88868074 capital budgeting solved problems

5/23/2018 88868074 Capital Budgeting Solved Problems

FINANCIAL MANAGEMENT Solved Problems

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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) 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) 1,00,000herefore, 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 asingle 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. 70,000and 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 cashflows.

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 1,80,000Tax @ 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.

Problem 3



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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 machinecosting 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 (beforedepreciation 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 = 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 incrementaldepreciation 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 whenthe 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 newmachine. 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 valuemethod). 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 90,0003,10,000

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 40.5Depreciation (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 ofinstallation 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 1,40,000Tax 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 inflowsOn 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 30,000Depreciation (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 5 thyear in the form ofworking 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

Cost 0 Rs. 70,000 Rs. 70,000



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Cash inflows 1 10,000 50,000

2 20,000 40,000

3 30,000 20,0004 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 twoprojects.

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 45,4502 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 = 2.121Project 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 theProject 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 12,2003 30,000 0.488 0.477 14,640 14,310

4 45,000 0.384 0.373 17,280 16,7855 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 21,3203 20,000 0.398 0.389 7,640 7,780

4 10,000 0.292 0.284 2.920 2,8405 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 than37%. The results of the above calculations may be summarized as follows:

Project X Project YBPV 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 years time. The cash receipts expected are as follows:

Year (at the end) A B

1 Rs. 20,000

2 60,000 Rs. 60,0003 40,000 60,000

4 30,000 80,0005 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 -60,0001 20,000 -60,000 .935 18,700 -56,1002 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 MachineA 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 asfollows:

0 1 2 3 4 5

Machine A -25 - 5 20 14 14

Machine B -40 10 14 16 17 15

The companys 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; and4. 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 B0 -25 -40 1.00 -25.00 -40.001 - 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 11.565 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 53.58PV 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 5 243 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 B0 -25.00 -40.00 - -

1 - 9.10 - 9.102 4.15 11.62 4.15 20.72

3 15.00 12.00 19.15 32.724 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 7.28In 4

thyear, 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

2. Profitability index 1.494 1.339 A



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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 Companys 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. Theinitial capital outlay and annual cash inflows are as under:

AXE BXE

Initial capital outlay Rs. 22,50,000 Rs. 30,00,000Salvage value at the end of the life 0 0Economic life (years) 4 7

After tax annual cash inflows Year 1 Rs. 6,00,000 Rs. 5,00,0002 12,50,000 7,50,000

3 10,00,000 7,50,0004 7,50,000 12,00,000

5 - 12,50,0006 - 10,00,0007 - 8,00,000

The companys 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) PV0 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 4.814 7.50 0.552 4.14 12.50 0.552 6.90

5 - - - 12.50 0.476 5.95

6 - - - 10.00 0.410 4.107 - - - 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. lacs1 0.826 6.00 4.95 5.00 4.122 0.683 12.50 8.53 7050 5.13



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3 0.564 10.00 5.64 7.50 4.23

4 0.467 7.50 3.50 12.50 5.835 0.386 - - 12.50 4.836 0.319 - - 10.00 3.19

7 0.263 - - 8.00 2.10

Present value 22.62 29.44Less: 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 isRs. 100 lacs and that of B is Rs. 10 lacs. Both projects are expected to have a life of 8 years only and atthe 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 thecompany expects a rate of return of 10%. The companys 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 thecompany 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 119,23,800 177,25,800Less: 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

Bright Metals Ltd. is considering two different investment proposals, a and B. The details are as under:



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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 8,000Year 3 4,500 12,000

Suggest the most attractive proposal on the basis of the NPV method considering that the future incomesare 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 7,1442 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)

Project X Project Y



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Project cost 700 700

Cash inflows: Year 1 100 500

Year 2 200 400Year 3 300 200

Year 4 450 100Year 5 600 100

Assume no residual values at the end of the fifth year. The firms 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 1065.50Less: 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 78.102 200 .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 703.70 685.65Less: 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 .525 213.20 210.003 200 .389 .381 77.80 76.20

4 100 .284 .276 28.40 27.605 100 .207 .200 20.70 20.70

Total PV 705.10 697.00

Less: Initial cash outflow 700.00 700.00Net 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 lacsProject X = = 1.522

Rs. 700 lacs

Problem 12

Pioneer Steels Ltd. is considering two mutually exclusive projects. Both require an initial cash outlay ofRs. 10,000 each and have a life of five years. The companys 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 begenerated by the projects are as follows:

Year 1 2 3 4 5Project 1 Rs. 4,000 4,000 4,000 4,000 4,000Project 2 Rs. 6,000 3,000 2,000 5,000 5,000

You are required to calculate:a) The payback of each projectb) The average rate of return for each projectc) The net present value and profitability index for each projectd) 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 areto 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. 3,0002 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 12,0005 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. 4,0002 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 12,0005 5,000 2,000 3,000 1,500 1,500 3,500 15,000

Project 1 Project 2Calculation 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. 5,000Average 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. 11,373Less cash outflow = 10,000

Net present value = 1,373

Project 2:

Year Cash flow PVF (10%,n) PV0 - Rs. 10,000 1,000 Rs. 10,000

1 4,000 .909 3,636

2 2,500 .826 2,0653 2,000 .751 1,502

4 3,500 .683 2,391



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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 aremore 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%

56IRR = 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. 10,0001 4,000 .862 3,448 .855 3,4202 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 13A 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 withgreater capacity (Project Y). The cash flows under each alternative have been estimated and given below. Thecompanys 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 shouldbe used and he has calculated for each project:

i) The Net Present Valueii) The Profitability Indexiii) 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 relevantcashflows are:

Year Project X Project Y0 Rs. 27,000 Rs. 40,0001 - 10,000

2 5,000 14,000

3 22,000 16,0004 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. 40,0001 - 10,000 .909 - 9,0902 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 11,6115 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. 9,0902 Rs. 4,130 20,654

3 20,652 32,6704 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 berequired to advertise the product. This will produce net annual cash inflows of Rs. 3,00,000 at the end ofthe 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 thefifth 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 thefirms cost of capital is 20%.

b) Calculate the internal rate of return for alternative 2.



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Solution

Calculation of NPV

Alternative 1Outflows: Initial expenditure Rs. 5,00,000

Inflows: Annual Cash inflow Rs. 3,000,000Less Payment to agent 50,000

Net cash inflow 2,50,000

PVAF (20%,5y) 2.791Present value of inflows (2,50,000 x 2.791) 7,47,750Outflow: at the end of year 5 (Pyt. To agents) 1,80,000

PVF (20%,5y) .402Present Value 40,200 -40,200

Net present value Rs. 2,07,550

Alternative 2

Outflows: Initial expenditure Rs. 2,50,000Inflows: Annual Cash inflow Rs. 1,50,000

Less out of pocket expenses 50,000

Net inflow 1,00,000PVAF (20%,5y) 2.991

Present value of inflows (2.991 x 1,00,000) 2,99,100Net 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.



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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 asthat 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 Ltds 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 ifsold at the end of 5thyear. 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 existingmachine.

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% 2,80,000Net benefit 4,20,000

3. Cash inflow at the end of year 5Salvage value of new Rs. 2,00,000

4. Calculation of NPVCash 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 tosame tax rate @ 40%, then the position would be as follows:



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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 2,60,000Savings before tax 4,40,000- Tax @ 40% 1,76,000

Net benefit 2,64,000

+ Depreciation added back 2,60,000Cash 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 NPVCash 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 becomesacceptable.

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. Operatingefficiencies with the new machine will also produce savings of Rs. 2 lacs a year. Depreciation is on astraight-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 presentvalue 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



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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. 2,00,000Savings 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) 1,40,000Less tax @ 50% 70,000

Profit after tax 70,000Cash flow (PAT + Depreciation) 3,30,000PVAF (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 5

thyear Rs. 2,00,000

PVF (8%,5y) .681

Present value (2,00,000 x .681) 1,36,200Net 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 existingmachine.

Problem 17

Central Gas Ltd. in considering to enhance its production capacity. The following tw mutually exclusiveproposals are being considered:

Proposal I Proposal IIPlant Rs. 2,00,000 Rs. 3,00,000

Building 50,000 1,00,000Installation 10,000 15,000Working capital required 50,000 65,000Annual earnings (before depreciation) 70,000 95,000

Sales promotion expenses - 15,000Scrap value of plant 10,000 15,000Disposable 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:



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Proposal I Proposal IIInitial cash outflow

Cost of plant Rs. 2,00,000 Rs. 3,00,000

Installation expenses 10,000 15,000

Cost of building 50,000 1,00,000Working capital required 50,000 65,000

Total outflow 3,10,000 4,80,000

Present value of annual inflows: Proposal I Proposal IIProfit before depreciation Rs. 70,000 Rs. 95,000PVAF(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 InflowsRelease of working capital Rs. 50,000 Rs. 65,000Sale value of plant 10,000 15,000

Disposable value of building 30,000 60,00090,000 1,40,000

PVF(8%,10) .463 .463

Present value of terminal inflows Rs. 41,670 Rs. 64,820

Calculation of net present valuePV 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 B0 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, andiii)

Will it make any difference in project selection as per IRR, if the cash flows from Project B are for 8years 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 31,40916 6,000 7,000 4.040 4.344 24,240 28,280 30,408



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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 28,55619 6,000 7,000 3.706 3.954 22,235 25,942 27,67820 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 1,28017% 23,532 1,532 27,454 45418% 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 comesto 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 comesto 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 IRRmust 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 as19%, 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 lifeof 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



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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 butcould 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 30,000Book value 20,000

Profit on sale 10,000

Tax on sale (Rs. 10,000x.50) 5,000After-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 25,000Net cash flow to replace old machine with new 75,000

iii) Depreciation on new machine= 1,00,000 / 10 = Rs. 10,000Depreciation 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 2,000Increased 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

H outflow Rs. 75,000



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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 theassumption that the tax liability arises on that day itself. Moreover, in view of the advance tax payments,

this assumption seems to be logical.

88868074 capital budgeting solved problems

Documents

tax of rs

scrap value of rs

salvage value of rs

new machinecosting rs

annual fixed cost rs

allocated overheads

tax purpose

cost of new machine