is 3.791
at 10%. In the case of Project Y, Cash inflow in the initial years are
considerably larger than the average cash flows, the IRR is likely to be much
higher than 10%. Project Y may be tried at 14% and 15%
|
Year |
Project Y (Rs.) |
PVF @ 14 % |
PVF @ 15 % |
PV of cash inflow @ 14 % |
PV of cash inflow @ 15 % |
|
0 |
(1,00,000) |
1 |
1 |
(1,00,000) |
(1,00,000) |
|
1 |
45,000 |
0.877 |
0.87 |
39465 |
39150 |
|
2 |
45,000 |
0.769 |
0.756 |
34605 |
34020 |
|
3 |
22,000 |
0.675 |
0.658 |
14850 |
14476 |
|
4 |
10,000 |
0.592 |
0.572 |
5920 |
5720 |
|
5 |
10,000 |
0.519 |
0.497 |
5190 |
4970 |
|
Total of PV of cash inflows |
100030 |
98336 |
|||
|
NPV |
30 |
1,664 |
|||
IRR = Lower discount rate + [NPV at lower rate / (NPV at
lower rate – NPV at higher rate) × (Difference between two rates)]
= 14 % + [ (30 / 30 + 1,664) × 1] = 14.02 %
8. A Company requires an initÃal
investment of Rs. 50,000. The estimated net cash flow are as follows-
|
Year |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Cash inflow |
8000 |
8000 |
8000 |
10000 |
10000 |
15000 |
8000 |
10000 |
8000 |
5000 |
Using 10% as the cost of capital
(rate of discount), determine (i) Pay-back period (ii) Net Present Value and
(iii) Internal Rate of Return.
Solution
Payback period:
Payback refers to time period in which initial cash outflow
is recovered. Cash inflow generated in first 5 year = Rs. 44,000
Remaining cash outlay to be recovered = Rs.50,000 –
Rs.44,000 = Rs.6,000
6th year cash inflow = Rs. 15,000
Payback period = 5 years + (6000/15,000) = 5.4 years
|
Year |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Cash inflow |
8000 |
8000 |
8000 |
10000 |
10000 |
15000 |
8000 |
10000 |
8000 |
5000 |
|
PVF@ 10% |
0.909 |
0.826 |
0.751 |
0.683 |
0.621 |
0.564 |
0.513 |
0.467 |
0.424 |
0.386 |
|
PV of cash inflow |
7272 |
6608 |
6008 |
6830 |
6210 |
8460 |
4104 |
4670 |
3392 |
1930 |
NPV = PV of cash inflow – PV of cash outflow = Rs.55,484 –
Rs.50,000 = Rs.5,484
Calculating PVAF using Payback period method
Payback value = Initial cash outflow / average cash inflow
Average cash inflow = Rs. 90,000 / 10 = Rs. 9,000
Payback value (PVAFr,10) = Rs. 50,000 / Rs.9,000
= 5.556
Looking at present value annuity factor table, the value
nearest to 5.556 in the year 10 in interest rate column is 12 % (5.650) and 13
% (5.426).
|
Year |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Cash inflow |
8000 |
8000 |
8000 |
10000 |
10000 |
15000 |
8000 |
10000 |
8000 |
5000 |
|
PVFat12% |
0.893 |
0.797 |
0.712 |
0.636 |
0.567 |
0.507 |
0.452 |
0.404 |
0.361 |
0.322 |
|
PV of cash inflow at 12 % |
7144 |
6376 |
5696 |
6360 |
5670 |
7605 |
3616 |
4040 |
2888 |
1610 |
|
PVF@13% |
0.885 |
0.783 |
0.693 |
0.613 |
0.543 |
0.48 |
0.425 |
0.376 |
0.333 |
0.295 |
|
PV of cash inflow at 13% |
7080 |
6264 |
5544 |
6130 |
5430 |
7200 |
3400 |
3760 |
2664 |
1475 |
NPV at 12 % = Rs. 51,005 – Rs. 50,000 = Rs. 1,005
NPV at 13 % = Rs. 48,947 – Rs.50,000 = (Rs.1,053)
IRR = IRR = Lower discount rate + [NPV at lower rate / (NPV
at lower rate – NPV at higher rate) × (Difference between two rates)]
= 12% + [ 1005/(1005 + 1,053) × 1] = 12.49%
9. RBL Academy Ltd. is considering
the introduction of a new product. It is estimated that profits before depreciation
would increase by Rs. 2, 00,000 each year for first four years and Rs. 1,00,000
each for the remaining period. An advertisement cost of Rs. 20,000 is expected
to be incurred in the first year, which is not included in the above estimate
of profits. The cost will be allowed for tax purpose in the first year. A new
plant costing Rs.4,00,000 will be installed for the production of the new
product. The salvage value of the plant after its life of 10 years is estimated
to be Rs. 50,000. Working capital investment of Rs. 50,000 will be required in
the year of installing the plant and a further Rs. 30,000 in the following
year. The company's tax rate is 30% and written down value depreciation at 25%.
If the company's required rate of return is 20%, should the company introduce
the new product? Ignore tax effect on Profit/Loss on sale of asset.
Solution
Calculation of
Depreciation
|
Year |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
WDV |
400000 |
300000 |
225000 |
168750 |
126563 |
94922 |
71191 |
53394 |
40045 |
30034 |
|
Depreciation |
100000 |
75000 |
56250 |
42188 |
31641 |
23730 |
17798 |
13348 |
10011 |
7508 |
Calculation of PV of
Cash inflow
|
Year |
PBDT |
less:Dep |
PBT |
Less:Tax |
PAT |
Add:Dep |
Cash inflow |
PVF @20% |
PV of cash inflow |
|
1 |
180000 |
100000 |
80000 |
24000 |
56000 |
100000 |
156000 |
0.833 |
129948 |
|
2 |
200000 |
75000 |
125000 |
37500 |
87500 |
75000 |
162500 |
0.694 |
112775 |
|
3 |
200000 |
56250 |
143750 |
43125 |
100625 |
56250 |
156875 |
0.579 |
90831 |
|
4 |
200000 |
42188 |
157813 |
47344 |
110469 |
42188 |
152656 |
0.482 |
73580 |
|
5 |
100000 |
31641 |
68359 |
20508 |
47852 |
31641 |
79492 |
0.402 |
31956 |
|
6 |
100000 |
23730 |
76270 |
22881 |
53389 |
23730 |
77119 |
0.335 |
25835 |
|
7 |
100000 |
17798 |
82202 |
24661 |
57542 |
17798 |
75339 |
0.279 |
21020 |
|
8 |
100000 |
13348 |
86652 |
25995 |
60656 |
13348 |
74005 |
0.233 |
17243 |
|
9 |
100000 |
10011 |
89989 |
26997 |
62992 |
10011 |
73003 |
0.194 |
14163 |
|
10 |
100000 |
7508 |
92492 |
27748 |
64744 |
7508 |
72252 |
0.162 |
11705 |
|
10 |
80000 |
0.162 |
12960 |
||||||
|
10 |
50000 |
0.162 |
8100 |
||||||
|
|
Total of PV of Cash inflow |
550115 |
|||||||
Note: PBDT for year 1
has been taken after subtracting advertisement expense.
PV of cash outflow = Initial outflow + working capital in
year zero + working capital in year 1
= Rs. 4,00,000 + Rs.50,000 + Rs.24,990 = Rs. 4,74,990
Working capital in year 1 after discounting at 20 % = Rs.30,000
×
0.833(PVF0.2,1) = Rs.24,990
NPV = PV of cash outflow – PV of cash inflow = Rs.5,50,115 -
Rs. 4,74,990 = Rs.75,125
Since, NPV is positive, hence project should be accepted.
10. A company is engaged in
evaluating an investment project which requires an initial cash outlay of Rs. 2,50,000
on equipment. The project's economic life is 10 years and its salvage value
30,000. It would require current assets of Rs. 5 0,000. An additional
investment of Rs. 60,000 would also be necessary at the end of five years to
restore the efficiency of the equipment. This would be written off completely
over the last five years. The project is expected to yield annual profit
(before tax) of Rs. 1,20,000. The company follows the sum of the years digit
method of depreciation. Income-tax rate is assumed to be 30%. Should the
project be accepted if the minimum required rate of return is 22 %.
Solution
The depreciation of different years have been calculated as
per sum of the vear's digit method as follows:
Initial outlay - Salvage value
Rs. 2,50,000 - Rs.30,000 = Rs. 2,20,000 is to be depreciated
over 10 years.
The sum of the years digits for the vears 1-10 is 55.
1+2+3+4+5+6+7+8+9+10 = 55
So, depreciation for year 1 is Rs. 2,20,000 x (10/55) =
Rs.40,000
And for the year 2 it is 2,20,000 x (9/55) = Rs.36,00 and so on.
The total depreciation for first 5 years is Rs. 1,60,000 and
so the written down value of the asset at the end of year 5, is Rs. 90,000
(i.e., Rs. 2,50,000 – Rs. 1,60,000).
A capital expenditure of Rs. 60000 is required at that
stage. So, the total cost required to be depreciated is Rs. 1,20,000 ( ie, Rs. 90,000- Rs. 60,000 –
Rs.30,000) .
As per the sum of the years digit method for 5 years (ie,
remaining life), the depreciation for the year 6 is Rs. 1,20,.000 x (5/15) =
Rs.40,000
for year 2 is Rs. 1,20,000 x( 4/15) = Rs.32,000 and so on.
|
Year |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
EBDT |
120000 |
120000 |
120000 |
120000 |
120000 |
120000 |
120000 |
120000 |
120000 |
120000 |
|
Less: Dep |
40,000 |
36,000 |
32,000 |
28,000 |
24,000 |
40,000 |
32,000 |
24,000 |
16,000 |
8,000 |
|
EBT |
80,000 |
84,000 |
88,000 |
92,000 |
96,000 |
80,000 |
88,000 |
96,000 |
104,000 |
112,000 |
|
Less: Tax |
24000 |
25200 |
26400 |
27600 |
28800 |
24000 |
26400 |
28800 |
31200 |
33600 |
|
PAT |
56,000 |
58,800 |
61,600 |
64,400 |
67,200 |
56,000 |
61,600 |
67,200 |
72,800 |
78,400 |
|
Add: Dep |
40,000 |
36,000 |
32,000 |
28,000 |
24,000 |
40,000 |
32,000 |
24,000 |
16,000 |
8,000 |
|
Cash Inflow |
96,000 |
94,800 |
93,600 |
92,400 |
91,200 |
96,000 |
93,600 |
91,200 |
88,800 |
86,400 |
|
Terminal cash inflow |
Salvage value + current asset= Rs.30,000 + Rs.50,000 = Rs. 80,000 |
80000 |
||||||||
|
PVF at22% |
0.82 |
0.672 |
0.551 |
0.451 |
0.37 |
0.303 |
0.249 |
0.204 |
0.167 |
0.137 |
|
PV of cash inflow |
78720 |
63706 |
51574 |
41672 |
33744 |
29088 |
23306 |
18605 |
14830 |
11837 |
|
PV of Terminal cash inflow |
|
|
|
|
|
|
|
|
|
10,960 |
|
Total of PV of cash inflow including Terminal value |
|
|
|
|
|
|
|
|
|
3,78,041 |
Present value of cash outflow = Initial cost + current asset
+ PV of investment in 5th year
= Rs.2,50,000 + Rs.50,000 + Rs.60,000 ×
0.37 = Rs.3,22,200
NPV = Total of PV of cash inflow including Terminal value -
Present value of cash outflow
= Rs. 3,78,041 - Rs.3,22,200
= Rs.55,841
Since, NPV is positive, hence project should be accepted.
11. Delhi Machinery manufacturing
Company wants to replace its manual operations by new machine. There are two
alternative models A and B the new machine. Using Payback period, suggest the
most profitable investment. Ignore taxation.
|
|
A |
B |
|
Original Investment (Rs.) |
20,000 |
30,000 |
|
Estimated life of the Machine (Years) |
4 |
6 |
|
Estimated Savings in Cost (Rs. ) |
10,000 |
10,000 |
|
Estimated Savings in Wages (Rs.) |
6,000 |
4,000 |
|
Additional Cost of Maintenance (Rs.) |
5,000 |
2,000 |
|
Additional Cost of Supervision (Rs.) |
3,000 |
2,000 |
Solution:
|
|
A |
|
|
Estimated Savings in Cost (Rs. ) |
10,000 |
10,000 |
|
Estimated Savings in Wages (Rs.) |
6,000 |
4,000 |
|
Less: Additional Cost of Maintenance (Rs.) |
(5,000) |
(2,000) |
|
Less: Additional Cost of Supervision (Rs.) |
3,000) |
(2,000) |
|
Net cash inflow |
8,000 |
10,000 |
|
Payback period |
20,000/8,000 = 2.5 years |
30,000/10,000= 3 years |
|
Project A should be opted |
||
12. RST is evaluating two mutually
exclusive proposals, A and B. Following information is available about these projects:
|
|
Project A |
Project B |
|
Project Cost (Rs.) |
6,00,000 |
8,00,000 |
|
Annual Cash Expenses (Rs.) |
1,00,000 |
1,30,000 |
|
Life (Years) |
10 years |
10 years |
|
Salvage Value (Rs.) |
1,00,000 |
1,00,000 |
Other Information: Tax rate 40%,
Required Rate of Return 12%; Evaluate the proposals on the basis of incremental
Cash flows. (Proposal B over Proposal A).
Solution
|
Project A |
Project B |
B over A |
|
|
Initial Cost |
(600000) |
(800000) |
-200000 |
|
Annual Expenses |
(100000) |
(130000) |
(30000) |
|
Depreciation P.a. |
(50000) |
70000 |
20000 |
|
Annual deductible expenses (Annual Expenses + Depreciation P.a.) |
(150000) |
(200000) |
(50000) |
|
Annual tax saving @40 % |
60000 |
80000 |
20000 |
|
Net outflow (annual deductible Expense - Tax saving ) |
(90000) |
(120000) |
(30000) |
|
Terminal inflow (salvage value) |
100000 |
100000 |
0 |
|
Calculation of NPV |
|||
|
PV of Annual outflows |
90000 * 5.65 = (5,08,500) |
120000* 5.65 = (6,78,000) |
(169500) |
|
Initial Cost /outflow |
(600000) |
(800000) |
(200000) |
|
Total outflows (PV) = PV of Annual outflows +Initial Cost /outflow |
(1108500) |
(1478000) |
(369500) |
|
Less PV of salvage (100000*0.322) |
32200 |
32200 |
0 |
|
NET Present Value |
1076300) |
(1445800) |
(369500) |
Since Project B has negative NPV over A , Proposal A should
be preferred.
13. The Eastern Corporation Ltd., a
firm in the 30% tax bracket with a 15% required rate of return, is considering
a new project. This project involves the introduction of a new product. This
project is expected to last five years and then to be terminated. Given the
following information, determine the after-tax cash flows associated with the
project and then find the project's net present value and advise the company
whether it should invest in the project or not.
Cost of new Plant and Equipment: Rs.
20,90,000
Shipping and Installation Cost Rs. 30,000
Unit sales
|
Year |
Units Sold |
|
1 |
10,000 |
|
2 |
13,000 |
|
3 |
16,000 |
|
4 |
10,000 |
|
5 |
6,000 |
Sales Price per unit: Rs. 500/unit
in years 1-4 and Rs. 380/unit in year 5
Variable Cost per unit: 260/unit
There will be an initial Working
capital requirement of Rs. 80,000 just to get production started. For each
year, the total investment in net working capital will be equal to 10% of the
rupee value of sales for that year. Thus, the investment in working capital
will increase during years 1 through 3, then decrease in year 4. Finally, all working
capital is liquidated at the termination of the project at the end of year 5. Use
straight-line method for providing depreciation over five years assuming that
the plant and equipment will have no salvage value after five years.
Solution
Initial Cash outflow = Cost of machine + Installation cost +
Initial Working Capital requirement + Working Capital required for Year 1 in
the beginning of the year
= Rs. 20,90,000 + 30,000 + 80,000 + 5,00,000(10 % of sales
of first year = 10 % of Rs.50,00,000)
= Rs.27,00,000
Depreciation = (Cost of machine + Installation cost –
salvage value) ÷ estimated life
= (Rs. 20,90,000 + Rs.30,000) ÷ 5 = Rs.4,24,000
Change in WC = New WC – Existing WC = Current Year WC – Previous Year WC
|
Particulars |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
|
Sales (Units) |
10,000 |
13,000 |
16,000 |
10,000 |
6,000 |
|
Selling Price /unit ) |
500 |
500 |
500 |
500 |
500 |
|
Sales |
50,00,000 |
65,00,000 |
80,00,000 |
50,00,000 |
22,80,000 |
|
Less: Variable Cost at Rs. 260 |
(26,00,000) |
(33,80,000) |
(41,60,000) |
(26,00,000) |
(15,60,000) |
|
PBDT |
24,00,000 |
31,20,000 |
38,40,000 |
24,00,000 |
7,20,000 |
|
Less: Depreciation |
(4,24,000) |
(4,24,000) |
(4,24,000) |
(4,24,000) |
(4,24,000) |
|
PBT |
19,76,000 |
26,96000 |
34,16,000 |
19,76,000 |
2,96,000 |
|
Less: Tax @ 30 % |
(5,92800) |
(8,08,800) |
(10,24,800) |
(5,92,800) |
(88,800) |
|
PAT |
13,73,200 |
18,87200 |
23,91,200 |
13,83,200 |
2,07200 |
|
Add: Depreciation |
4,24,000 |
4,24,000 |
4,24,000 |
4,24,000 |
4,24,000 |
|
Operating Cash inflow (1) |
17,97,200 |
23,11,200 |
28,15,200 |
18,07,200 |
6,31200 |
|
WC requirement for N+1 year |
6,50,000 |
8,00,000 |
5,00,000 |
2,28,000 |
----- |
|
Change in WC (2) |
1,50,000(6,50,000-5,00,000) |
1,50,000 |
(3,00,000) |
(2,72,000) |
(2,28,000) |
|
Release of WC in year 5 (3) |
|
|
|
|
80,000 |
|
Net cash flow (1-2+3) |
16,47,200 |
21,61200 |
31,15,200 |
20,79,200 |
9,39,200 |
|
PVF at 15% |
.870 |
.756 |
.658 |
.572 |
.497 |
|
PV of cash inflow |
14,33,064 |
16,33,867 |
20,49,802 |
11,89,302 |
4,66,782 |
NPV = PV of cash inflow – PV of cash outflow
= Rs.67,72,817 – Rs.27,00,000 = Rs.40,72817
Since NPV is positive, project should be accepted.
14. A particular project has a four
years life with yearly projected net profit of Rs. 10,000 after charging yearly
depreciation of Rs.8000 but before charging tax in order to write off the capital
cost of Rs. 32,000. Out of the capital cost, Rs. 20,000 is payable immediately
(year 0) and balance in next year (which will be needed for evaluation). Stock
amounting to Rs. 6,000 (to be invested in year 0) will be required throughout
the project and for debtors a further sum of 8,000 will have to be invested in
year 1. The working capital will be recouped in year 5. It is expected that the
machinery will fetch a residual value of Rs. 2,000 at the end of 4th year.
Income tax is payable @ 40% and the cost of capital is 10%. Income tax is payable next year. The residual value of the
machine, Rs. 2,000 will also bear tax @ 40%. Although the profit is for 4
years, for computation of tax and realization of working capital, the
computation will be required up to 5 years. Advise the firm.
Solution
Initial Outflows = capital cost at T0 + capital
cost at T1 + Working Capital (Stocks) at T0 + Working
Capital (Debtors) at T1
Rs.20,000 + (Rs.12,000 × 0.909) + Rs.6,000 + (Rs.8,000
×
0.909) = Rs.44,180
Subsequent annual Cash inflows
|
|
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
|
Net Profit |
10,000 |
10,000 |
10,000 |
10,000 |
10,000 |
|
Add: Residual Value |
|
|
|
|
2,000 |
|
Less: Tax @ 40% of preceding year profit |
|
(4,000) |
(4,000) |
(4,000) |
(4,800) |
|
Add: Depreciation |
8,000 |
8,000 |
8,000 |
8,000 |
|
|
Add: Working capital recovered |
|
|
|
|
14,000 |
|
Cash inflow |
18,000 |
14,000 |
14,000 |
16,000 |
9,200 |
|
PVF @ 10% |
0.909 |
.826 |
.751 |
.683 |
.621 |
|
PV |
16,362 |
11,564, |
10,514 |
10,928 |
5,713 |
|
Total PV of cash inflow |
|
|
|
|
55,081 |
|
Less: Initial cash outflow |
|
|
|
|
(44,180) |
|
NPV |
|
|
|
|
10,901 |
Since NPV is positive, hence project should be accepted.
15. ABC & Co.is considering a
proposal to replace one of its plants costing Rs. 60,000 and having a written
down value of Rs. 24,000. The remaining economic life of the plant is 4 years
after which it will have no salvage value. However, if sold today, it has a
salvage of Rs. 20,000. The new machine costing Rs. 1,30,000 is also expected to
have a lite of 4 years with a scrap value of Rs. 18,000. The machine, due to
its technological superiority, is expected to contribute additional annual
benefit (before depreciation tax) of Rs. 60,000. Find out the cash flows
associated with the decision given that the tax rate applicable to the firm is
40%. (The capital gain or loss may be taken as not subject to tax).
Solution
Initial cash outflow
= cost of machine – Salvage value of existing machine
= Rs.1,30,000 - Rs.20,000 = Rs.1,10,000
Subsequent annual
cash inflow
|
|
Rs. |
|
Annual benefits (PBDT) |
60,000 |
|
Less: Incremental Depreciation (Rs.28,000 – Rs.6,000) [Dep on new
machine – Dep on old machine] |
(22,000) |
|
Incremental Profit before Tax |
38,000 |
|
Less: Tax @ 40 % |
(15,200) |
|
Incremental Profit after Tax |
22,800 |
|
Add: Incremental Depreciation |
22,000 |
|
Incremental cash inflows |
44,800 |
|
Terminal inflow at the end of the year of Project |
18,000 |
16. A machine purchased six years
back for Rs. 1,80,000 has been depreciated to a book value of Rs. 1,08,000. It
originally had a projected life of 15 years (Salvage nil). There is a proposal
to replace this machine. A new machine will cost Rs. 2,50,000 and result in
reduction of operating cost by Rs. 30,000 p.a. for next nine years. The
existing machine can now be scrapped away for Rs. 60,000. The new machine will
also be depreciated over 9 years period as per straight line method with
salvage of 25,000. Find out whether the existing machine be replaced or not
given that the tax rate applicable is 30% and cost of capital 10% (profit or
loss on sale of assets is to be ignored for tax purposes).
Solution
Initial outflow = Cost of new machine – Salvage value of
existing machine
= Rs. 2,50,000 – Rs.60,000 = Rs.1,90,000
Depreciation on new machine = (Cost of machine – Salvage
value)/ estimated life = (Rs.2,50,000- Rs.25,000) /9 = Rs.25,000
Depreciation on old machine = Rs.1,80,000/15 or
Rs.1,08,000/9 = Rs.12,000
Incremental Depreciation = Depreciation on new machine –
Depreciation on old machine
= Rs.25,000 – Rs.12,000 = Rs.13,000
Annual incremental Cash inflow calculation
|
Particulars |
Rs. |
|
Decrease in operating cost (PBDT) |
30,000 |
|
Less: Incremental Depreciation |
(13,000) |
|
Incremental PBT |
17,000 |
|
Less: Tax @ 30% |
(5,100) |
|
Incremental PAT |
11,900 |
|
Add: Incremental Depreciation |
13,000 |
|
Incremental Annual cash inflow |
24,900 |
|
Terminal cash inflow (Salvage value ) |
25,000 |
|
PV of Incremental Annual cash inflow = 24,900 ×5.758 (PVAF.1, 9) |
1,43,374 |
|
PV of terminal cash inflow = 25,000 × 0.424 (PVF0.1, 9) |
10,600 |
|
Total Present value of inflow = 1,43,374 + 10,600 |
1,53,974 |
|
NPV = Total Present value of inflow - Initial outflow = 1,53,974 –
1,90,000 |
(36,026) |
Since, NPV is negative, hence old machine should be kept and
replacement decision should not be opted.
17. RBL Ltd. has a machine having an
additional life of 5 years which costs Rs. 10,00,000 and has a book value of Rs.
4,00,000. A new machine costing Rs.20,00,000 is available. Though its capacity
is the same as that of the old machine, it will mean a saving inn variable
costs to the extent of Rs. 7,00,000 per annum. The life of the machine will be
5 years at the end of which it will have a scrap value of Rs. 2,00,000. The
rate of income-tax is 40% and P. Ltd.'s policy is not to make an investment if
the yield is less than 12% per annum. The old machine, if sold today, will
realize Rs. 1,00,000; it will have no salvage value if sold at the end of 5th
year. Advise P. Ltd. whether or not the old machine should be replaced. Capital
gain is tax free.. Will it make any difference, if the additional depreciation
(on new machine) and loss on sale of old machine is also subject to same tax at
the rate of 30%, and the scrap value of the new machine is Rs. 3, 00,000.
Solution
Case : Ignoring income-tax saving on additional depreciation
as well as on loss due to sale of existing machine:
Initial Cash outflow
= Cost of new machine – Scrap value of old machine
= Rs.20,00,000 – Rs.1,00,000 = Rs.19,00,000
Annual cash inflow
|
|
|
|
Net saving in variable cost |
7,00,000 |
|
Less: Tax at 30% |
(2,10,000) |
|
Net benefit / Annual cash inflow |
4,90,000 |
|
Terminal cash inflow at the end of year 5 (Salvage value of new
machine) |
2,00,000 |
|
PV of cash inflow: Annual cash inflow × PVAF0.12, 5 = 4,90,000 ×
3.605 = 17,66,450 Terminal cash inflow × PVF0.12, 5 = 2,00,000 × 0.567
= 1,13,400 Total
of PV of Cash Inflow = |
18,79,850 |
|
Less: PV of cash outflow |
(19,00,000) |
|
NPV |
(20,150) |
|
Since NPV is negative, there is no need to replace existing machine. |
|
Case II: if the
additional depreciation (on new machine) and loss on sale of old machine is
also subject to same tax at the rate of 30%, and the scrap value of the new
machine is Rs. 3, 00,000.
Incremental Depreciation = Depreciation on new machine –
Depreciation on old machine
= (Rs.20,00,000 – Rs.3,00,000)/5 – Rs.4,00,000/5= Rs.
2,60,000
Cash outflow = Cost of new machine – salvage value of old
machine – Tax saving on capital loss on sale of old machine
= Rs.20,00,000 – Rs.1,00,000 – Rs. 90,000 (30 % of
Rs.4,00,000 – Rs.1,00,000) = Rs.18,10,000
|
|
|
|
Net saving in variable cost (PBDT) |
7,00,000 |
|
Less: Incremental depreciation |
(2,60,000) |
|
Incremental PBT |
4,40,000 |
|
Less: Tax at 30% |
(1,32,000) |
|
Incremental PAT |
3,08,000 |
|
Add: Incremental Depreciation |
2,60,000 |
|
Incremental annual cash inflow |
5,68,000 |
|
Terminal cash inflow at the end of year 5 (Salvage value of new
machine) |
3,00,000 |
|
PV of cash inflow: Annual cash inflow × PVAF0.12, 5 = 5,68,000 ×
3.605 = 20,47,640 Terminal cash inflow × PVF0.12, 5 = 3,00,000 × 0.567
= 1,70,100 Total
of PV of Cash Inflow = |
22,17,740 |
|
Less: PV of cash outflow |
(18,10,000) |
|
NPV |
4,07,740 |
|
Since NPV is positive, company should replace existing machine |
|
18. XYZ Ltd. is considering the
purchase of a new computer system for its Research and Development Division,
which would cost Rs. 35,00,000. The operation and maintenance costs (excluding
depreciation) are expected to be Rs. 7 lacs per annum. It is estimated that the
useful life of the system would be 6 years, at the end of which the disposal
value is expected to be Rs. 1,00,000. The tangible benefits expected from the
system in the form of reduction in design and draftsmanship costs would be Rs.12,00,000
per annum. Besides, the disposal of used drawing office equipment and
furniture, initially, is anticipated to net Rs. 10,00,000. Capital expenditure
in research and development would attract 100 % write-off for tax purposes. The
gains arising on disposal of used assets may be considered tax-free. If company's
effective tax rate is 40%. The average cost of capital to the company is 12%.
After appropriate analysis of cash flows, please advise the company of the
financial viability of the proposal.
Solution
Cash outflow = Cost of new computer – Disposal of used
drawing office
= Rs.35,00,000 – Rs.10,00,000 = Rs.25,00,000
Annual cash inflow
calculation
|
Particulars |
Rs. |
|
Saving in Design and draftsmanship cost |
12,00,000 |
|
Less : Operation and maintenance cost |
(7,00,000) |
|
PBT |
5,00,000 |
|
Less: Tax @ 40 % |
(2,00,000) |
|
PAT/ Annual cash inflow |
3,00,000 |
|
Tax saving on purchase of computer system to be available at the end
of year 1 =35,00,000 × 0.4 |
14,00,000 |
|
Terminal value (Disposal/salvage value) |
1,00,000 |
Calculation of
Present value of annual cash flow and NPV
|
Year |
Cash flow |
PVF at 12% |
PV |
|
0 |
(25,00,000) |
1 |
(25,00,000) |
|
1 |
3,00,000 + 14,00,000(Tax saving) = 17,00,000 |
0.893 |
15,18,100 |
|
2 |
3,00,000 |
0.797 |
2,39,100 |
|
3 |
3,00,000 |
0.712 |
2,13,600 |
|
4 |
3,00,000 |
0.636 |
1,90,800 |
|
5 |
3,00,000 |
0.567 |
1,70,100 |
|
6 |
3,00,000 + 1,00,000 (Terminal value) = 4,00,000 |
0.507 |
2,02,800 |
|
|
NPV |
|
34,500 |
|
Since NPV is positive, hence project should be opted. |
|||
19. Central
Gas Ltd. is considering enhancing its production capacity. The following two mutually
exclusive proposals are being considered
|
|
Proposal I |
Proposal II |
|
Plant |
2,00,000 |
3,00,000 |
|
Building |
50,000 |
1,00,000 |
|
Installation cost |
10,000 |
15,000 |
|
Working capital required |
50,000 |
65,000 |
|
Annual Earnings (before depreciation) |
70,000 |
95,000 |
|
Sales Promotion expenses |
------------ |
15,000 |
|
Scrap Value of Plant |
10,000 |
15,000 |
|
Disposable Value of Building |
30,000 |
60,000 |
Life of the Project is 10 years.
Sales promotion expenses of Proposal l are required to be incurred at the end
of 2nd year? These expenses have not been considered to find out the Annual
earnings (given above). Which proposal be accepted given that the cost of
capital of the firm is 10%. Ignore taxation.
Solution
In this case, the Annual earnings before depreciation are
given for the proposals. As the tax is to be ignored, these earning may be
considered as cash flows also. (It may be noted that there is no tax benefit of
depreciation in this case). The two proposals may be evaluated as follows:
|
|
Proposal I |
Proposal II |
|
Initial cash outflow: Cost of Plant Add: Installation cost Add: Cost of Building Add: WC required |
2,00,000 10,000 50,000 50,000 |
3,00,000 15,000 1,00,000 65,000 |
|
Total Initial cash outflow (I) |
3,10,000 |
4,80,000 |
|
Annual cash inflow Profit before Depreciation PVAF0.1, 10 PV (Profit before Depreciation × PVAF0.1, 10) Less: Present value of sales promotion expenses 15,000 ×0.826 (PVF0.1, 2) |
70,000 6.145 4,30,150 |
95,000 6.145 5,83,775 (12,390) |
|
Total of Present value Annual
cash inflow (II) |
4,30,150 |
5,71,385 |
|
Terminal value Working capital released Sale value of plant Disposable value of building Total Terminal value PVF0.1, 10 |
50,000 10,000 30,000 90,000 0.386 |
65,000 15,000 60,000 1,40,000 0.386 |
|
Total of Present value of
Terminal value (III) |
34,740 |
54,040 |
|
NPV = II + III - I |
1,54,890 |
1,45,425 |
|
Since NPV of Project I has higher NPV than Project II. Hence Project
I should be accepted. |
||
20. ABC Ltd. is in the business of
manufacturing coir mattresses. It has a plant on a piece of land measuring two
acres which was purchased ten years ago for Rs. 10 lacs. The firm is now
planning to set up another plant on the same land. 50% of the existing plot is
to be earmarked for this purpose. The accountant has supplied the following
information:
Capital Expenditure for setting up
new plant (incurred in the beginning of the year):
Year 1:
Cost of land Rs. 5,00,000
Land Development Rs. 17,00,000
Payment for purchase of Machine Rs.18,00,000
Year 2:
Final payment for Land Development
Rs. 13,00,000
Final payment to Machine supplier Rs.
67,00,000
The Plant has an estimated useful
life of 5 years and company follows SL method of depreciation. The information
regarding sales and operational expenses is as follows:
|
Year |
1 |
2 |
3 |
4 |
5 |
|
Sales (Rs.) |
25 Lakh |
30 Lakh |
35 Lakh |
40 Lakh |
45 Lakh |
|
Expenses (Rs.) |
5 Lakh |
7 Lakh |
10 Lakh |
12 Lakh |
15 Lakh |
During first year and last year, all
sales will be cash sales. In others, 10% of sales will be on credit for a
period of one year. If the company’s rate of discount is 15% and the tax rate
is 30% should the above proposal be accepted, given that payment for Land
Development does not quality for tax rebate.
Solution
Calculation of PV
of cash outflows
|
Outflow in the beginning of the year |
|
|
Land development |
17,00,000 |
|
Payment for machinery |
18,00,000 |
|
|
35,00,000 |
|
Outflow in the beginning of year 2 |
|
|
Final payment for land development |
13,00,000 |
|
Final Payment for Machine |
67,00,000 |
|
|
80,00,000 |
|
PV of outflow in the beginning of year 2 or at the end of year 1 80,00,000 × .870 (PVF0.15, 1) = |
69,60,000 |
|
Total Cash outflow = 35,00,000
+ 69,60,000 |
1,04,60,000 |
Change in Working Capital arising out of credit sales:
In First year 100 % cash sales - So No change in Working capital.
Year 2: 10 % of sales Rs. 30,00,000 is on credit, hence Rs.
3,00,000 has been subtracted
Year 3 : Previous year credit sales received Rs. 3,00,000
Current Year Credit sales = 10 % of Rs. 35,00,000 = Rs.
3,50,000
Hence change in working capital = Rs. 3,00,000 – Rs. 3,50,000
= (Rs.50,000)
Year 4: Previous year credit sales received Rs. 3,50,000
Current Year Credit sales = 10 % of Rs. 40,00,000 = Rs. 4,00,000
Hence change in working capital = Rs. 3,50,000 – Rs. 4,00,000
= (Rs.50,000)
Year 5: Previous year credit sales received Rs. 4,00,000
Current Year 100% sales is on cash, so no credit sales and
debtor exist and an extra of Rs.4,00,000 received of previous year. Hence
change in working capital = Rs.4,00,000 – Rs.0 = Rs.4,00,000.
Cash Inflow calculation along with NPV
|
Particulars |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
|
Sales |
2500000 |
3000000 |
3500000 |
4000000 |
4500000 |
|
Less: Expenses |
(500000) |
(700000) |
(1000000) |
(1200000) |
(1500000) |
|
Less: Depreciation |
(1800000) |
(1800000) |
(1800000) |
(1800000) |
(1800000) |
|
PBT |
200000 |
500000 |
700000 |
1000000 |
1200000 |
|
Less Tax @ 30 % |
(60000) |
(150000) |
(210000) |
(300000) |
(360000) |
|
PAT |
140000 |
350000 |
490000 |
700000 |
840000 |
|
Add: Depreciation |
1800000 |
1800000 |
1800000 |
1800000 |
1800000 |
|
Change in WC |
(300000) |
(50000) |
(50000) |
400000 |
|
|
Cash Flow |
1940000 |
1850000 |
2240000 |
2450000 |
3040000 |
|
PVF at 15 % |
0.87 |
0.756 |
0.658 |
0.572 |
0.497 |
|
PV of cash inflow |
1687800 |
1398600 |
1473920 |
1401400 |
1510880 |
|
Total PV of Cash Inflow |
74,72,600 |
||||
|
Total PV of Cash Outflow |
(1,04,60,000) |
||||
|
NPV |
(29,87,400) |
||||
|
Since NPV is negative, hence the project should not be opted. |
|||||
21. The Income Statement of X Ltd.
for the current year is as follows
|
Particulars |
Rs. |
|
Sales |
7,00,000 |
|
Less: Cost of Material Labour Other operating cost Depreciation |
(2,00,000) (2,50,000) (2,50,000) (80,000) |
|
EBIT |
1,00,000 |
|
Less: Tax @ 30 % |
(30,000) |
|
Profit after Tax |
70,000 |
The Plant
Manager proposes to replace an existing machine by another machine costing Rs.
2,40,000. The new machine will have 8 years life having no salvage value. It is
estimated that new machine will reduce the labour costs by Rs. 50,000 per year.
The old machine will realize Rs. 40,000. Income statement does not include the
depreciation on old machine (the one that is going to be replaced) as the same
had been fully depreciated for tax purposes last year though it will still
continue to function, if not replaced, for a few years more. It is believed
that there will be no change in other expenses and revenue of the firm due to
his replacement. The company requires a "After-Tax Return of 10%. The rate
of tax applicable to company's income is 30%. Should the company buy the new machine,
assuming that the company follows straight line method of depreciation?
Solution
Initial Cash Outflow
Cost of new Machine – Salvage value of existing machine +
Tax on gain of sale of existing machine
= Rs.2,40,000 – Rs.40,000
+ Rs.12,000 = Rs.2,12,000.
Profit on sale of existing Machine = Salvage value - Book
value = Rs.40,000 – Re. 0 = Rs.40,000
Tax on gain on sale of existing machine = 30 % of Rs.40,000
= Rs.12,000.
Calculation of Annual incremental Cash inflow
|
Particulars |
Rs. |
|
Saving in Labour expenses |
50,000 |
|
Less: Depreciation on new Machine |
(30,000) |
|
Incremental PBT |
20,000 |
|
Less: Tax @ 30 % |
(6,000) |
|
PAT |
14,000 |
|
Add: Depreciation |
30,000 |
|
Incremental Cash inflow |
44,000 |
|
PVAF0.1, 8 |
5.335 |
|
PV of incremental cash inflow |
2,34,740 |
|
Less: PV of cash outflow |
(2,12,000) |
|
NPV |
22,740 |
|
Since NPV is positive, hence
replacement of machine should be opted.  |
|
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