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SOLVED PROBLEMS – CAPITAL BUDGETING
Problem 1The cost of a plant is Rs. 5,00,000. It has an estimated life of 5 years after which it would be disposed off (scrap value nil). Profit before depreciation, interest and taxes (PBIT) is estimated to be Rs. 1,75,000 p.a. Find out the yearly cash flow from the plant. Tax rate 30%.
Solution
Annual depreciation charge (Rs. 5,00,000/5) 1,00,000
Profit before depreciation, interest and taxes 1,75,000
- Depreciation 1,00,000
Profit before tax 75,000
Tax @ 30% 22,500
Profit after Tax 52,500
+ depreciation (added back) 1,00,000
Therefore, cash flow 1,52,500
Problem 2
A cosmetic company is considering to introduce a new lotion. The manufacturing equipment will cost Rs. 5,60,000. The expected life of the equipment is 8 years. The company is thinking of selling the lotion in a single standard pack of 50 grams at Rs. 12 each pack. It is estimated that variable cost per pack would be Rs. 6 and annual fixed cost Rs. 4,50,000. Fixed cost includes (straight line) depreciation of Rs. 70,000 and allocated overheads of Rs. 30,000. The company expects to sell 1,00,000 packs of the lotion each year. Assume that tax is 45% and straight line depreciation is allowed for tax purpose. Calculate the cash flows.
Solution
Initial cash outflow
Cost of equipments Rs. 5,60,000
Subsequent cash flows
Units sold 1,00,000
Sales @ Rs. 12/- Rs. 12,00,000
- Variable cost @ Rs. 6/- 6,00,000
- Fixed cost (4,50,000 – 30,000 – 70,000) 3,50,000
- Depreciation 70,000
Profit before tax 1,80,000
Tax @ 45% 81,000
Profit after tax 99,000
Depreciation (added back) 70,000
Cash flow 1,69,000
There is no terminal cash inflow. It may be noted that the allocated overheads of Rs. 30,000 gave been ignored as they are irrelevant.
Rushi Ahuja 2 ABC and 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 value of Rs. 20,000. The new machine costing Rs. 1,30,000 is also expected to have a life of 4 years with a scrap value of Rs. 18,000. The new machine, due to its technological superiority, is expected to contribute additional annual benefit (before depreciation and tax) of Rs. 60,000. Find out the cash flows associated with this 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
(Amount in Rs.)
1. Initial cash outflow: 1,30,000
Cost of new machine 20,000
- Scrap value of old machine 1,10,000
2. Subsequent cash inflows (annual)
Incremental benefit 60,000
- Incremental depreciation
Dep. On new machine 28,000
Dep. On old machine 6,000 22,000
Profit before tax 38,000
- Tax @ 40% 15,200
Profit after tax 22,800
+ Depreciation (added back) 22,000
Annual cash inflow 44,800
The amount of depreciation of Rs. 28,000 on the new machine is ascertained as follows: (Rs. 1,30,000-Rs. 18,000)/4 = 1,30,000-Rs. 28,000. It may be noted that in the given situation, the benefits are given in the incremental form i.e., the additional benefits contributed by the proposal. Therefore, only the incremental depreciation of Rs. 22,000 has been deduced to find out the taxable profits. The same amount of depreciation has been added back to find out the incremental annual cash inflows.
Terminal cash inflow: There will be an additional cash inflow of Rs. 18,000 at the end of 4th year when the new machine will be scrapped away. Therefore, total inflow of the last year would be Rs. 62,800 (i.e. Rs. 44,800 + Rs. 18,000).
Problem 4
XYZ is interested in assessing the cash flows associated with the replacement of an old machine by a new machine. The old machine bought a few years ago has a book value of Rs. 90,000 and it can be sold for Rs. 90,000. It has a remaining life of five years after which its salvage value is expected to be nil. It is being depreciated annually at the rate of 20 per cent (written down value methd).
The new machine costs Rs. 4,00,000. It is expected to fetch Rs. 2,50,000 after five years when it will no longer be required. It will be depreciated annually at the rate of 33 1/3 per cent (written down value method). The new machine is expected to bring a saving of Rs. 1,00,000 in manufacturing costs. Investment in working capital would remain unaffected. The tax rate applicable to the firm is 50 percent. Find out the relevant cash flow for this replacement decision. (Tax on capital gain / loss to be ignored).
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Solution
Initial cash flows: Amt. (Rs.)
Cost of new machine 4,00,000
- Salvage value of old machine 90,000
3,10,000 Subsequent annual cash flows:
(Amount Rs. ‘000)
Yr.1 Yr.2 Yr.3 Yr.4 Yr.5
Savings in costs (A) 100 100 100 100 100
Depreciation on new machine 133.3 88.9 59.3 39.5 26.3
- Depreciation on old machine 18.0 14.4 11.5 9.2 7.4
Therefore, incremental depreciation (B) 115.3 74.5 47.8 30.3 18.9
Net incremental saving (A – B) -15.3 25.5 52.2 69.7 81.1
Less: Incremental Tax @ 50% -7.6 12.8 26.1 34.8 40.6
Incremental Profit -7.7 12.7 26.1 34.9 40.5
Depreciation (added back) 115.3 74.5 47.8 30.3 18.9
Net cash flow 107.6 87.2 73.9 65.2 59.4
Terminal cash flow: There will be a cash inflow of Rs. 2,50,000 at the end of 5th year when the new machine will be scrapped away. So, in the last year the total cash inflow will be Rs. 3,09,400 (i.e. Rs. 2,50,000 + Rs. 59,400).
Problem 5
A firm is currently using a machine which was purchased two years ago for Rs. 70,000 and has a remaining useful life of 5 years.
It is considering to replace the machine with a new one which will cost Rs. 1,40,000. The cost of installation will amount to Rs. 10,,000. The increase in working capital will be Rs. 20,000. The expected cash inflows before depreciation and taxes for both the machines are as follows:
Year Existing Machine New Machine
1 Rs. 30,000 Rs. 50,000
2 30,000 60,000
3 30,000 70,000
4 30,000 90,000
5 30,000 1,00,000
The firm use Straight Line Method of depreciation. The average tax on income as well as on capital gains / losses is 40%.
Calculate the incremental cash flows assuming sale value of existing machine: (i) Rs. 80,000, (ii) Rs. 60,000, (iii) Rs. 50,000, and (iv) Rs. 30,000.
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Solution
(Figures in Rs.)
Different Scrap Values
Cost of new machine 1,40,000 1,40,000 1,40,000 1,40,000
+ Installation cost 10,000 10,000 10,000 10,000
+ Additional working capital 20,000 20,000 20,000 20,000
- Scrap value 80,000 60,000 50,000 30,000
90,000 1,10,000 1,20,000 1,40,000
Tax liability / saving 12,000 4,000 – -8,000
Cash outflow 1,02,000 1,14,000 1,02,000 1,32,000
Calculate of tax paid / saved:
Book value of old plant 50,000 50,000 50,000 50,000
- Scrap value 80,000 60,000 50,000 30,000
Profit / Loss 30,000 10,000 – (20,000)
Tax @ 40% on capital gain / loss 12,000 4,000 – -8,000
Subsequent Cash inflows (Annual)
(Amount Rs. ‘000)
Yr.1 Yr.2 Yr.3 Yr.4 Yr.5
Cash inflows
On new machine 50,000 60,000 70,000 90,000 1,00,000
On old machine 30,000 30,000 30,000 30,000 30,000
Incremental cash inflow 20,000 30,000 40,000 60,000 70,000
- Incremental depreciation 20,000 20,000 20,000 20,000 20,000
Profit before tax - 10,000 20,000 40,000 50,000
- Tax at 40% - 4,000 8,000 16,000 20,000
Profit after tax - 6,000 12,000 24,000 30,000
Depreciation (added back) 20,000 20,000 20,000 20,000 20,000
Net cash inflow 20,000 26,000 32,000 44,000 50,000
The amount of incremental depreciation has been calculated as follows: Depreciation of new machine = (Rs. 1,40,000 + Rs. 10,000)/5
= Rs. 30,000 Depreciation on old machine = Rs. 70,000/7
= Rs. 10,000 Therefore, incremental depreciation = Rs. 20,000
Terminal cash flow: There will be a terminal cash flow of Rs. 20,00 at the end of 5th year in the form of working capital released.
Problem 6
A firm whose cost of capital is 10% is considering two mutually exclusive projects X and Y, the details of which are:
Year Project X Project Y
Rushi Ahuja 5 Cash inflows 1 10,000 50,000 2 20,000 40,000 3 30,000 20,000 4 45,000 10,000 5 60,000 10,000
Compute the Net Present Value at 10%, Profitability Index, and Internal Rate of Return of the two projects. Solution Calculation of NPV: CF (Rs.) PVF (10%,n) Total PV (Rs.) Year X Y X Y 1 10,000 50,000 0.909 9,090 45,450 2 20,000 40,000 0.826 16,520 33,040 3 30,000 20000 0.751 22,530 15,020 4 45,000 10,000 0.683 30,735 6,830 5 60,000 10,000 0.621 37,260 6,210 Total PV 1,16,135 1,06,550
Less cash outflow 70,000 70,000
NPV 46,135 36,550
PI = (PV of inflows / PV of outflows) 1.659 1.552
Calculation of IRR:
Payback value = Initial cash outlays / average cash inflows Project X = Rs. 70,000 / Rs. 33,000 = 2.121
Project Y = Rs. 70,000 / Rs. 26,000 = 2.692
The PVAF table indicates that for Project X, the PV Factor closest to 2.121 against 5 years is 2.143 at 37% and Project Y, the PV factor closest to 2.692 is 2.689 at 25%. In the case of Project X, since CF in the initial years are considerably smaller than the average cash flows, the IRR is likely to be much smaller than 37%. In the case of Project Y, CF in the initial years are considerably larger than the average cash flows, the IRR is likely to be much higher than 25%. So, Project X may be tried at 27% and 28% and the Project Y may be tried at 36% and 37%.
Project X
Year CP (Rs.) PV Factor Total PV (Rs.)
27% 28% 27% 28% 1 10,000 0.787 0.781 7,870 7,810 2 20,000 0.620 0.610 12,400 12,200 3 30,000 0.488 0.477 14,640 14,310 4 45,000 0.384 0.373 17,280 16,785 5 60,000 0.303 0.291 18,180 17,460 70,370 68,565 Since the NPV is Rs. 370 (i.e. Rs. 70,370 – 70,000) only, at 27%, the IRR is 27% approx.
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Project Y
Year CP (Rs.) PV Factor Total PV (Rs.)
27% 28% 27% 28% 1 50,000 0.735 0.730 36,750 36,500 2 40,000 0.541 0.533 21,640 21,320 3 20,000 0.398 0.389 7,640 7,780 4 10,000 0.292 0.284 2.920 2,840 5 10,000 0.215 0.207 2,150 2,070 71,420 70,510
Since the NPV @ 37% is Rs. 510 (i.e. 70,510 – 70,000) only, the IRR is likely to be slightly more than 37%. The results of the above calculations may be summarized as follows:
Project X Project Y
BPV Rs. 46,130 Rs. 36,550
PI 1.659 1.522
IRR 27% 37%
Problem 5.6
Machine A costs Rs. 1,00,000, payable immediately. Machine B costs Rs. 1,20,000, half payable immediately and half payable in one year’s time. The cash receipts expected are as follows:
Year (at the end) A B
1 Rs. 20,000 –
2 60,000 Rs. 60,000
3 40,000 60,000
4 30,000 80,000
5 20,000 –
With 7% cost of capital, which machine should be selected? Solution
The NPV of both the machines may be found as follows:
Year CF(A) CF(B) PVF (7%,n) PV(A) PV(B)
0 Rs. -1,00,000 Rs. -60,000 1.000 -1,00,000 -60,000 1 20,000 -60,000 .935 18,700 -56,100 2 60,000 60,000 .873 52,380 52,380 3 40,000 60,000 .816 32,640 48,960 4 30,000 80,000 .763 22,890 61,040 5 20,000 - .713 14,260 -
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Net Present Value 40,780 46,280
The Machine B has a higher NPV and it should be selected. Problem 7
A company is considering the replacement of its existing machine which is obsolete and unable to meet the rapidly rising demand for its product. The company is faced with two alternatives: (i) to buy Machine A which is similar to the existing machine or (ii) to go in for Machine B which is more expensive and has much greater capacity. The cash flows at the present level of operations under the two alternatives are as follows:
0 1 2 3 4 5
Machine A -25 - 5 20 14 14
Machine B -40 10 14 16 17 15
The company’s cost of capital is 10%. The finance manager tries to evaluate the machines by calculating the following:
1. Net Present Value; 2. Profitability Index; 3. Payback period; and 4. Discounted Payback period
At the end of his calculations, however, the finance manager is unable to make up his mind as to which machine to recommend.
You are required to make these calculation and in the light thereof to advise the finance manager about the proposed investment.
Note: Present values of Rs. 1 at 10% discount rate are as follow:
Year 0 1 2 3 4 5
PV 1.00 .91 .83 .75 .68 .62
Solution
Calculation of Net Present Value
Year CF (Rs. in lacs) PVF(10%,n) Total PV (Rs. in lacs)
Machine A Machine B Machine A Machine B
0 -25 -40 1.00 -25.00 -40.00 1 - 10 0.91 - 9.10 2 5 14 0.83 4.15 11.62 3 20 16 0.75 15.00 12.00 4 14 17 0.68 9.52 11.56 5 14 15 0.62 8.68 9.30 NPV 12.35 13.58
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Calculation of Profitability Index:
Machine A (Rs. in lakhs) Machine B (Rs. in lakhs) PV of Cash inflow = 37.35 53.58 PV of Cash outflow 25.00 40.00 = 1.494 1.339
Calculation of Pay Back Period
(Rs. in Lacs)
Year Cash inflows Cumulative cash inflows
Machine A Machine B Machine A Machine B
0 -25 -40 - - 1 - 10 - 10 2 5 14 5 24 3 20 16 25 40 4 14 17 39 57 5 14 15 53 72
In both cases, the Payback Period is 3 years.
Calculation of Discounted Payback Period
(Rs. in lacs)
Year Present value Cumulative present value
Machine A Machine B Machine A Machine B
0 -25.00 -40.00 - - 1 - 9.10 - 9.10 2 4.15 11.62 4.15 20.72 3 15.00 12.00 19.15 32.72 4 9.52 11.56 28.67 44.28 5 8.68 9.30 37.35 53.58 Machine A Machine B Outflow -25.00 -40.00
In 3 years, Payback were 19.15 32.72
Unrecouped oputflow 5.85 7.28
In 4th year, Net present value 9.52 11.56
Thus pay back = 3 + 5.85 = 3 + 7.28
9.52 11.56
= 3.614 years = 3.629 years
Conclusion
Machine A Machine B Choice
1. NPV 12.35 13.58 B
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3. Payable period 3 years 3 years Indifferent
4. Discounted payback 3.614 years 3.629 years A
Because of rising demand of Company’s product, Machine B should be the choice as it has higher capacity and its NPV is also higher.
Problem 8
A company proposes to undertake one of two mutually exclusive projects namely, AXE and BXE. The initial capital outlay and annual cash inflows are as under:
AXE BXE
Initial capital outlay Rs. 22,50,000 Rs. 30,00,000
Salvage value at the end of the life 0 0
Economic life (years) 4 7
After tax annual cash inflows Year 1 Rs. 6,00,000 Rs. 5,00,000
2 12,50,000 7,50,000 3 10,00,000 7,50,000 4 7,50,000 12,00,000 5 - 12,50,000 6 - 10,00,000 7 - 8,00,000
The company’s cost of capital is 16%
Calculate for each project. (a) Net present value of cash flows. (b) Internal rate of return Solution
(i) NPV of the two proposals
(Figures in Rs. lacs)
Year AXE BXE
CF PFV (16%,n) PV CF PFV (16%,n) PV 0 Rs. (22.50) 1.000 Rs. (22.50) (30.00) 1.000 (30.00) 1 6.00 0.862 5.17 5.00 0.862 4.30 2 12.50 0.743 9.29 7.50 0.743 5.57 3 10.00 0.641 6.41 7.50 0.641 4.81 4 7.50 0.552 4.14 12.50 0.552 6.90 5 - - - 12.50 0.476 5.95 6 - - - 10.00 0.410 4.10 7 - - - 8.00 0.354 2.83
Net present value 2.51 4.46
(ii) Calculation of IRR: Both the proposals have positive NPV at 16%. In order to calculate IRR, the NPV of these proposals may be found @ 21% as under:
Year Discount AXE BXE
Cash flows PVs Cash flows Total PVs Factor @21% Rs. lacs Rs. lacs Rs. lacs Rs. lacs
1 0.826 6.00 4.95 5.00 4.12
Rushi Ahuja 10 3 0.564 10.00 5.64 7.50 4.23 4 0.467 7.50 3.50 12.50 5.83 5 0.386 - - 12.50 4.83 6 0.319 - - 10.00 3.19 7 0.263 - - 8.00 2.10 Present value 22.62 29.44
Less: Initial outlay 22.50 30.00
NPV 0.12 -.56
Project AXE: As the NPV of the proposal AXE at 21% discount rate is Rs. 12,000 only, the IRR may be taken as slightly more than 21%.
Project BXE: As the NPV of the proposal BXE @21% discount rate is negative Rs. 56,000 only, the IRR may be taken as slightly lower than 21%.
Problem 9
XYZ Ltd. has decided to diversity its production and wants to invest its surplus funds on the most profitable project. It has under consideration only two projects – “A” and “B”. The cost of project “A” is Rs. 100 lacs and that of “B” is Rs. 10 lacs. Both projects are expected to have a life of 8 years only and at the end of this period “A” will have a salvage value of Rs. 4 lacs and “B” Rs. 14 lacs. The running expenses of “A” will be Rs. 35 lacs per year and that of “B” Rs. 20 lacs per year. In either case the company expects a rate of return of 10%. The company’s tax rate is 50%. Depreciation is charged on straight line basis. Which project should be company take up?
Solution
In this case, it is given that the company expects a rate of return of 10%. It may be interpreted as that the company will be able to earn 10% on its investments. The cost of capital is also to be taken at 10%. Computation of NPV of the projects
Particulars Project A Project B
Profit after Tax (10% of cost of Project) Rs. 10,00,000 Rs. 15,00,000
Add: Depreciation 12,00,000 17,00,000
Net cash inflow (annual) 22,00,000 32,00,000
PVAF(10%,8) 5.335 5.335
Present value of net cash inflow 117,37,000 170,72,000
Salvage value 4,00,000 14,00,000
PVF(10%,8) .467 .467
Present value of salvage value 1,86,800 6,53,800
PV of total cash inflow 119,23,800 177,25,800
Less: Initial investment 100,00,000 150,00,000
Net present value 19,23,800 27,25,800
Analysis: Under the NPV analysis of Projects. Project B is having higher NPV. Hence, Project B is suggested for implementation.
Problem 10
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Proposal A Proposal B
Investment cost Rs. 9,500 Rs. 20,000
Estimated income Year 1 4,000 8,000
Year 2 4,000 8,000
Year 3 4,500 12,000
Suggest the most attractive proposal on the basis of the NPV method considering that the future incomes are discounted at 12%. Also find out the IRR of the two proposals.
Solution
Evaluation of investment proposal (net present value method)
Year Cash inflows (Rs.) PVF (12%,n) Present value (Rs.)
A B A B
0 -9,500 -20,000 1.000 -9,500 -20,000
1 4,000 8,000 0.893 3,572 7,144
2 4,000 8,000 0.797 3,188 6,376
3 4,500 12,000 0.712 3,204 8,544
Net present value (NPV) 464 2,064
NPV is more in proposal B and therefore, it should be accepted. Calculation of Internal Rate of Return
In case of Proposal A, the discount factor should be raised from 12% and tested at, say, 14% and 15%. Similarly, for B the same should be tried at, say, 17% and 18%. The purpose is to find out at which point the present value of inflows are equal to Rs. 9500 and Rs. 20,000.
Project A Project B
NPV @ 12% Rs. 464 NPV @ 12% Rs. 2064
NPV @ 14% Rs. 122 NPV @ 17% Rs. 176
NPV @ 15% Rs. -35 NPV @ 18% Rs. -172
Interpolation between 14% and 15% Interpolation between 17% and 18% IRR = 14% + 122 / 122+35 IRR = 17% + 176 / 176+172
= 14.78% = 17.51%
Problem 11
Precision Instruments is considering two mutually exclusive Projects X and Y: Following details are made available to you:
(Rs. in lacs)
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Project cost 700 700
Cash inflows: Year 1 100 500
Year 2 200 400
Year 3 300 200
Year 4 450 100
Year 5 600 100
Assume no residual values at the end of the fifth year. The firm’s cost of capital is 10% required, in respect of each of the two projects:
(i) Net present value, using 10% discounting (ii) Internal rate of return: (iii) Profitability index
Solution
Net present value (NPV)
(Rs. in lacs)
Year CF PVF (10%,n) Present value
X Y X Y 1 100 500 0.909 90.90 454.50 2 200 400 0.826 165.20 330.40 3 300 200 0.751 225.30 150.20 4 450 100 0.683 307.35 68.30 5 600 100 0.621 372.60 62.10 Total PV 1065.50
Less: Initial cash outflow 700.00 700.00
Net present value 461.35 365.50
Internal Rate of Return (IRR): Project X
Year CFX PV factor at Present Value
27% 28% 27% 28% 1 100 .787 .781 78.70 78.10 2 200 .620 .610 124.00 122.00 3 300 .488 .477 146.40 143.10 4 450 .384 .373 172.80 167.85 5 600 .303 .291 181.80 174.60 Total PV 703.70 685.65
Less: Initial cash outflow 700.00 700.00
Net present value 3.70 (14.35)
IRR = 27 + 3.70 / 3.70 + 14.35 x 1 = 27 + 0.205 = 27.21% Project Y
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Year CFY PV factor at Present Value
27% 28% 27% 28% 1 500 .730 .725 365.00 362.50 2 400 .533 .525 213.20 210.00 3 200 .389 .381 77.80 76.20 4 100 .284 .276 28.40 27.60 5 100 .207 .200 20.70 20.70 Total PV 705.10 697.00
Less: Initial cash outflow 700.00 700.00
Net present value 5.10 (3.00)
IRR = 37 + 5.10 / 5.10 + 3.00 x 1 = 37 + 0.63 = 37.63% Profitability Index
Total Present Value of cash inflow @ 10% PI =
Initial cash outlay Rs. 1,161.35 lacs Project X = = 1.659 Rs. 700 lacs Rs. 1,065.50 lacs Project X = = 1.522 Rs. 700 lacs Problem 12
Pioneer Steels Ltd. is considering two mutually exclusive projects. Both require an initial cash outlay of Rs. 10,000 each and have a life of five years. The company’s required rate of return is 10% and pays tax at a 50% rate. The projects will be depreciated on a straight line basis. The net cash flow expected to be generated by the projects are as follows:
Year 1 2 3 4 5
Project 1 Rs. 4,000 4,000 4,000 4,000 4,000
Project 2 Rs. 6,000 3,000 2,000 5,000 5,000
You are required to calculate: a) The payback of each project
b) The average rate of return for each project
c) The net present value and profitability index for each project d) The Internal rate of returns for each project
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Which project should be accepted and why? Solution
Calculation of cash inflows:
In the question it has been mentioned that the depreciation will be provided on straight line basis. It appears that the net cash flows given in the question are the profits before depreciation and tax. These are to be adjusted to find out the cash flows as follows:
Project 1:
Year PBD Dep. PBT Tax PAT CF Cum. CF
1 Rs. 4,000 Rs. 2,000 Rs. 2,000 Rs. 1,000 Rs. 1,000 Rs. 3,000 Rs. 3,000 2 4,000 2,000 2,000 1,000 1,000 3,000 6,000 3 4,000 2,000 2,000 1,000 1,000 3,000 9,000 4 4,000 2,000 2,000 1,000 1,000 3,000 12,000 5 4,000 2,000 2,000 1,000 1,000 3,000 15,000 Project 2: 1 Rs. 6,000 Rs. 2,000 Rs. 4,000 Rs. 2,000 Rs. 2,000 Rs. 4,000 Rs. 4,000 2 3,000 2,000 1,000 500 500 2,500 6,500 3 2,000 2,000 – – – 2,000 8,500 4 5,000 2,000 3,000 1,500 1,500 3,500 12,000 5 5,000 2,000 3,000 1,500 1,500 3,500 15,000 Project 1 Project 2
Calculation of payback period 3 years + 1,000 / 3,000 3 years + 1,500 / 3,500
= 3 1/3 years = 3 3/7 years
Calculation of accounting rate of return
Average cost Rs. 5,000 Rs. 5,000
Average profit after tax Rs. 1,000 Rs. 1,100
Rate of return 20% 22%
Calculation of NPV (cost of capital 10%)
Project 1: Annuity of cash inflows for 5 years = Rs. 3,000
PVAF (10%,5y) = 3.791
PV of Annuity (3,000 x 3.791) = Rs. 11,373
Less cash outflow = 10,000
Net present value = 1,373
Project 2:
Year Cash flow PVF (10%,n) PV
0 - Rs. 10,000 1,000 Rs. 10,000
1 4,000 .909 3,636
2 2,500 .826 2,065
3 2,000 .751 1,502
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5 3,500 .621 2,173
Net present value 1,767
Calculation of profitability index
PI = PV of inflows / PV of outflows Project 1 PI = Rs. 11,373 / Rs. 11,767 = 1.137 Project 2 PI = Rs. 11,767 / Rs. 10,000 = 1.177 Calculation of Internal Rate of Return
The IRR of a Project is the rate at which the NPV of the project comes to zero. In the above calculation of NPV (at 10%), both projects were found to be having positive NPV. So, the IRR for both the projects are more than 10%. The exact IRR may be ascertained as follows:
Project 1:
In this case, the cash inflows are equal for 5 years, therefore, the situation can be presented like this: Rs. 10,000 = Rs. 3,000 x PVAF(r,5)
PVAF(r,5y) = 10,000 3,000
= 3.333
In the PVAF table, the value of 3.333 in 5 years raw may be found between 15% and 16% column. So, the IRR falls between 15% and 16%.
At 15%, NPV is = (3,000 x PVAF(15%, 5y)) – 10,000 = (3,000 x 3.352) – 10,000 = Rs. 56 at 16%, NPV is = (3,000 x PVAF(16%, 5y)) – 10,00 = (3,000 x 3.274) – 10,000 = Rs. – 178
The exact IRR may be found by interpolating between 15% and 16% 56
IRR = 15% + = 15.24%
(56+178) Project 2:
As the Project 2 is having higher NPV and the inflows are scattered, the NPV may be found at 16% and 17% Year CF PVF(16%,n) PV PVF (17%,n) PV 0 - Rs. 10,000 1,000 - Rs. 10,000 1.000 - Rs. 10,000 1 4,000 .862 3,448 .855 3,420 2 2,500 .743 1,858 .731 1,828 3 2,000 .641 1,282 .624 1,248 4 3,500 .552 1,932 .534 1,869
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5 3,500 .476 1,666 .456 1,596
186 -39
Now, the IRR is = 16% + 186 / 186 + 39 = 16.83%
Problem 13
A company is manufacturing a consumer product, the demand for which at current price is in excess of its ability to produce. The capacity of a particular machine, now due for replacement, is the limiting factor on production. The possibilities exist either of acquiring a similar machine (Project X) or of purchasing a more expensive machine with greater capacity (Project Y). The cash flows under each alternative have been estimated and given below. The company’s opportunity cost of capital is 10%, after tax. In deciding between the two alternatives the Managing Director favors the ‘pay back method’. The Chief Accountant, however, thinks that a more specific method should be used and he has calculated for each project:
i) The Net Present Value
ii) The Profitability Index
iii) The Discounted Pay Back Period
Having made these calculations, however, he finds himself still uncertain about which project to recommended. You are required to make these calculations and to discuss their relevance to the decision to be taken. The relevant cashflows are:
Year Project X Project Y
0 Rs. – 27,000 Rs. – 40,000 1 - 10,000 2 5,000 14,000 3 22,000 16,000 4 14,000 17,000 5 14,000 15,000 Solution: Calculation of NPV
Year CF (X) CF (Y) PVF(10%,n) PV (X) PV (Y)
0 Rs. – 27,000 Rs. – 40,000 1.000 Rs. – 27,000 Rs. – 40,000 1 - 10,000 .909 - 9,090 2 5,000 14,000 .826 4,130 11,564 3 22,000 16,000 .751 16,522 12,016 4 14,000 17,000 .683 9,562 11,611 5 14,000 15,000 .621 8,694 9,315
Net present value 11,908 13,596 Calculation of Profitability Index
PI = PV of Inflows / PV of Outflows Project X = Rs. 38,908 / Rs. 27,000 = 1.44 Project Y = Rs. 53,596 / Rs. 40,000 = 1.34
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Calculation of Discounted Payback Period
Cumulative Discounted PV
Year Project X Project Y
1 - Rs. 9,090
2 Rs. 4,130 20,654
3 20,652 32,670
4 30,214 44,281
5 39,908 53,596
Payback Period 3 years + 27,000 – 20,652 / 30,214 – 20,652 = 3.56 years
3 years + 40,000 – 32,670 / 44,281 – 32,670 = 3.63 years
Problem 14
A firm is considering the introduction of a new product which will have a life of five years. Two alternatives of promoting the product have been identified:
Alternative 1:
This will involve employing a number of agents. An immediate expenditure of Rs. 5,00,000 will be required to advertise the product. This will produce net annual cash inflows of Rs. 3,00,000 at the end of the each of the subsequent five years. However, the agents will have to be paid Rs. 50,000 each year. On termination of the contract, the agents will have to be paid a lump sum of Rs. 1,00,000 at the end of the fifth year.
Alternative 2
Under this alternative, the firm will not employ agents but will sell directly to the consumers. The initial expenditure on advertising will be Rs. 2,50,000. This will bring in cash at the end of each year of Rs. 1,50,000. However, this alternative will involve out-of-pocket costs for sales administration to the extent of Rs. 50,000. The firm also proposes to allocate fixed costs worth Rs. 20,000 per year to this product if this alternative is pursued.
Required:
a) Advise the management as to the method of promotion to be adopted. You may assume that the firm’s cost of capital is 20%.
Rushi Ahuja 18
Solution
Calculation of NPV Alternative 1
Outflows: Initial expenditure Rs. – 5,00,000
Inflows: Annual Cash inflow Rs. 3,000,000
Less Payment to agent 50,000
Net cash inflow 2,50,000
PVAF (20%,5y) 2.791
Present value of inflows (2,50,000 x 2.791) 7,47,750
Outflow: at the end of year 5 (Pyt. To agents) 1,80,000
PVF (20%,5y) .402
Present Value 40,200 -40,200
Net present value Rs. 2,07,550
Alternative 2
Outflows: Initial expenditure Rs. – 2,50,000
Inflows: Annual Cash inflow Rs. 1,50,000
Less out of pocket expenses 50,000
Net inflow 1,00,000
PVAF (20%,5y) 2.991
Present value of inflows (2.991 x 1,00,000) 2,99,100
Net present value (2,99,100 – 2,50,000) 49,100
Calculation of internal rate of return for alternative 2: Rs. 2,50,000 = Rs. 1,00,000 x PVAF(r,5Y)
PVAF(r,5Y) = 2,50,000 1,00,000
= 2.5
For 5 years in the PVAF table, the value of 2.5 may be traced between 28% and 29%. At 28% NPV = (1,00,000 x 2.532) – 2,50,000
= Rs. 3,200
At 29% NPV = (1,00,000 x 2.483) – 2,50,000 = Rs. -1,700
The exact IRR may be found by interpolating between 28% and 29% as follows: IRR = 28% + 3,200 / (3,200 + 1,700) = 28.65%
Note: The allocated fixed costs in case of Alternative 2 have been ignored because these do not involve any incremental cash outflow.
Rushi Ahuja 19
Problem 15
P. Ltd. has a machine having an additional life of 5 years which costs Rs. 10,00,000 an 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 in variable costs to the extent of Rs. 7,00,000 per annum. The life of the old 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, of 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. Ignore income tax saving on additional depreciation as well as on loss due to sale of existing machine.
Will it make any difference, if the additional depreciation (on new machine) and gain on sale of old machine is also subject to same tax at the rate of 40%, and the scrap value of the new machines is Rs. 3,00,00.
Solution 1. Cash Outflows:
Cost of new machine Rs. 20,00,000
- Scrap value of old 1,00,000 Rs. 19,00,000
2. Cash inflow (annual)
Net savings in variable costs Rs. 7,00,000
- Tax @ 40% 2,80,000
Net benefit 4,20,000
3. Cash inflow at the end of year 5
Salvage value of new Rs. 2,00,000
4. Calculation of NPV
Cash outflow at year 0 Rs. – 19,00,000
Cash inflow: 4,20,000x3,605 (i.e. PVAF(12%,5y)) 15,14,100
: 2,00,000x.567 (i.e. PVF(12%,5y)) 1,13,400
Net present value - 2,72,500
As the NPV of the new machine is negative, the firm need not replace the old machine with the new machine.
However, in case, the additional depreciation and capital gain on sale of old machine is also subject to same tax rate @ 40%, then the position would be as follows:
Rushi Ahuja 20
1. Cash Outflows:
Cost of new machine Rs. 20,00,000
- Scrap value of old 1,00,000
- Tax saving on capital loss 1,20,000 Rs. 17,80,000
40% of (4,00,000-1,00,000)
2. Cash inflows (Annual)
Net savings in variable costs Rs. 7,00,000
- Additional depreciation 2,60,000
Savings before tax 4,40,000
- Tax @ 40% 1,76,000
Net benefit 2,64,000
+ Depreciation added back 2,60,000
Cash inflows (annual) 5,24,000
3. Cash inflow at the end of year 5
Salvage value of new Rs. 3,00,000
4. Calculation of NPV
Cash outflow at year 0 Rs. – 17,80,000
Cash inflow : 5,24,000x3.605 (i.e. PVAF(12%,5y)) 18,89,020
: 3,00,000x.567 (i.e. PVF(12%,5y)) 1,70,100
Net present value 2,79,120
As the NPV of the new machine is Rs. 2,79,120, the firm may replace the old machine. The depreciation (additional) on new machine has been calculated as follows:
Depreciation on new machine (20,00,000 – 3,00,000)/5 3,40,000
Depreciation on old machine (4,00,000/5) 80,000
Additional depreciation 2,60,000
It may be noted that the proposal is not acceptable in one set of assumptions, however, when the assumption regarding taxability of depreciation and capital gains / loss is charged, the proposal becomes acceptable.
Problem 16
National Bottling Company is contemplating to replace one of its bottling machines with a new more efficient machine. The old machine had a cost of Rs. 10 lacs and a useful life of ten years. The machine was bought five years back. The company does not expect to realize any return from scrapping the old machine at the end of 10 years but if it is sold at present to another company in the industry, National Bottling Company would receive Rs. 6 lacs for it. The new machine has a purchase price of Rs. 20 lacs. It has an estimated salvage value of Rs. 6 lacs and has useful life of five years. The new machine will have a greater capacity and annual sales are expected to increase from Rs. 10 lacs to Rs. 12 lacs. Operating efficiencies with the new machine will also produce savings of Rs. 2 lacs a year. Depreciation is on a straight-line basis over a ten year life.
The cost of capital is 8% and a 50% tax rate is applicable to both revenue and capital gains. The present value interest factor for an annuity for five years at 8% is 3.993 and present value interest factor at the end of five years is 0.681. Should the company replace the old machine?
Rushi Ahuja 21
Cash outflows:
Cost of new machine Rs. 20,00,000
- Disposal value of existing machine 6,00,000
14,00,000
+50% Tax on Profit on sale (6,00,000 – 5,00,000) 50,000
Net outflow 14,50,000
Cash inflows (Annual)
Incremental Sales Rs. 2,00,000
Savings in expenses 2,00,000
Rs. 4,00,000
- Incremental depreciation (3,60,000 – 1,00,000) 2,60,000
Net profit after tax (incremental) 1,40,000
Less tax @ 50% 70,000
Profit after tax 70,000
Cash flow (PAT + Depreciation) 3,30,000
PVAF (8%,5y) 3.993
Present value of cash inflows (3,30,000 x 3.993) Rs. 13,17,690
Cash inflow (terminal)
Scrap value at the end of 5th year Rs. 2,00,000
PVF (8%,5y) .681
Present value (2,00,000 x .681) 1,36,200
Net present value (13,17,690 + 1,36,200 – 14,50,000) 3,890
The replacement decision has a NPV of Rs. 3,890. The firm may go for replacement of the existing machine.
Problem 17
Central Gas Ltd. in considering to enhance its production capacity. The following tw mutually exclusive proposals are being considered:
Proposal I Proposal II
Plant Rs. 2,00,000 Rs. 3,00,000
Building 50,000 1,00,000
Installation 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 II are required to be incurred at the end of 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 8%. 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:
Rushi Ahuja 22
Proposal I Proposal II Initial cash outflow
Cost of plant Rs. 2,00,000 Rs. 3,00,000
Installation expenses 10,000 15,000
Cost of building 50,000 1,00,000
Working capital required 50,000 65,000
Total outflow 3,10,000 4,80,000
Present value of annual inflows: Proposal I Proposal II
Profit before depreciation Rs. 70,000 Rs. 95,000
PVAF(8%,7) 6.710 6.710
Present value Rs. 4,69,700 Rs. 6,37,450
- Present value of sales promotion exp – (12,855)
(15000 x PVF(8%,2)) – –
Present value of inflows (Annual) 4,69,700 6,24,595
Present value of Terminal Inflows
Release of working capital Rs. 50,000 Rs. 65,000
Sale value of plant 10,000 15,000
Disposable value of building 30,000 60,000
90,000 1,40,000
PVF(8%,10) .463 .463
Present value of terminal inflows Rs. 41,670 Rs. 64,820
Calculation of net present value
PV of annual inflows Rs. 4,69,700 Rs. 6,24,395
+ PV of terminal inflows 41,670 64,820
Total 5,11,370 68,9415
- PV of outflows 3,10,000 4,80,000
Net present value 2,01,370 2,09,415
Proposal II has higher NPV and so, it may be accepted by the firm. Problem 18
The cash flows from two mutually exclusive Projects A and B are as under:
Years Project A Project B
0 Rs. -22,000 Rs. -27,000
1-7 (annual) 6,000 7,000
Project life 7 years 7 years
i) Calculate NPV of the proposals at different discount rates of 15%, 16%, 17%, 18%, 19% and 20%. ii) Advise on the project on the basis of IRR method, and
iii) Will it make any difference in project selection as per IRR, if the cash flows from Project B are for 8 years instead of 7 years (Rs. 7,000 per year).
Solution
Computation of present value of cash inflows of different projects Dis. Rate
%
Cash flow (Rs.) PVAF P.V. Cash flows (Rs.) Proj.A Proj.B 7 yrs 8 yrs Prof.A Prof.B Prof.B(8y)
15 6,000 7,000 4.160 4.487 24,960 29,120 31,409
Rushi Ahuja 23 17 6,000 7,000 3.922 4.207 23,532 27,454 29,119 18 6,000 7,000 3.812 4.078 22,872 26,684 28,556 19 6,000 7,000 3.706 3.954 22,235 25,942 27,678 20 6,000 7,000 3.605 3.837 21,630 25,235 26,859 Calculation of NPV
Dis. Rate PV of inflows (A) NPV (A) PV of inflows (B) NPV (B)
15% Rs. 24,960 Rs. 2,960 Rs. 29,120 Rs. 2,120 16% 24,240 2,240 28,280 1,280 17% 23,532 1,532 27,454 454 18% 22,872 872 26,784 -216 19% 22,235 235 25,942 -1,058 20% 21,630 -370 25,235 -1,765 Calculation of IRR
Project A: Since outflow of Rs. 22,000 is falling between Rs. 22,235 and Rs. 21,630, the IRR must be between 19% to 20%. So, interpolating the difference of Rs. 605 between 19% and 20%, the IRR comes to 19.39%.
Rs. 22,235 – 22,000 Rs. 235
= 19% + = 19% = 19.39%
Rs. 22,235 – 21,630 Rs. 605
Project B: Since outflow of Rs. 27,000 is falling between Rs. 27,454 and Rs. 26,684, the IRR must be between 17% to 18%. So, interpolating the difference of Rs. 770 between 17% and 18%, the IRR comes to 17.59%.
Rs. 27,454 – 27,000 Rs. 454
= 17% + = 17% = 17.59%
Rs. 27,454 – 26,684 Rs. 770
Project B (8 years): Since outflow of Rs. 27,000 is falling between Rs. 27,678 and Rs. 26,859, the IRR must be between 19% to 20%. So, interpolating the difference of Rs. 819 between 19% and 20%, the IRR comes to 19.83%.
Rs. 27,678 – 27,000 Rs. 678
= 19% + = 19% = 19.83%
Rs. 27,678 – 26,859 Rs. 819
Conclusion: As per the NPV technique, the Project A is acceptable even if the discount rate is as high as 19%, whereas, the Project B becomes unviable even at 18%. As per IRR technique, the Project A is acceptable and is having an IRR of 19.39% against the IRR of 17.59% of Project B. However, if the life of the Project B extends to 8 years, then as per the IRR method, the Project B becomes acceptable (IRR = 19.83%) as against Project A (IRR = 19.39%).
Rushi Ahuja 24
AP Udyog is considering a new automatic blender. The new blender would last fir 10 years and would be depreciated to zero over the 10 year period. The old blender would also last for 10 more years and would be depreciated to zero over the same 10 year period. The old blender has a book value of Rs. 20,000 but could be sold for Rs. 30,000 (the original cost was Rs. 40,000). The new blender would cost Rs. 1,0,000. It would reduce labour expense by Rs. 12,000 a year. The company is subject to a 50% tax fate on regular income as well as on capital gains. Their cost of capital is 8%. There is no investment tax credit in effect. You are required to –
i) Identify all the relevant cash flows for this replacement decision. ii) Compute the present value, Net Present Value and Profitability Index. iii) Find out whether this is an attractive project.
Solution
i) Tax on the sale of the old machine: Rs.
Sale price 30,000
Book value 20,000
Profit on sale 10,000
Tax on sale (Rs. 10,000x.50) 5,000
After-tax cash receipts from sale of old machine
Sale Price 30,000
After tax cash receipt 25,000
ii) Cash outflow to replace old machine with new:
Cost of new machine 1,00,000
After-tax receipt from sale of old machine 25,000
Net cash flow to replace old machine with new 75,000
iii) Depreciation on new machine = 1,00,000 / 10 = Rs. 10,000 Depreciation on new machine = 20,000 / 10 = Rs. 2,000 iv) Annual inflow
Cash flow
Annual labour savings Rs. 12,000
- Increased earnings before tax 8,000
Increased earnings before tax 4,000
Increased tax 2,000
Increased earnings after tax 2,000
+ Depreciation 8,000
Increased after-tax cash flow (Annual) 10,000
v) Calculation of present value at 8% discount rate:
Year Cash flow PVAF(8%,10y) Present value
1-10 Rs. 10,000 6.710 Rs. 67,100
Rushi Ahuja 25
PV of cash inflow Rs. 67,100
NPV of the Project Rs. -7,900
Profitability Index = 67,100 / 75,000 = 0.895
iii) Since the Net present value is negative and Profitability Index is less than one, the project is not an attractive project.
Working Note: The tax on profit on sale has been deducted from the sale price of old machine on the assumption that the tax liability arises on that day itself. Moreover, in view of the advance tax payments, this assumption seems to be logical.
