Capital Budgeting - Solved Problems

FINANCIAL MANAGEMENT

Solved Problems

SOLVED PROBLEMS – CAPITAL BUDGETING Problem 1 The 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) Profit before depreciation, interest and taxes - Depreciation Profit before tax Tax @ 30% Profit after Tax + depreciation (added back) Therefore, cash flow

1,00,000 1,75,000 1,00,000 75,000 22,500 52,500 1,00,000 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 Subsequent cash flows Units sold Sales @ Rs. 12/- Variable cost @ Rs. 6/- Fixed cost (4,50,000 – 30,000 – 70,000) - Depreciation Profit before tax Tax @ 45% Profit after tax Depreciation (added back) Cash flow

Rs. 5,60,000 1,00,000 Rs. 12,00,000 6,00,000 3,50,000 70,000 1,80,000 81,000 99,000 70,000 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. Problem 3 Rushi Ahuja

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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

1.

Initial cash outflow: Cost of new machine - Scrap value of old machine

2.

Subsequent cash inflows (annual) Incremental benefit - Incremental depreciation Dep. On new machine Dep. On old machine Profit before tax - Tax @ 40% Profit after tax + Depreciation (added back) Annual cash inflow

(Amount in Rs.) 1,30,000 20,000 1,10,000

60,000 28,000 6,000

22,000 38,000 15,200 22,800 22,000 44,800

The amount of depreciation of Rs. 28,000 on the new machine is ascertained as follows: (Rs. 1,30,000Rs. 18,000)/4 = 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 4 th 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). Rushi Ahuja

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Solution Initial cash flows: Cost of new machine - Salvage value of old machine

Amt. (Rs.) 4,00,000 90,000 3,10,000

Subsequent annual cash flows: (Amount Rs. ‘000) Savings in costs (A) Depreciation on new machine - Depreciation on old machine Therefore, incremental depreciation (B) Net incremental saving (A – B) Less: Incremental Tax @ 50% Incremental Profit Depreciation (added back) Net cash flow

Yr.1 100 133.3 18.0 115.3 -15.3 -7.6 -7.7 115.3 107.6

Yr.2 100 88.9 14.4 74.5 25.5 12.8 12.7 74.5 87.2

Yr.3 100 59.3 11.5 47.8 52.2 26.1 26.1 47.8 73.9

Yr.4 100 39.5 9.2 30.3 69.7 34.8 34.9 30.3 65.2

Yr.5 100 26.3 7.4 18.9 81.1 40.6 40.5 18.9 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 1 2 3 4 5

Existing Machine Rs. 30,000 30,000 30,000 30,000 30,000

New Machine Rs. 50,000 60,000 70,000 90,000 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 1,40,000 10,000 20,000 80,000 90,000 12,000 1,02,000

Cost of new machine + Installation cost + Additional working capital - Scrap value Tax liability / saving Cash outflow Calculate of tax paid / saved: Book value of old plant - Scrap value Profit / Loss Tax @ 40% on capital gain / loss

50,000 80,000 30,000 12,000

Scrap 1,40,000 1,40,000 10,000 10,000 20,000 20,000 60,000 50,000 1,10,000 1,20,000 4,000 – 1,14,000 1,02,000 50,000 60,000 10,000 4,000

50,000 50,000 – –

Values 1,40,000 10,000 20,000 30,000 1,40,000 -8,000 1,32,000 50,000 30,000 (20,000) -8,000

Subsequent Cash inflows (Annual) (Amount Rs. ‘000) Cash inflows On new machine On old machine Incremental cash inflow - Incremental depreciation Profit before tax - Tax at 40% Profit after tax Depreciation (added back) Net cash inflow

Yr.1

Yr.2

Yr.3

Yr.4

Yr.5

50,000 30,000 20,000 20,000 20,000 20,000

60,000 30,000 30,000 20,000 10,000 4,000 6,000 20,000 26,000

70,000 30,000 40,000 20,000 20,000 8,000 12,000 20,000 32,000

90,000 30,000 60,000 20,000 40,000 16,000 24,000 20,000 44,000

1,00,000 30,000 70,000 20,000 50,000 20,000 30,000 20,000 50,000

The amount of incremental depreciation has been calculated as follows: Depreciation of new machine Depreciation on old machine Therefore, incremental depreciation

= = = = =

(Rs. 1,40,000 + Rs. 10,000)/5 Rs. 30,000 Rs. 70,000/7 Rs. 10,000 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:

Cost

Year 0

Project X Rs. 70,000

Project Y Rs. 70,000 Rushi Ahuja

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FINANCIAL MANAGEMENT Cash inflows

1 2 3 4 5

10,000 20,000 30,000 45,000 60,000

Solved Problems

50,000 40,000 20,000 10,000 10,000

Compute the Net Present Value at 10%, Profitability Index, and Internal Rate of Return of the two projects. Solution Calculation of NPV: Year 1 2 3 4 5 Total PV Less cash outflow NPV PI = (PV of inflows / PV of outflows)

CF (Rs.) X Y 10,000 50,000 20,000 40,000 30,000 20000 45,000 10,000 60,000 10,000

PVF (10%,n)

0.909 0.826 0.751 0.683 0.621

Total PV (Rs.) X Y 9,090 45,450 16,520 33,040 22,530 15,020 30,735 6,830 37,260 6,210 1,16,135 1,06,550 70,000 70,000 46,135 36,550 1.659 1.552

Calculation of IRR: Payback value Project X Project Y

= Initial cash outlays / average cash inflows = Rs. 70,000 / Rs. 33,000 = 2.121 = 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.)

1 2 3 4 5

10,000 20,000 30,000 45,000 60,000

PV Factor 27% 28% 0.787 0.781 0.620 0.610 0.488 0.477 0.384 0.373 0.303 0.291

Total PV (Rs.) 27% 28% 7,870 7,810 12,400 12,200 14,640 14,310 17,280 16,785 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. Rushi Ahuja

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Project Y Year

CP (Rs.)

1 2 3 4 5

50,000 40,000 20,000 10,000 10,000

PV Factor 27% 28% 0.735 0.730 0.541 0.533 0.398 0.389 0.292 0.284 0.215 0.207

Total PV (Rs.) 27% 28% 36,750 36,500 21,640 21,320 7,640 7,780 2.920 2,840 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:

BPV PI IRR

Project X Rs. 46,130 1.659 27%

Project Y Rs. 36,550 1.522 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) 1 2 3 4 5

A Rs. 20,000 60,000 40,000 30,000 20,000

B – Rs. 60,000 60,000 80,000 –

With 7% cost of capital, which machine should be selected? Solution The NPV of both the machines may be found as follows: Year 0 1 2 3 4 5

CF(A) Rs. -1,00,000 20,000 60,000 40,000 30,000 20,000

CF(B) Rs. -60,000 -60,000 60,000 60,000 80,000 -

PVF (7%,n) 1.000 .935 .873 .816 .763 .713

PV(A) -1,00,000 18,700 52,380 32,640 22,890 14,260

PV(B) -60,000 -56,100 52,380 48,960 61,040 -

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FINANCIAL MANAGEMENT Net Present Value

40,780

Solved Problems

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:

Machine A Machine B

0 -25 -40

1 10

2 5 14

3 20 16

4 14 17

5 14 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 PV

0 1.00

1 .91

2 .83

3 .75

4 .68

5 .62

Solution Calculation of Net Present Value Year 0 1 2 3 4 5

CF (Rs. in lacs) Machine A Machine B -25 -40 10 5 14 20 16 14 17 14 15

PVF(10%,n) 1.00 0.91 0.83 0.75 0.68 0.62 NPV

Total PV (Rs. in lacs) Machine A Machine B -25.00 -40.00 9.10 4.15 11.62 15.00 12.00 9.52 11.56 8.68 9.30 12.35 13.58

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Calculation of Profitability Index:

PV of Cash inflow PV of Cash outflow

=

Machine A (Rs. in lakhs) 37.35 25.00

Machine B (Rs. in lakhs) 53.58 40.00

1.494

1.339

= Calculation of Pay Back Period

(Rs. in Lacs) Year

Cash inflows Machine A Machine B 0 -25 -40 1 10 2 5 14 3 20 16 4 14 17 5 14 15 In both cases, the Payback Period is 3 years.

Cumulative cash inflows Machine A Machine B 10 5 24 25 40 39 57 53 72

Calculation of Discounted Payback Period (Rs. in lacs) Year 0 1 2 3 4 5

Present value Machine A Machine B -25.00 -40.00 9.10 4.15 11.62 15.00 12.00 9.52 11.56 8.68 9.30

Outflow In 3 years, Payback were Unrecouped oputflow In 4th year, Net present value Thus pay back

=3+

Cumulative present value Machine A Machine B 9.10 4.15 20.72 19.15 32.72 28.67 44.28 37.35 53.58

Machine A -25.00 19.15 5.85 9.52 5.85 9.52 = 3.614 years

=3+

Machine B -40.00 32.72 7.28 11.56 7.28 11.56 = 3.629 years

Conclusion

1. NPV 2. Profitability index

Machine A 12.35 1.494

Machine B 13.58 1.339

Choice B A Rushi Ahuja

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FINANCIAL MANAGEMENT 3. Payable period 4. Discounted payback

3 years 3.614 years

3 years 3.629 years

Solved Problems

Indifferent 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: Initial capital outlay Salvage value at the end of the life Economic life (years) After tax annual cash inflows

Year 1 2 3 4 5 6 7

AXE Rs. 22,50,000 0 4 Rs. 6,00,000 12,50,000 10,00,000 7,50,000 -

BXE Rs. 30,00,000 0 7 Rs. 5,00,000 7,50,000 7,50,000 12,00,000 12,50,000 10,00,000 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 CF PFV (16%,n) Rs. (22.50) 1.000 6.00 0.862 12.50 0.743 10.00 0.641 7.50 0.552 Net present value

0 1 2 3 4 5 6 7

PV Rs. (22.50) 5.17 9.29 6.41 4.14 2.51

CF (30.00) 5.00 7.50 7.50 12.50 12.50 10.00 8.00

BXE PFV (16%,n) 1.000 0.862 0.743 0.641 0.552 0.476 0.410 0.354

PV (30.00) 4.30 5.57 4.81 6.90 5.95 4.10 2.83 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

1 2

Discount Factor @21% 0.826 0.683

AXE Cash flows Rs. lacs 6.00 12.50

BXE PVs Rs. lacs 4.95 8.53

Cash flows Rs. lacs 5.00 7050

Total PVs Rs. lacs 4.12 5.13

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FINANCIAL MANAGEMENT 3 4 5 6 7 Present value Less: Initial outlay NPV

0.564 0.467 0.386 0.319 0.263

10.00 7.50 -

5.64 3.50 22.62 22.50 0.12

7.50 12.50 12.50 10.00 8.00

Solved Problems

4.23 5.83 4.83 3.19 2.10 29.44 30.00 -.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 Profit after Tax (10% of cost of Project) Add: Depreciation Net cash inflow (annual) PVAF(10%,8) Present value of net cash inflow Salvage value PVF(10%,8) Present value of salvage value PV of total cash inflow Less: Initial investment Net present value

Project A Rs. 10,00,000 12,00,000 22,00,000 5.335 117,37,000 4,00,000 .467 1,86,800 119,23,800 100,00,000 19,23,800

Project B Rs. 15,00,000 17,00,000 32,00,000 5.335 170,72,000 14,00,000 .467 6,53,800 177,25,800 150,00,000 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 Bright Metals Ltd. is considering two different investment proposals, a and B. The details are as under: Rushi Ahuja 10

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Investment cost Estimated income

Year 1 Year 2 Year 3

Proposal A Rs. 9,500 4,000 4,000 4,500

Solved Problems

Proposal B Rs. 20,000 8,000 8,000 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 NPV @ 12% Rs. 464 NPV @ 14% Rs. 122 NPV @ 15% Rs. -35

Project B NPV @ 12% Rs. 2064 NPV @ 17% Rs. 176 NPV @ 18% Rs. -172

Interpolation between 14% and 15%

Interpolation between 17% and 18%

IRR = 14% + 122 / 122+35 = 14.78%

IRR = 17% + 176 / 176+172 = 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) Project X

Project Y Rushi Ahuja 11

FINANCIAL MANAGEMENT Project cost Cash inflows: Year 1 Year 2 Year 3 Year 4 Year 5

700 100 200 300 450 600

Solved Problems

700 500 400 200 100 100

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 1 2 3 4 5 Total PV Less: Initial cash outflow Net present value

CF X 100 200 300 450 600

PVF (10%,n) Y 500 400 200 100 100

0.909 0.826 0.751 0.683 0.621

Present value X Y 90.90 454.50 165.20 330.40 225.30 150.20 307.35 68.30 372.60 62.10 1065.50 700.00 700.00 461.35 365.50

Internal Rate of Return (IRR): Project X Year

CFX

1 2 3 4

100 200 300 450

5 Total PV Less: Initial cash outflow Net present value

600

PV factor at 27% 28% .787 .781 .620 .610 .488 .477 .384 .373 .303

.291

Present Value 27% 28% 78.70 78.10 124.00 122.00 146.40 143.10 172.80 167.85 181.80 703.70 700.00 3.70

174.60 685.65 700.00 (14.35)

IRR = 27 + 3.70 / 3.70 + 14.35 x 1 = 27 + 0.205 = 27.21% Project Y Rushi Ahuja 12

FINANCIAL MANAGEMENT

Year

CFY

1 2 3 4 5

PV factor at 27% 28% .730 .725 .533 .525 .389 .381 .284 .276 .207 .200

500 400 200 100 100

Total PV Less: Initial cash outflow Net present value

Solved Problems

Present Value 27% 28% 365.00 362.50 213.20 210.00 77.80 76.20 28.40 27.60 20.70 20.70 705.10 700.00 5.10

697.00 700.00 (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 Project 1 Project 2

1 Rs. 4,000 Rs. 6,000

2 4,000 3,000

3 4,000 2,000

4 4,000 5,000

5 4,000 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 1 2 3 4 5

PBD Rs. 4,000 4,000 4,000 4,000 4,000

Dep. Rs. 2,000 2,000 2,000 2,000 2,000

PBT Rs. 2,000 2,000 2,000 2,000 2,000

Tax Rs. 1,000 1,000 1,000 1,000 1,000

PAT Rs. 1,000 1,000 1,000 1,000 1,000

CF Rs. 3,000 3,000 3,000 3,000 3,000

Cum. CF Rs. 3,000 6,000 9,000 12,000 15,000

Rs. 2,000 2,000 2,000 2,000 2,000

Rs. 4,000 1,000 – 3,000 3,000

Rs. 2,000 500 – 1,500 1,500

Rs. 2,000 500 – 1,500 1,500

Rs. 4,000 2,500 2,000 3,500 3,500

Rs. 4,000 6,500 8,500 12,000 15,000

Project 2: 1 2 3 4 5

Rs. 6,000 3,000 2,000 5,000 5,000

Project 1 3 years + 1,000 / 3,000 = 3 1/3 years

Calculation of payback period Calculation of accounting rate of return Average cost Average profit after tax Rate of return

Project 2 3 years + 1,500 / 3,500 = 3 3/7 years

Rs. 5,000 Rs. 1,000 20%

Rs. 5,000 Rs. 1,100 22%

Calculation of NPV (cost of capital 10%) Project 1:

Annuity of cash inflows for 5 years PVAF (10%,5y) PV of Annuity (3,000 x 3.791) Less cash outflow Net present value

= = = = =

Rs. 3,000 3.791 Rs. 11,373 10,000 1,373

Project 2: Year 0 1 2 3 4

Cash flow - Rs. 10,000 4,000 2,500 2,000 3,500

PVF (10%,n) 1,000 .909 .826 .751 .683

PV Rs. 10,000 3,636 2,065 1,502 2,391

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FINANCIAL MANAGEMENT 5

3,500

.621 Net present value

Solved Problems

2,173 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 Rs. 10,000 = PVAF(r,5y) = =

are equal for 5 years, therefore, the situation can be presented like this: Rs. 3,000 x PVAF(r,5) 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 0 1 2 3 4

CF - Rs. 10,000 4,000 2,500 2,000 3,500

PVF(16%,n) 1,000 .862 .743 .641 .552

PV - Rs. 10,000 3,448 1,858 1,282 1,932

PVF (17%,n) 1.000 .855 .731 .624 .534

PV - Rs. 10,000 3,420 1,828 1,248 1,869

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FINANCIAL MANAGEMENT 5

3,500

.476

1,666 186

.456

Solved Problems

1,596 -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) ii) iii)

The Net Present Value The Profitability Index 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 0 1 2 3 4 5

Project X Rs. – 27,000 5,000 22,000 14,000 14,000

Project Y Rs. – 40,000 10,000 14,000 16,000 17,000 15,000

Solution: Calculation of NPV Year 0 1 2 3 4 5

CF (X) Rs. – 27,000 5,000 22,000 14,000 14,000

CF (Y) Rs. – 40,000 10,000 14,000 16,000 17,000 15,000

PVF(10%,n) 1.000 .909 .826 .751 .683 .621 Net present value

PV (X) Rs. – 27,000 4,130 16,522 9,562 8,694 11,908

PV (Y) Rs. – 40,000 9,090 11,564 12,016 11,611 9,315 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 Rushi Ahuja 16

FINANCIAL MANAGEMENT

Solved Problems

Calculation of Discounted Payback Period Cumulative Discounted PV Project X Project Y Rs. 9,090 Rs. 4,130 20,654 20,652 32,670 30,214 44,281 39,908 53,596

Year 1 2 3 4 5 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%. b) Calculate the internal rate of return for alternative 2.

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FINANCIAL MANAGEMENT

Solved Problems

Solution Calculation of NPV Alternative 1 Outflows: Initial expenditure Inflows: Annual Cash inflow Less Payment to agent Net cash inflow PVAF (20%,5y) Present value of inflows (2,50,000 x 2.791) Outflow: at the end of year 5 (Pyt. To agents) PVF (20%,5y) Present Value Net present value

Rs. – 5,00,000 Rs. 3,000,000 50,000 2,50,000 2.791 7,47,750 1,80,000 .402 40,200

-40,200 Rs. 2,07,550

Alternative 2 Outflows: Initial expenditure Inflows: Annual Cash inflow Less out of pocket expenses Net inflow PVAF (20%,5y) Present value of inflows (2.991 x 1,00,000) Net present value (2,99,100 – 2,50,000)

Rs. – 2,50,000 Rs. 1,50,000 50,000 1,00,000 2.991 2,99,100 49,100

Calculation of internal rate of return for alternative 2: Rs. 2,50,000 = PVAF(r,5Y) = =

Rs. 1,00,000 x 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

At

29% NPV

= = = =

(1,00,000 x 2.532) – 2,50,000 Rs. 3,200 (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.

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FINANCIAL MANAGEMENT

Solved Problems

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 - Scrap value of old 2. Cash inflow (annual) Net savings in variable costs - Tax @ 40% Net benefit 3. Cash inflow at the end of year 5 Salvage value of new 4. Calculation of NPV Cash outflow at year 0 Cash inflow: 4,20,000x3,605 (i.e. PVAF(12%,5y)) : 2,00,000x.567 (i.e. PVF(12%,5y)) Net present value

Rs. 20,00,000 1,00,000

Rs. 19,00,000

Rs. 7,00,000 2,80,000 4,20,000 Rs. 2,00,000 Rs. – 19,00,000 15,14,100 1,13,400 - 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:

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FINANCIAL MANAGEMENT

1. Cash Outflows: Cost of new machine - Scrap value of old - Tax saving on capital loss 40% of (4,00,000-1,00,000) 2. Cash inflows (Annual) Net savings in variable costs - Additional depreciation Savings before tax - Tax @ 40% Net benefit + Depreciation added back Cash inflows (annual) 3. Cash inflow at the end of year 5 Salvage value of new 4. Calculation of NPV Cash outflow at year 0 Cash inflow : 5,24,000x3.605 (i.e. PVAF(12%,5y)) : 3,00,000x.567 (i.e. PVF(12%,5y)) Net present value

Rs. 20,00,000 1,00,000 1,20,000

Solved Problems

Rs. 17,80,000

Rs. 7,00,000 2,60,000 4,40,000 1,76,000 2,64,000 2,60,000 5,24,000 Rs. 3,00,000 Rs. – 17,80,000 18,89,020 1,70,100 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 Depreciation on old machine (4,00,000/5) Additional depreciation

3,40,000 80,000 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? Solution Rushi Ahuja 20

FINANCIAL MANAGEMENT Cash outflows: Cost of new machine - Disposal value of existing machine +50% Tax on Profit on sale (6,00,000 – 5,00,000) Net outflow Cash inflows (Annual) Incremental Sales Savings in expenses - Incremental depreciation (3,60,000 – 1,00,000) Net profit after tax (incremental) Less tax @ 50% Profit after tax Cash flow (PAT + Depreciation) PVAF (8%,5y) Present value of cash inflows (3,30,000 x 3.993) Cash inflow (terminal) Scrap value at the end of 5 th year PVF (8%,5y) Present value (2,00,000 x .681) Net present value (13,17,690 + 1,36,200 – 14,50,000)

Solved Problems

Rs. 20,00,000 6,00,000 14,00,000 50,000 14,50,000 Rs. 2,00,000 2,00,000 Rs. 4,00,000 2,60,000 1,40,000 70,000 70,000 3,30,000 3.993 Rs. 13,17,690 Rs. 2,00,000 .681 1,36,200 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: Plant Building Installation Working capital required Annual earnings (before depreciation) Sales promotion expenses Scrap value of plant Disposable value of building

Proposal I Rs. 2,00,000 50,000 10,000 50,000 70,000 10,000 30,000

Proposal II Rs. 3,00,000 1,00,000 15,000 65,000 95,000 15,000 15,000 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 21

FINANCIAL MANAGEMENT

Initial cash outflow Cost of plant Installation expenses Cost of building Working capital required Total outflow Present value of annual inflows: Profit before depreciation PVAF(8%,7) Present value - Present value of sales promotion exp (15000 x PVF(8%,2)) Present value of inflows (Annual) Present value of Terminal Inflows Release of working capital Sale value of plant Disposable value of building PVF(8%,10) Present value of terminal inflows Calculation of net present value PV of annual inflows + PV of terminal inflows Total - PV of outflows Net present value

Proposal I

Proposal II

Rs. 2,00,000 10,000 50,000 50,000 3,10,000 Proposal I Rs. 70,000 6.710 Rs. 4,69,700 – – 4,69,700

Rs. 3,00,000 15,000 1,00,000 65,000 4,80,000 Proposal II Rs. 95,000 6.710 Rs. 6,37,450 (12,855) – 6,24,595

Rs. 50,000 10,000 30,000 90,000 .463 Rs. 41,670

Rs. 65,000 15,000 60,000 1,40,000 .463 Rs. 64,820

Rs. 4,69,700 41,670 5,11,370 3,10,000 2,01,370

Rs. 6,24,395 64,820 68,9415 4,80,000 2,09,415

Solved Problems

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 Rs. -22,000 6,000 7 years

0 1-7 (annual) Project life

Project B Rs. -27,000 7,000 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 % 15 16

Cash flow (Rs.) Proj.A Proj.B 6,000 7,000 6,000 7,000

PVAF 7 yrs 4.160 4.040

8 yrs 4.487 4.344

P.V. Cash flows (Rs.) Prof.A Prof.B Prof.B(8y) 24,960 29,120 31,409 24,240 28,280 30,408

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FINANCIAL MANAGEMENT 17 18 19 20

6,000 6,000 6,000 6,000

7,000 7,000 7,000 7,000

3.922 3.812 3.706 3.605

4.207 4.078 3.954 3.837

23,532 22,872 22,235 21,630

27,454 26,684 25,942 25,235

Solved Problems

29,119 28,556 27,678 26,859

Calculation of NPV Dis. Rate 15% 16% 17% 18% 19% 20%

PV of inflows (A) Rs. 24,960 24,240 23,532 22,872 22,235 21,630

NPV (A) Rs. 2,960 2,240 1,532 872 235 -370

PV of inflows (B) Rs. 29,120 28,280 27,454 26,784 25,942 25,235

NPV (B) Rs. 2,120 1,280 454 -216 -1,058 -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 = 19% +

Rs. 235 = 19%

Rs. 22,235 – 21,630

= 19.39% 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 = 17% +

Rs. 454 = 17%

Rs. 27,454 – 26,684

= 17.59% 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 = 19% +

Rs. 678 = 19%

Rs. 27,678 – 26,859

= 19.83% 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%). Problem 19 Rushi Ahuja 23

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Solved Problems

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)

ii)

Tax on the sale of the old machine: Sale price Book value Profit on sale Tax on sale (Rs. 10,000x.50) After-tax cash receipts from sale of old machine Sale Price After tax cash receipt Cash outflow to replace old machine with new: Cost of new machine After-tax receipt from sale of old machine Net cash flow to replace old machine with new

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

30,000 25,000

1,00,000 25,000 75,000

Cash flow Rs. 12,000 8,000 4,000 2,000 2,000 8,000 10,000

Annual labour savings - Increased earnings before tax Increased earnings before tax Increased tax Increased earnings after tax + Depreciation Increased after-tax cash flow (Annual) v)

Rs. 30,000 20,000 10,000 5,000

Calculation of present value at 8% discount rate:

Year 1-10 H outflow

Cash flow Rs. 10,000

PVAF(8%,10y) 6.710

Present value Rs. 67,100 Rs. 75,000 Rushi Ahuja 24

FINANCIAL MANAGEMENT PV of cash inflow NPV of the Project

Solved Problems

Rs. 67,100 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.

Rushi Ahuja 25