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Showing posts with label Capital Budgeting numerical with solutions pdf. Show all posts

Sunday, May 30, 2021

#Techniques of Capital Budgeting solved problems pdf techniques of capital budgeting numerical with solutions pdf capital budgeting solved illustrations pdf capital budgeting notes with illustrations Financial management notes with solved illustrations

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 Techniques of Capital Budgeting

1. RBL Ltd. is considering purchasing a machinery to increase its production capacity to meet demand of its products. It is evaluating three machines. The relevant details including estimated yearly expenditure and sales are given below: Corporate Income Tax rate is 30 %.

 

Machine I

Machine II

Machine III

Initial Investment

30,00,000

30,00,000

30,00,000

Projected sales p.a.

50,00,000

40,00,000

45,00,000

Projected Cost

 

 

 

Direct Material

4,00,000

5,00,000

4,80,000

Direct Wages

5,00,000

3,00,000

3,60,000

Factory Overhead

6,00,000

5,00,000

5,80,000

Administration overhead

2,00,000

1,00,000

1,50,000

Selling and Distribution Overhead

1,00,000

1,00,000

1,00,000

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The economic life of Machine 1 is 4 years, while it is 5 years for the machine II and 6 years for machine III. The scrap values are Rs. 4,00,000, Rs. 5,00,000, and Rs. 6,00,000 respectively. Using Payback method, find out the best alternative out of three machines you will recommend to company.

Solution

 

Machine I

Machine II

Machine III

Initial Investment (1)

30,00,000

30,00,000

30,00,000

Projected sales p.a. (2)

50,00,000

40,00,000

45,00,000

Projected Cost

 

 

 

Direct Material

4,00,000

5,00,000

4,80,000

Direct Wages

5,00,000

3,00,000

3,60,000

Factory Overhead

6,00,000

5,00,000

5,80,000

Administration overhead

2,00,000

1,00,000

1,50,000

Selling and Distribution Overhead

1,00,000

1,00,000

1,00,000

Total Cost (3)

18,00,000

15,00,000

16,70,000

EBDT (2-3)

32,00,000

25,00,000

28,30,000

Less: Depreciation

(6,50,000)

(5,00,000)

(4,00,000)

EBT

25,50,000

20,00,000

24,30,000

Less tax @ 30 %

(7,65,000)

(6,00,000)

(7,29,000)

PAT

17,85,000

14,00,000

17,01,000

Add: Depreciation

6,50,000

5,00,000

4,00,000

Cash inflow (4)

24,35,000

19,00,000

21,01,000

Payback period (1÷4)

1.23 years

1.58 years

1.43 years

 

Since Machine I has lowest payback, hence company should invest in machine I.

Note: When annual cash inflows are equal

Payback Period = Initial Investment / Annual cash inflow

Depreciation = Initial investment / cost of machine – scrap value / Estimated life

Depreciation on Machinery I = (Rs.30,00,000 – Rs. 4,00,000) / 4 = Rs.6,50,000

Depreciation on Machinery II = (Rs.30,00,000 – Rs. 5,00,000) / 5 = Rs. 5,00,000

Depreciation on Machinery III = (Rs.30,00,000 – Rs. 6,00,000) / 6 = Rs. 4,00,000

2. RBL Academy Ltd. Wants to replaceone of its machines in its plant. First option available to company is Installation of equipment "King" having cost of Rs. 7,50,000 with an expectation of cash inflow of Rs. 2,00,000 p.a. for next 6 years. Second is to Install equipment "Queen" having cost of Rs. 5,00,000 which is expected to generate a cash inflow of Rs. 1,80,000 per annum for next 4 years. Which equipment should be preferred under (a) Payback period (b) Internal Rateof Return?

Solution

Payback Period Method

Since annual cash inflows are equal;

Payback period for Equipment “King” = Initial investment or cost of equipment ÷ annual cash inflow

= Rs. 7,50,000 / 2,00,000 = 3.75 years.

Payback period for Equipment “Queen” = Initial investment or cost of equipment ÷ annual cash inflow

= Rs. 5,00,000 / 1,80,000 = 2.78 years.

From Payback Period method, equipment “Queen” is better.

Internal Rate ofReturn method (IRR)

Since cash annual cash inflows are equal for both equipment;

Equipment “King”-

Initial outflow or investment = Rs. 7,50,000

Annual cash inflow = Rs.2,00,000

Calculating PVAF using Payback period method

PVAFr,6  = Rs. 7,50,000 / Rs.2,00,000 = 3.75

Looking at present value annuity factor table, the value nearest to 3.75 in the year 6 in interest rate column is 15 % (3.784) and 16 % (3.685).

Using interpolation formula

15 % +[ (3.784 – 3.75) / (3.784 – 3.685)] × (16 % - 15%) = 15.34 %

Equipment “Queen”-

Initial outflow or investment = Rs. 5,00,000

Annual cash inflow = Rs.1,80,000

PVAFr,6  = Rs. 5,00,000 / Rs.1,80,000 = 2.778

Looking at present value annuity factor table, the value nearest to 2.778 in the year 4 in interest rate column is 16 % (2.798) and 17 % (2.743).

Using interpolation formula


16 % +[ (2.798 – 2.778) / (2.798 – 2.743)] × (17 % - 16%) = 16.36 %

Since IRR of Equipment “Queen” has higher IRR so equipment “Queen”should be preferred.

3. Machine A costs 1,80,000 payable immediately. Machine B costs Rs. 2,00,000 half payable immediately and half payable in one year's time. The cash receipts expected are as follows:

Year at end

Machine A

Machine B

1

40,000

----------

2

60,000

80,000

3

70,000

1,00,000

4

50,000

1,20,000

5

50,000

-----------

At 8 % opportunity cost, which machine should be selected on the basis of NPV?

Solution

Year

Machine A

Machine B

 

Cash Flow

PVF0.08

PV = Cash Flow × PVF0.08

Cash Flow

PVF0.08

PV= Cash Flow × PVF0.08

0

(1,80,000)

1.000

(1,80,000)

(1,00,000)

1.000

(1,00,000)

1

40,000

0.926

37,040

(1,00,000)

0.926

(92,600)

2

60,000

0.857

51,420

80,000

0.857

68,560

3

70,000

0.794

55,580

1,00,000

0.794

79,400

4

50,000

0.735

36,750

1,20,000

0.735

88,200

5

50,000

0.681

34,050

-----------

0.681

--------

 

NPV

34,840

NPV

43,560

NPV = PV of Cash inflow – PV of Cash outflow

NPV of Machine B is higher than Machine A. Hence, Machine B should be selected.

4. A company is considering a new project for which requires a Capital outlay of Rs. 5,00,000 and depreciation is to be allowed at 20 % on SLM basis. Forecasted annual earnings before charging depreciation is as follows:

Year

Earnings (Rs.)

1

2,50,000

2

2,50,000

3

1,00,000

4

1,20,000

5

80,000

Total

8,00,000

Evaluate the project using (a) Payback method. (b) Rate of return on original investment.


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Solution

Payback Period

Year

Rs.

Cumulative

1

2,50,000

2,50,000

2

2,50,000

5,00,000

3

1,00,000

6,00,000

4

1,20,000

7,20,000

5

80,000

8,00,000

Total

8,00,000

 

 

Payback period = 2 years (Money invested or Capital outlay of Rs. 2,00,000 has been recovered in 2 years.)

Rate of return onoriginal investment

Year

Earnings (Rs.)

Less: Depreciation

Net Earnings

1

2,50,000

(1,00,000)

1,50,000

2

2,50,000

(1,00,000)

1,50,000

3

1,00,000

(1,00,000)

0

4

1,20,000

(1,00,000)

20,000

5

80,000

(1,00,000)

(20,000)

Total

 

 

3,00,000

 

Average income = Total net income / no. of years = Rs.3,00,000 / 5 = Rs. 60,000

Rate of return on original investment = (Average income ÷ original investment) × 100

= (Rs. 60,000 ÷ Rs.5,00,000) × 100 = 12 %.

5. RBL Academy is considering a project with an initial outflow of Rs. 1,20,000 with following cash inflow:

Year

Cash inflow

1

32,000

2

28,000

3

30,000

4

30,000

5

29,000

Total

1,49,000

Comment on the project considering cost of capital to be 7% using internal rate of return method.

Solution

Calculation of Internal rate of return

Cash outflow = Rs.1,20,000

Average cash inflow = Total cash inflow / number of years = Rs. 1,49,000 / 5 = Rs. 29,800

Approximate payback period = Cash outflow / average cash inflow

= Rs. 1,20,000 /Rs.29,800 = 4.0268

In PVAF table, value near to 4.0268 in year 5 is 4.1002 at 7 % and 3.9927 at 15%.

Year

Cash inflow

PVF at 7%

PVF at 8%

PV at 7% = Cash inflow × PVF at 7%

PV at 8% = Cash inflow × PVF at 8%

0

(1,20,000)

1

1

(1,20,000)

(1,20,000)

1

32,000

0.9346

0.9259

29907.2

29628.8

2

28,000

0.8734

0.8573

24455.2

24004.4

3

30,000

0.8163

0.7938

24489

23814

4

30,000

0.7629

0.735

22887

22050

5

29,000

0.713

0.6806

20677

19737.4

Total of PV of cash inflow

122415.4

119234.6

NPV= Total of PV of cash inflow – PV of cash outflow

2415

(765.4)

 

Using interpolation formula

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 7% + [2415/2415-(-765.4) × (11% - 10%)]

= 7% + [(2415/3180.4) × 1 %]

7% + 0.7593% = 7.7593 %

Since cost of capital is 7% and IRR is 7.7593%. Hence project should be included.

6. RBL Academy Ltd. is considering two mutually exclusive projects. The after-tax cash flows of these projects are as follows:

Year

Project A Cash flow (Rs.)

Project B Cash flow (Rs.)

0

(1,00,000)

(1,00,000)

1

30,000

 

2

30,000

 

3

30,000

 

4

30,000

 

5

30,000

1,82,500

 

Opportunity cost of capital for these projects is 10 %. Calculate

a. NPV and IRR of each project.

b. Is there any conflict in ranking of projects? Which project should be accepted?

Solution

NPV of Project A = PV of cash inflow – PV of cash outflow

= Rs. 30,000 × PVAF0.1, 5 – Rs.1,00,000

(Since there is equal cash flow, hence PVAF has been taken)

= (Rs. 30,000 × 3.7908) – Rs.1,00,000

= Rs. 1,13,724 – Rs.1,00,000 = Rs.13,724

NPV of Project B = PV of cash inflow – PV of cash outflow

= Rs. 1,90,000 × PVF0.1, 5 – Rs.1,00,000

= (Rs. 1,82,500 × 0.6209) – Rs.1,00,000 = Rs.13,314

Calculation of Internal rate of return

Project A

Initial outflow or investment = Rs. 1,00,000

Annual cash inflow = Rs.30,000

Calculating PVAF using Payback period method

PVAFr,5 = Rs. 1,00,000 / Rs.30,000 = 3.333

Looking at present value annuity factor table, the value nearest to 3.333 in the year 5 in interest rate column is 15 % (3.352) and 16 % (3.274).

We can calculate IRR using both methods

Method 1: Using interpolation formula

IRR = Lower discount rate +  × (Higher discount rate – Lower discount rate)

=   15 % +[ (3.352– 3.333) / (3.352– 3.274)] × (16 % - 15%) = 15.34 % = 15.24

Method 2 : Using NPV for IRR calculation

NPV @ 15 % = PV of cash inflow – PV of cash outflow

= Rs.30,000 × 3.352 – Rs. 1,00,000 = Rs. 560

NPV @ 16% = Rs.30,000 × 3.274 – Rs. 1,00,000 = (Rs.1,780)

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 15 % + [(560/560 + 1780) × 1) = 15.24%

Project B:

In this case, there is only one cash inflow in the year 5. We can use Trial and error method. In PVF table, at year 5, we need to find an interest rate whose value when multiplied by cash inflow gives positive return and other which gives negative return and difference between two rates is 1.

Looking into PVF table at year 5, 12 % (0.567)and 13 % (0.543)will be considered.

NPV at 12 % = PV of cash inflow – PV of cash outflow

= (Rs. 1,82,500 × 0.567) – Rs.1,00,000 = Rs. 3,477.5

NPV at 12 % = =( Rs. 1,82,500 × 0.543) – Rs.1,00,000  = (Rs. 902.5)

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 12 % + [ (3,477.5/ 3,477.5 + 902.5)] × 1 = 12.79 %

According to NPV method and IRR method, Project A is better. There is no difference in ranking A. Difference in ranking of projects arises because of difference in patterns of inflows. However, in this case from both methods, Project A is better than project B, hence, Project A should be opted.

7. A firm whose cost of capital is 10% is considering two mutually exclusive projects X and Y, The after-tax cash flows of these projects are as follows:

Year

Project X (Rs.)

Project Y (Rs.)

0

(1,00,000)

(1,00,000)

1

15,000

45,000

2

18,000

45,000

3

30,000

22,000

4

45,000

10,000

5

60,000

10,000

 

 

 

Compute the Net Present Value at 10%, Profitability Index, and Internal Rate of Return for the two projects.

Solution

Calculation of NPV & IRR

Year

Project X (Rs.)

Project Y (Rs.)

PVF @ 10 %

PV of X = PVF × cash flow

PV of Y = PVF × cash flow

0

(1,00,000)

(1,00,000)

1

(1,00,000)

(1,00,000)

1

15,000

45,000

0.909

13,635

40,905

2

18,000

45,000

0.826

14,868

37,170

3

30,000

22,000

0.751

22,530

16,522

4

45,000

10,000

0.683

30,735

6,830

5

60,000

10,000

0.621

37,260

6,210

Total of cash inflows

1,68,000

 

 

 

 

Total of PV of cash inflows

1,19,028

1,07,637

PV of cash outflow

(1,00,000)

(1,00,000)

NPV = Total of PV of cash inflows - PV of cash outflow

19,028

7,637

Profitability index = PV of cash inflows / PV of cash outflow

1.19028

1.07637

 

Calculation of IRR

Project X

Calculating PVAF using Payback period method

Payback value = Initial cash outflow / average cash inflow

Project X average cash inflow = Rs. 1,68,000 / 5 = Rs. 33,600

Payback value (PVAFr,5) = Rs. 1,00,000 / Rs.33,600 = 2.976

The PVAF table indicates that for Project X, the PV Factor closest to 2.976 against 5 years is 2.991 at 20% and In the case of Project X, since Cash inflow in the initial years are considerably smaller than the average cash flows, the IRR is likely to be much smaller than 19%. So, Project X may be tried at 15% and 16% .

Year

Project X (Rs.)

PVF @ 16 %

PVF @ 15 %

PV of cash inflow @ 15 %

PV of cash inflow @ 16 %

0

(1,00,000)

1

1

(1,00,000)

(1,00,000)

1

15,000

0.87

0.862

13050

12930

2

18,000

0.756

0.743

13608

13374

3

30,000

0.658

0.641

19740

19230

4

45,000

0.572

0.552

25740

24840

5

60,000

0.497

0.476

29820

28560

Total of PV of cash inflows

101958

98934

NPV

1,958

(1,066)

 

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 15 % + [ (1,958/ 1,958 + 1,066) × 1] = 15.65%

Project Y

Calculating PVAF using Payback period method

Payback value = Initial cash outflow / average cash inflow

Project Y average cash inflow = Rs.1,32,000/5 = Rs.26,400

Payback value (PVAFr,5) = Rs. 1,00,000 / Rs.26,400 = 3.788

Looking at present value annuity factor table, the value nearest to 3.788 in the year 5 in interest rate column for Project Y, is 3.791 at 10%. In the case of Project Y, Cash inflow in the initial years are considerably larger than the average cash flows, the IRR is likely to be much higher than 10%. Project Y may be tried at 14% and 15%

Year

Project Y (Rs.)

PVF @ 14 %

PVF @ 15 %

PV of cash inflow @ 14 %

PV of cash inflow @ 15 %

0

(1,00,000)

1

1

(1,00,000)

(1,00,000)

1

45,000

0.877

0.87

39465

39150

2

45,000

0.769

0.756

34605

34020

3

22,000

0.675

0.658

14850

14476

4

10,000

0.592

0.572

5920

5720

5

10,000

0.519

0.497

5190

4970

Total of PV of cash inflows

100030

98336

NPV

30

1,664

 

IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 14 % + [ (30 / 30 + 1,664) × 1] = 14.02 %

8. A Company requires an initíal investment of Rs. 50,000. The estimated net cash flow are as follows-

Year

1

2

3

4

5

6

7

8

9

10

Cash inflow

8000

8000

8000

10000

10000

15000

8000

10000

8000

5000

 

Using 10% as the cost of capital (rate of discount), determine (i) Pay-back period (ii) Net Present Value and (iii) Internal Rate of Return.

Solution

Payback period:

Payback refers to time period in which initial cash outflow is recovered. Cash inflow generated in first 5 year = Rs. 44,000

Remaining cash outlay to be recovered = Rs.50,000 – Rs.44,000 = Rs.6,000

6th year cash inflow = Rs. 15,000

Payback period = 5 years + (6000/15,000) = 5.4 years

NPV calculation

Year

1

2

3

4

5

6

7

8

9

10

Cash inflow

8000

8000

8000

10000

10000

15000

8000

10000

8000

5000

PVF@ 10%

0.909

0.826

0.751

0.683

0.621

0.564

0.513

0.467

0.424

0.386

PV of cash inflow

7272

6608

6008

6830

6210

8460

4104

4670

3392

1930

 

NPV = PV of cash inflow – PV of cash outflow = Rs.55,484 – Rs.50,000 = Rs.5,484

IRR calculation

Calculating PVAF using Payback period method

Payback value = Initial cash outflow / average cash inflow

Average cash inflow = Rs. 90,000 / 10 = Rs. 9,000

Payback value (PVAFr,10) = Rs. 50,000 / Rs.9,000 = 5.556

Looking at present value annuity factor table, the value nearest to 5.556 in the year 10 in interest rate column is 12 % (5.650) and 13 % (5.426).

Year

1

2

3

4

5

6

7

8

9

10

Cash inflow

8000

8000

8000

10000

10000

15000

8000

10000

8000

5000

PVFat12%

0.893

0.797

0.712

0.636

0.567

0.507

0.452

0.404

0.361

0.322

PV of cash inflow at 12 %

7144

6376

5696

6360

5670

7605

3616

4040

2888

1610

PVF@13%

0.885

0.783

0.693

0.613

0.543

0.48

0.425

0.376

0.333

0.295

PV of cash inflow at 13%

7080

6264

5544

6130

5430

7200

3400

3760

2664

1475

 

NPV at 12 % = Rs. 51,005 – Rs. 50,000 = Rs. 1,005

NPV at 13 % = Rs. 48,947 – Rs.50,000 = (Rs.1,053)

IRR = IRR = Lower discount rate + [NPV at lower rate / (NPV at lower rate – NPV at higher rate) × (Difference between two rates)]

= 12% + [ 1005/(1005 + 1,053) × 1] = 12.49%

 

9. RBL Academy Ltd. is considering the introduction of a new product. It is estimated that profits before depreciation would increase by Rs. 2, 00,000 each year for first four years and Rs. 1,00,000 each for the remaining period. An advertisement cost of Rs. 20,000 is expected to be incurred in the first year, which is not included in the above estimate of profits. The cost will be allowed for tax purpose in the first year. A new plant costing Rs.4,00,000 will be installed for the production of the new product. The salvage value of the plant after its life of 10 years is estimated to be Rs. 50,000. Working capital investment of Rs. 50,000 will be required in the year of installing the plant and a further Rs. 30,000 in the following year. The company's tax rate is 30% and written down value depreciation at 25%. If the company's required rate of return is 20%, should the company introduce the new product? Ignore tax effect on Profit/Loss on sale of asset.

Solution

Calculation of Depreciation

Year

1

2

3

4

5

6

7

8

9

10

WDV

400000

300000

225000

168750

126563

94922

71191

53394

40045

30034

Depreciation

100000

75000

56250

42188

31641

23730

17798

13348

10011

7508

 

Calculation of PV of Cash inflow

Year

PBDT

less:Dep

PBT

Less:Tax

PAT

Add:Dep

Cash inflow

PVF @20%

PV of cash inflow

1

180000

100000

80000

24000

56000

100000

156000

0.833

129948

2

200000

75000

125000

37500

87500

75000

162500

0.694

112775

3

200000

56250

143750

43125

100625

56250

156875

0.579

90831

4

200000

42188

157813

47344

110469

42188

152656

0.482

73580

5

100000

31641

68359

20508

47852

31641

79492

0.402

31956

6

100000

23730

76270

22881

53389

23730

77119

0.335

25835

7

100000

17798

82202

24661

57542

17798

75339

0.279

21020

8

100000

13348

86652

25995

60656

13348

74005

0.233

17243

9

100000

10011

89989

26997

62992

10011

73003

0.194

14163

10

100000

7508

92492

27748

64744

7508

72252

0.162

11705

10

Working capital released

80000

0.162

12960

10

Scrap value of plant

50000

0.162

8100

 

Total of PV of Cash inflow

550115

 

Note: PBDT for year 1 has been taken after subtracting advertisement expense.

PV of cash outflow = Initial outflow + working capital in year zero + working capital in year 1

= Rs. 4,00,000 + Rs.50,000 + Rs.24,990  = Rs. 4,74,990

Working capital in year 1 after discounting at 20 % = Rs.30,000 × 0.833(PVF0.2,1) = Rs.24,990

NPV = PV of cash outflow – PV of cash inflow = Rs.5,50,115 - Rs. 4,74,990 = Rs.75,125

Since, NPV is positive, hence project should be accepted.

10. A company is engaged in evaluating an investment project which requires an initial cash outlay of Rs. 2,50,000 on equipment. The project's economic life is 10 years and its salvage value 30,000. It would require current assets of Rs. 5 0,000. An additional investment of Rs. 60,000 would also be necessary at the end of five years to restore the efficiency of the equipment. This would be written off completely over the last five years. The project is expected to yield annual profit (before tax) of Rs. 1,20,000. The company follows the sum of the years digit method of depreciation. Income-tax rate is assumed to be 30%. Should the project be accepted if the minimum required rate of return is 22 %.

Solution

The depreciation of different years have been calculated as per sum of the vear's digit method as follows:

Initial outlay - Salvage value

 Rs. 2,50,000 -  Rs.30,000 = Rs. 2,20,000 is to be depreciated over 10 years.

The sum of the years digits for the vears 1-10 is 55.

1+2+3+4+5+6+7+8+9+10 = 55

So, depreciation for year 1 is Rs. 2,20,000 x (10/55) = Rs.40,000

And for the year 2 it is 2,20,000 x (9/55)  = Rs.36,00 and so on.

The total depreciation for first 5 years is Rs. 1,60,000 and so the written down value of the asset at the end of year 5, is Rs. 90,000 (i.e., Rs. 2,50,000 – Rs. 1,60,000).

A capital expenditure of Rs. 60000 is required at that stage. So, the total cost required to be depreciated is Rs.  1,20,000 ( ie, Rs. 90,000- Rs. 60,000 – Rs.30,000) .

As per the sum of the years digit method for 5 years (ie, remaining life), the depreciation for the year 6 is Rs. 1,20,.000 x (5/15) = Rs.40,000

for year 2 is Rs. 1,20,000 x( 4/15) = Rs.32,000 and so on.

Year

1

2

3

4

5

6

7

8

9

10

EBDT

120000

120000

120000

120000

120000

120000

120000

120000

120000

120000

Less: Dep

40,000

36,000

32,000

28,000

24,000

40,000

32,000

24,000

16,000

8,000

EBT

80,000

84,000

88,000

92,000

96,000

80,000

88,000

96,000

104,000

112,000

Less: Tax

24000

25200

26400

27600

28800

24000

26400

28800

31200

33600

PAT

56,000

58,800

61,600

64,400

67,200

56,000

61,600

67,200

72,800

78,400

Add: Dep

40,000

36,000

32,000

28,000

24,000

40,000

32,000

24,000

16,000

8,000

Cash Inflow

96,000

94,800

93,600

92,400

91,200

96,000

93,600

91,200

88,800

86,400

Terminal cash inflow

Salvage value + current asset= Rs.30,000 +  Rs.50,000 = Rs. 80,000

80000

PVF at22%

0.82

0.672

0.551

0.451

0.37

0.303

0.249

0.204

0.167

0.137

PV of cash inflow

78720

63706

51574

41672

33744

29088

23306

18605

14830

11837

PV of Terminal cash inflow

 

 

 

 

 

 

 

 

 

10,960

Total of PV of cash inflow including Terminal value

 

 

 

 

 

 

 

 

 

3,78,041

Present value of cash outflow = Initial cost + current asset + PV of investment in 5th year

= Rs.2,50,000 + Rs.50,000 + Rs.60,000 × 0.37 = Rs.3,22,200

NPV = Total of PV of cash inflow including Terminal value - Present value of cash outflow

= Rs. 3,78,041 - Rs.3,22,200  = Rs.55,841

Since, NPV is positive, hence project should be accepted.

11. Delhi Machinery manufacturing Company wants to replace its manual operations by new machine. There are two alternative models A and B the new machine. Using Payback period, suggest the most profitable investment. Ignore taxation.

 

A

B

Original Investment (Rs.)

20,000

30,000

Estimated life of the Machine  (Years)

4

6

Estimated Savings in Cost (Rs. )

10,000

10,000

Estimated Savings in Wages (Rs.)

6,000

4,000

Additional Cost of Maintenance (Rs.)

5,000

2,000

Additional Cost of Supervision (Rs.)

3,000

2,000

 

Solution:

 

A

 

Estimated Savings in Cost (Rs. )

10,000

10,000

Estimated Savings in Wages (Rs.)

6,000

4,000

Less: Additional Cost of Maintenance (Rs.)

(5,000)

(2,000)

Less: Additional Cost of Supervision (Rs.)         

3,000)

(2,000)

Net cash inflow

8,000

10,000

Payback period

20,000/8,000 = 2.5 years

30,000/10,000= 3 years

Project A should be opted

 

12. RST is evaluating two mutually exclusive proposals, A and B. Following information is available about these projects:

 

Project A

Project B

Project Cost (Rs.)

6,00,000

8,00,000

Annual Cash Expenses (Rs.)

1,00,000

1,30,000

Life (Years)

10 years

10 years

Salvage Value (Rs.)

1,00,000

1,00,000

 

Other Information: Tax rate 40%, Required Rate of Return 12%; Evaluate the proposals on the basis of incremental Cash flows. (Proposal B over Proposal A).

Solution

Project A

Project B

B over A

Initial Cost

(600000)

(800000)

-200000

Annual Expenses

(100000)

(130000)

(30000)

Depreciation P.a.

(50000)

70000

20000

Annual deductible expenses (Annual Expenses + Depreciation P.a.)

(150000)

(200000)

(50000)

Annual tax saving @40 %

60000

80000

20000

Net outflow (annual deductible Expense - Tax saving  )

(90000)

(120000)

(30000)

Terminal inflow (salvage value)

100000

100000

0

Calculation of NPV

PV of Annual outflows

90000 * 5.65 = (5,08,500)

120000* 5.65 = (6,78,000)

(169500)

Initial Cost /outflow

(600000)

(800000)

(200000)

Total outflows (PV) = PV of Annual outflows +Initial Cost /outflow

(1108500)

(1478000)

(369500)

Less PV of salvage (100000*0.322)

32200

32200

0

NET Present Value

1076300)

(1445800)

(369500)

 

Since Project B has negative NPV over A , Proposal A should be preferred.

13. The Eastern Corporation Ltd., a firm in the 30% tax bracket with a 15% required rate of return, is considering a new project. This project involves the introduction of a new product. This project is expected to last five years and then to be terminated. Given the following information, determine the after-tax cash flows associated with the project and then find the project's net present value and advise the company whether it should invest in the project or not.

Cost of new Plant and Equipment: Rs. 20,90,000

Shipping and Installation Cost Rs. 30,000

Unit sales

Year

Units Sold

1

10,000

2

13,000

3

16,000

4

10,000

5

6,000

 

Sales Price per unit: Rs. 500/unit in years 1-4 and Rs. 380/unit in year 5

Variable Cost per unit: 260/unit

There will be an initial Working capital requirement of Rs. 80,000 just to get production started. For each year, the total investment in net working capital will be equal to 10% of the rupee value of sales for that year. Thus, the investment in working capital will increase during years 1 through 3, then decrease in year 4. Finally, all working capital is liquidated at the termination of the project at the end of year 5. Use straight-line method for providing depreciation over five years assuming that the plant and equipment will have no salvage value after five years.

Solution

Initial Cash outflow = Cost of machine + Installation cost + Initial Working Capital requirement + Working Capital required for Year 1 in the beginning of the year

= Rs. 20,90,000 + 30,000 + 80,000 + 5,00,000(10 % of sales of first year = 10 % of Rs.50,00,000)

= Rs.27,00,000

Depreciation = (Cost of machine + Installation cost – salvage value) ÷ estimated life

= (Rs. 20,90,000 + Rs.30,000) ÷ 5 = Rs.4,24,000

Change in WC = New WC – Existing WC = Current Year  WC – Previous Year WC

Particulars

Year 1

Year 2

Year 3

Year 4

Year 5

Sales (Units)

10,000

13,000

16,000

10,000

6,000

Selling Price /unit )

500

500

500

500

500

Sales

50,00,000

65,00,000

80,00,000

50,00,000

22,80,000

Less: Variable Cost at Rs. 260

(26,00,000)

(33,80,000)

(41,60,000)

(26,00,000)

(15,60,000)

PBDT

24,00,000

31,20,000

38,40,000

24,00,000

7,20,000

Less: Depreciation

(4,24,000)

(4,24,000)

(4,24,000)

(4,24,000)

(4,24,000)

PBT

19,76,000

26,96000

34,16,000

19,76,000

2,96,000

Less: Tax @ 30 %

(5,92800)

(8,08,800)

(10,24,800)

(5,92,800)

(88,800)

PAT

13,73,200

18,87200

23,91,200

13,83,200

2,07200

Add: Depreciation

4,24,000

4,24,000

4,24,000

4,24,000

4,24,000

Operating Cash inflow (1)

17,97,200

23,11,200

28,15,200

18,07,200

6,31200

WC requirement for N+1 year

6,50,000

8,00,000

5,00,000

2,28,000

-----

Change in WC (2)

1,50,000(6,50,000-5,00,000)

1,50,000

(3,00,000)

(2,72,000)

(2,28,000)

Release of WC in year 5 (3)

 

 

 

 

80,000

Net cash flow (1-2+3)

16,47,200

21,61200

31,15,200

20,79,200

9,39,200

PVF at 15%

.870

.756

.658

.572

.497

PV of cash inflow

14,33,064

16,33,867

20,49,802

11,89,302

4,66,782

 

NPV = PV of cash inflow – PV of cash outflow

= Rs.67,72,817 – Rs.27,00,000 = Rs.40,72817

Since NPV is positive, project should be accepted.

14. A particular project has a four years life with yearly projected net profit of Rs. 10,000 after charging yearly depreciation of Rs.8000 but before charging tax in order to write off the capital cost of Rs. 32,000. Out of the capital cost, Rs. 20,000 is payable immediately (year 0) and balance in next year (which will be needed for evaluation). Stock amounting to Rs. 6,000 (to be invested in year 0) will be required throughout the project and for debtors a further sum of 8,000 will have to be invested in year 1. The working capital will be recouped in year 5. It is expected that the machinery will fetch a residual value of Rs. 2,000 at the end of 4th year. Income tax is payable @ 40% and the cost of capital is 10%. Income tax is payable next year. The residual value of the machine, Rs. 2,000 will also bear tax @ 40%. Although the profit is for 4 years, for computation of tax and realization of working capital, the computation will be required up to 5 years. Advise the firm.

Solution

Initial Outflows = capital cost at T0 + capital cost at T1 + Working Capital (Stocks) at T0 + Working Capital (Debtors) at T1

Rs.20,000 + (Rs.12,000 × 0.909) + Rs.6,000 + (Rs.8,000 × 0.909) = Rs.44,180

Subsequent annual Cash inflows

 

Year 1

Year 2

Year 3

Year 4

Year 5

Net Profit

10,000

10,000

10,000

10,000

10,000

Add: Residual Value

 

 

 

 

2,000

Less: Tax @ 40% of preceding year profit

 

(4,000)

(4,000)

(4,000)

(4,800)

Add: Depreciation

8,000

8,000

8,000

8,000

 

Add: Working capital recovered

 

 

 

 

14,000

Cash inflow

18,000

14,000

14,000

16,000

9,200

PVF @ 10%

0.909

.826

.751

.683

.621

PV

16,362

11,564,

10,514

10,928

5,713

Total PV of cash inflow

 

 

 

 

55,081

Less: Initial cash outflow

 

 

 

 

(44,180)

NPV

 

 

 

 

10,901

 

Since NPV is positive, hence project should be accepted.

15. ABC & Co.is considering a proposal to replace one of its plants costing Rs. 60,000 and having a written down value of Rs. 24,000. The remaining economic life of the plant is 4 years after which it will have no salvage value. However, if sold today, it has a salvage of Rs. 20,000. The new machine costing Rs. 1,30,000 is also expected to have a lite of 4 years with a scrap value of Rs. 18,000. The machine, due to its technological superiority, is expected to contribute additional annual benefit (before depreciation tax) of Rs. 60,000. Find out the cash flows associated with the decision given that the tax rate applicable to the firm is 40%. (The capital gain or loss may be taken as not subject to tax).

Solution

Initial cash outflow = cost of machine – Salvage value of existing machine

= Rs.1,30,000  - Rs.20,000 = Rs.1,10,000

Subsequent annual cash inflow

 

Rs.

Annual benefits (PBDT)

60,000

Less: Incremental Depreciation (Rs.28,000 – Rs.6,000) [Dep on new machine – Dep on old machine]

(22,000)

Incremental Profit before Tax

38,000

Less: Tax @ 40 %

(15,200)

Incremental Profit after Tax

22,800

Add: Incremental Depreciation

22,000

Incremental cash inflows

44,800

Terminal inflow at the end of the year of Project

18,000

 

16. A machine purchased six years back for Rs. 1,80,000 has been depreciated to a book value of Rs. 1,08,000. It originally had a projected life of 15 years (Salvage nil). There is a proposal to replace this machine. A new machine will cost Rs. 2,50,000 and result in reduction of operating cost by Rs. 30,000 p.a. for next nine years. The existing machine can now be scrapped away for Rs. 60,000. The new machine will also be depreciated over 9 years period as per straight line method with salvage of 25,000. Find out whether the existing machine be replaced or not given that the tax rate applicable is 30% and cost of capital 10% (profit or loss on sale of assets is to be ignored for tax purposes).

Solution

Initial outflow = Cost of new machine – Salvage value of existing machine

= Rs. 2,50,000 – Rs.60,000 = Rs.1,90,000

Depreciation on new machine = (Cost of machine – Salvage value)/ estimated life = (Rs.2,50,000- Rs.25,000) /9 = Rs.25,000

Depreciation on old machine = Rs.1,80,000/15 or Rs.1,08,000/9 = Rs.12,000

Incremental Depreciation = Depreciation on new machine – Depreciation on old machine

= Rs.25,000 – Rs.12,000 = Rs.13,000

Annual incremental Cash inflow calculation

Particulars

Rs.

Decrease in operating cost (PBDT)

30,000

Less: Incremental Depreciation

(13,000)

Incremental PBT

17,000

Less: Tax @ 30%

(5,100)

Incremental PAT

11,900

Add: Incremental Depreciation

13,000

Incremental Annual cash inflow

24,900

Terminal cash inflow (Salvage value )

25,000

PV of Incremental Annual cash inflow = 24,900 ×5.758 (PVAF.1, 9)

1,43,374

PV of terminal cash inflow = 25,000 × 0.424 (PVF0.1, 9)

10,600

Total Present value of inflow = 1,43,374 + 10,600

1,53,974

NPV = Total Present value of inflow - Initial outflow = 1,53,974 – 1,90,000

(36,026)

Since, NPV is negative, hence old machine should be kept and replacement decision should not be opted.

17. RBL Ltd. has a machine having an additional life of 5 years which costs Rs. 10,00,000 and has a book value of Rs. 4,00,000. A new machine costing Rs.20,00,000 is available. Though its capacity is the same as that of the old machine, it will mean a saving inn variable costs to the extent of Rs. 7,00,000 per annum. The life of the machine will be 5 years at the end of which it will have a scrap value of Rs. 2,00,000. The rate of income-tax is 40% and P. Ltd.'s policy is not to make an investment if the yield is less than 12% per annum. The old machine, if sold today, will realize Rs. 1,00,000; it will have no salvage value if sold at the end of 5th year. Advise P. Ltd. whether or not the old machine should be replaced. Capital gain is tax free.. Will it make any difference, if the additional depreciation (on new machine) and loss on sale of old machine is also subject to same tax at the rate of 30%, and the scrap value of the new machine is Rs. 3, 00,000.

Solution

Case : Ignoring  income-tax saving on additional depreciation as well as on loss due to sale of existing machine:

 Initial Cash outflow = Cost of new machine – Scrap value of old machine

= Rs.20,00,000 – Rs.1,00,000 = Rs.19,00,000

Annual cash inflow

 

 

Net saving in variable cost

7,00,000

Less: Tax at 30%

(2,10,000)

Net benefit / Annual cash inflow

4,90,000

Terminal cash inflow at the end of year 5 (Salvage value of new machine)

2,00,000

PV of cash inflow:

Annual cash inflow × PVAF0.12, 5 = 4,90,000 × 3.605 = 17,66,450

Terminal cash inflow × PVF0.12, 5 = 2,00,000 × 0.567 = 1,13,400

Total of PV of Cash Inflow =

 

 

 

18,79,850

Less: PV of cash outflow

(19,00,000)

NPV

(20,150)

Since NPV is negative, there is no need to replace existing machine.

 

 

Case II: if the additional depreciation (on new machine) and loss on sale of old machine is also subject to same tax at the rate of 30%, and the scrap value of the new machine is Rs. 3, 00,000.

Incremental Depreciation = Depreciation on new machine – Depreciation on old machine

= (Rs.20,00,000 – Rs.3,00,000)/5 – Rs.4,00,000/5= Rs. 2,60,000

Cash outflow = Cost of new machine – salvage value of old machine – Tax saving on capital loss on sale of old machine

= Rs.20,00,000 – Rs.1,00,000 – Rs. 90,000 (30 % of Rs.4,00,000 – Rs.1,00,000) = Rs.18,10,000

 

 

Net saving in variable cost (PBDT)

7,00,000

Less: Incremental depreciation

(2,60,000)

Incremental PBT

4,40,000

Less: Tax at 30%

(1,32,000)

Incremental PAT

3,08,000

Add: Incremental Depreciation

2,60,000

Incremental annual cash inflow

5,68,000

Terminal cash inflow at the end of year 5 (Salvage value of new machine)

3,00,000

PV of cash inflow:

Annual cash inflow × PVAF0.12, 5 = 5,68,000 × 3.605 = 20,47,640

Terminal cash inflow × PVF0.12, 5 = 3,00,000 × 0.567 = 1,70,100

Total of PV of Cash Inflow =

 

 

 

22,17,740

Less: PV of cash outflow

(18,10,000)

NPV

4,07,740

Since NPV is positive, company should replace existing machine

 


18. XYZ Ltd. is considering the purchase of a new computer system for its Research and Development Division, which would cost Rs. 35,00,000. The operation and maintenance costs (excluding depreciation) are expected to be Rs. 7 lacs per annum. It is estimated that the useful life of the system would be 6 years, at the end of which the disposal value is expected to be Rs. 1,00,000. The tangible benefits expected from the system in the form of reduction in design and draftsmanship costs would be Rs.12,00,000 per annum. Besides, the disposal of used drawing office equipment and furniture, initially, is anticipated to net Rs. 10,00,000. Capital expenditure in research and development would attract 100 % write-off for tax purposes. The gains arising on disposal of used assets may be considered tax-free. If company's effective tax rate is 40%. The average cost of capital to the company is 12%. After appropriate analysis of cash flows, please advise the company of the financial viability of the proposal.

Solution

Cash outflow = Cost of new computer – Disposal of used drawing office

= Rs.35,00,000 – Rs.10,00,000 = Rs.25,00,000

Annual cash inflow calculation

Particulars

Rs.

Saving in Design and draftsmanship cost

12,00,000

Less : Operation and maintenance cost

(7,00,000)

PBT

5,00,000

Less: Tax @ 40 %

(2,00,000)

PAT/ Annual cash inflow

3,00,000

Tax saving on purchase of computer system to be available at the end of year 1 =35,00,000 × 0.4

14,00,000

Terminal value (Disposal/salvage value)

1,00,000

 

Calculation of Present value of annual cash flow and NPV

Year

Cash flow

PVF at 12%

PV

0

(25,00,000)

1

(25,00,000)

1

3,00,000 + 14,00,000(Tax saving) = 17,00,000

0.893

15,18,100

2

3,00,000

0.797

2,39,100

3

3,00,000

0.712

2,13,600

4

3,00,000

0.636

1,90,800

5

3,00,000

0.567

1,70,100

6

3,00,000 + 1,00,000 (Terminal value) = 4,00,000

0.507

2,02,800

 

NPV

 

34,500

Since NPV is positive, hence project should be opted.

 

19. Central Gas Ltd. is considering enhancing its production capacity. The following two mutually exclusive proposals are being considered

 

Proposal I

Proposal II

Plant

2,00,000

3,00,000

Building

50,000

1,00,000

Installation cost

10,000

15,000

Working capital required

50,000

65,000

Annual Earnings (before depreciation)

70,000

95,000

Sales Promotion expenses

------------

15,000

Scrap Value of Plant

10,000

15,000

Disposable Value of Building

30,000

60,000

 

Life of the Project is 10 years. Sales promotion expenses of Proposal l are required to be incurred at the end of 2nd year? These expenses have not been considered to find out the Annual earnings (given above). Which proposal be accepted given that the cost of capital of the firm is 10%. Ignore taxation.

Solution

In this case, the Annual earnings before depreciation are given for the proposals. As the tax is to be ignored, these earning may be considered as cash flows also. (It may be noted that there is no tax benefit of depreciation in this case). The two proposals may be evaluated as follows:

 

Proposal I

Proposal II

Initial cash outflow:

Cost of Plant

Add: Installation cost

Add: Cost of Building

Add: WC required

 

2,00,000

10,000

50,000

50,000

 

3,00,000

15,000

1,00,000

65,000

Total Initial cash outflow (I)

3,10,000

4,80,000

Annual cash inflow

Profit before Depreciation

PVAF0.1, 10

PV (Profit before Depreciation × PVAF0.1, 10)

Less: Present value of sales promotion expenses

15,000 ×0.826 (PVF0.1, 2)

 

70,000

6.145

4,30,150

 

95,000

6.145

5,83,775

(12,390)

Total of Present value Annual cash inflow (II)

4,30,150

5,71,385

Terminal value

Working capital released

Sale value of plant

Disposable value of building

Total Terminal value

PVF0.1, 10

 

50,000

10,000

30,000

90,000

0.386

 

65,000

15,000

60,000

1,40,000

0.386

Total of Present value of Terminal value (III)

34,740

54,040

NPV = II + III - I

1,54,890

1,45,425

Since NPV of Project I has higher NPV than Project II. Hence Project I should be accepted.

 

20. ABC Ltd. is in the business of manufacturing coir mattresses. It has a plant on a piece of land measuring two acres which was purchased ten years ago for Rs. 10 lacs. The firm is now planning to set up another plant on the same land. 50% of the existing plot is to be earmarked for this purpose. The accountant has supplied the following information:

Capital Expenditure for setting up new plant (incurred in the beginning of the year):

Year 1:

 Cost of land Rs. 5,00,000

Land Development Rs.  17,00,000

Payment for purchase of Machine Rs.18,00,000

Year 2:

Final payment for Land Development Rs. 13,00,000

Final payment to Machine supplier Rs. 67,00,000

The Plant has an estimated useful life of 5 years and company follows SL method of depreciation. The information regarding sales and operational expenses is as follows:

Year

1

2

3

4

5

Sales (Rs.)

25 Lakh

30 Lakh

35 Lakh

40 Lakh

45 Lakh

Expenses (Rs.)

5 Lakh

7 Lakh

10 Lakh

12 Lakh

15 Lakh

During first year and last year, all sales will be cash sales. In others, 10% of sales will be on credit for a period of one year. If the company’s rate of discount is 15% and the tax rate is 30% should the above proposal be accepted, given that payment for Land Development does not quality for tax rebate.

Solution

Calculation of PV of cash outflows

Outflow in the beginning of the year

 

Land development

17,00,000

Payment for machinery

18,00,000

 

35,00,000

Outflow in the beginning of year 2

 

Final payment for land development

13,00,000

Final Payment for Machine

67,00,000

 

80,00,000

PV of outflow in the beginning of year 2 or at the end of year 1

80,00,000 × .870 (PVF0.15, 1) =

69,60,000

Total Cash outflow = 35,00,000 + 69,60,000

1,04,60,000

 

Change in Working Capital arising out of credit sales:

In First year 100 % cash sales  - So No change in Working capital.

Year 2: 10 % of sales Rs. 30,00,000 is on credit, hence Rs. 3,00,000 has been subtracted

Year 3 : Previous year credit sales received Rs. 3,00,000

Current Year Credit sales = 10 % of Rs. 35,00,000 = Rs. 3,50,000

Hence change in working capital = Rs. 3,00,000 – Rs. 3,50,000 = (Rs.50,000)

Year 4: Previous year credit sales received Rs. 3,50,000

Current Year Credit sales = 10 % of Rs. 40,00,000 = Rs. 4,00,000

Hence change in working capital = Rs. 3,50,000 – Rs. 4,00,000 = (Rs.50,000)

Year 5: Previous year credit sales received Rs. 4,00,000

Current Year 100% sales is on cash, so no credit sales and debtor exist and an extra of Rs.4,00,000 received of previous year. Hence change in working capital = Rs.4,00,000 – Rs.0 = Rs.4,00,000.

Cash Inflow calculation along with NPV

Particulars

Year 1

Year 2

Year 3

Year 4

Year 5

Sales

2500000

3000000

3500000

4000000

4500000

Less: Expenses

(500000)

(700000)

(1000000)

(1200000)

(1500000)

Less: Depreciation

(1800000)

(1800000)

(1800000)

(1800000)

(1800000)

PBT

200000

500000

700000

1000000

1200000

Less Tax @ 30 %

(60000)

(150000)

(210000)

(300000)

(360000)

PAT

140000

350000

490000

700000

840000

Add: Depreciation

1800000

1800000

1800000

1800000

1800000

Change in WC

(300000)

(50000)

(50000)

400000

Cash Flow

1940000

1850000

2240000

2450000

3040000

PVF at 15 %

0.87

0.756

0.658

0.572

0.497

PV of cash inflow

1687800

1398600

1473920

1401400

1510880

Total PV of Cash Inflow

74,72,600

Total PV of Cash Outflow

(1,04,60,000)

NPV

(29,87,400)

Since NPV is negative, hence the project should not be opted.

 

21. The Income Statement of X Ltd. for the current year is as follows

Particulars

Rs.

Sales

7,00,000

Less:

Cost of Material

Labour

Other operating cost

Depreciation

 

(2,00,000)

(2,50,000)

(2,50,000)

(80,000)

EBIT

1,00,000

Less: Tax @ 30 %

(30,000)

Profit after Tax

70,000

 

The Plant Manager proposes to replace an existing machine by another machine costing Rs. 2,40,000. The new machine will have 8 years life having no salvage value. It is estimated that new machine will reduce the labour costs by Rs. 50,000 per year. The old machine will realize Rs. 40,000. Income statement does not include the depreciation on old machine (the one that is going to be replaced) as the same had been fully depreciated for tax purposes last year though it will still continue to function, if not replaced, for a few years more. It is believed that there will be no change in other expenses and revenue of the firm due to his replacement. The company requires a "After-Tax Return of 10%. The rate of tax applicable to company's income is 30%. Should the company buy the new machine, assuming that the company follows straight line method of depreciation?

Solution

Initial Cash Outflow

Cost of new Machine – Salvage value of existing machine + Tax on gain of sale of existing machine

= Rs.2,40,000 – Rs.40,000  + Rs.12,000 = Rs.2,12,000.

Profit on sale of existing Machine = Salvage value - Book value = Rs.40,000 – Re. 0 = Rs.40,000

Tax on gain on sale of existing machine = 30 % of Rs.40,000 = Rs.12,000.

Calculation of Annual incremental Cash inflow

Particulars

Rs.

Saving in Labour expenses

50,000

Less: Depreciation on new Machine

(30,000)

Incremental PBT

20,000

Less: Tax @ 30 %

(6,000)

PAT

14,000

Add: Depreciation

30,000

Incremental Cash inflow

44,000

PVAF0.1, 8

5.335

PV of incremental cash inflow

2,34,740

Less: PV of cash outflow

(2,12,000)

NPV

22,740

Since NPV is positive, hence replacement of machine should be opted.

 

22. Strong Enterprises Ltd. is a manufacturer of high quality running shoes. Mr. RBL, President, is considering the company's ordering, inventory and billing procedures. He estimates that the annual savings from computerization include a reduction of ten clerical employees with annual salaries of Rs.  15,000 each, Rs. 18,000 from reduced production delays caused by raw materials inventory problems, Rs.12,000 from lost sales due to inventory stock outs and Rs.10,000 associated with timely billing procedures. The purchase price of the System is 2,00,000 and installation costs are Rs.50,000. These outlays will be capitalised (depreciated) on a straight-line basis to a zero book salvage value which is also its market value at the end of five years. Operation of the new system requires two computer specialists with annual salaries of Rs. 40,000 per person. Also annual maintenance and operating (cash) expenses of Rs.12,000 are estimated to be required. The company's tax rate is 30% and its required rate of return (cost of capital) for this project is 12%. You are required to

(a) Find the project's different cash flows.

(b) Evaluate the project using NPV method, PI method, and payback period method.

(c) Find the project's cash flows and NPV assuming that the system can be sold for Rs. 30,000 at the end of five years even though the book salvage value will be zero and that capital gain is subject to tax.

(d) Find the project's cash flows and NPV assuming that the book salvage value for depreciation purposes is Rs. 20,000 even though the machine is worthless is terms of its resale value, and that such loss of Rs.20,000 (book value) is allowed for tax purposes.

Solution

a. Initial cash outflow = Cost of system + Installation cost = Rs.2,00,000 + Rs.50,000 = Rs.2,50,000.

Depreciation = (Cost of system + Installation cost) ÷ Project life = Rs.2,50,000/5 = Rs.50,000.

Calculation of subsequent cash inflow

Particulars

Rs.

Saving due to installation of new system

 

Savings due to Reduction in clerk salaries

1,50,000

Savings due to reduction in production delays

18,000

Savings due to reduction in lost sales

12,000

Gains due to timely billing

10,000

Total savings

1,90,000

Less: additional specialists cost

(70,000)

Less: Maintenance cost

(20,000)

PBDT

1,00,000

Less: Depreciation

(50,000)

PBT

50,000

Less: Tax @ 30 %

(15,000)

PAT

35,000

Add: Depreciation

50,000

Annual Cash inflow

85,000

PVAF.12, 5

3.517

PV of cash inflow

2,98,945

PV of cash outflow

(2,50,000)

B. NPV = PV of cash inflow - PV of cash outflow

48,945

Profitability Index = PV of cash inflow / PV of cash outflow

1.2

Payback period = PV of cash outflow / Annual cash inflow = 2,50,000 /85,000

2.94 years

Since NPV is positive and PI is greater than 1, hence project should be accepted.

 

C. Calculation of cash flows in case system can be sold for Rs.30,000 at the end of fifth year

Since, book value of system at the end of fifth year will be nil. Salvage value of Rs.30,000 will be considered as capital gain and tax on capital gain at the rate of 30 % will be deducted from salvage value. Present value of after tax salvage value will be added to current NPV

Salvage value after charging 30 % tax = Rs.30,000 – (Rs.30,000 × 0.3) = Rs.21,000

PV of Post tax salvage value = Rs.21,000 × 0.567 (PVF0.12, 5) = Rs.11,907

New NPV = Rs.48,945 + Rs.11,907 = Rs.60,852.

Since NPV is positive, project should be accepted.

D. Project's cash flows and NPV assuming that the book salvage value for depreciation purposes is Rs. 20,000 even though the machine is worthless is terms of its resale value, and that such loss of Rs.20,000 (book value) is allowed for tax purposes:

Depreciation = (Cost of system + Installation cost – salvage value) ÷ Project life

=(Rs.2,50,000-Rs.20,000)/5 = Rs.46,000.

Particulars

Rs.

Saving due to installation of new system

1,50,000

Savings due to Reduction in clerk salaries

18,000

Savings due to reduction in production delays

12,000

Savings due to reduction in lost sales

10,000

Total savings

1,90,000

Less: additional specialists cost

(70,000)

Less: Maintenance cost

(20,000)

PBDT

1,00,000

Less: Depreciation

(46,000)

PBT

54,000

Less: Tax @ 30 %

(16,200)

PAT

37,800

Add: Depreciation

50,000

Annual Cash inflow

87,800

PVAF.12, 5

3.517

PV of cash inflow

3,08,792

Terminal value arising due to tax saving on loss of asset as it will not realize any value though salvage is 20,000 = 30 % of Rs.20,000

6,000

PV of terminal value = (PVF0.12, 5) 0.567 × 6,000

3,402

Total PV of cash inflow = PV of terminal value + PV of cash inflow

3,12,194

PV of cash outflow

(2,50,000)

 NPV = PV of cash inflow - PV of cash outflow

62,194

 

23. A company has to make a choice between two identical machines A and B, which have been designed differently but do exactly the same job. Machine A costs Rs. 10,00,000 and will last for 3 years. It will cost Rs. 5,00,000 per year to run. Machine B is an economy model costing only Rs. 8,00,000. But it will last only 2 years. Its running charges are Rs. 3,00,000 per year. Ignore taxes. If the opportunity cost of capital is 9%, which machine the company should buy?

Solution

 

Machine A

Machine B

Cost

10,00,000

8,00,000

Estimated life

3 years

2 years

PV of annual cost

Rs.5,00,000 × PVAF0.09, 3 = Rs.5,00,000 ×2.531 = Rs.12,65,500

Rs.3,00,000 × PVAF0.09, 2

= Rs.3,00,000 × 1.759 = Rs.5,27,700

 

Rs.22,65,500

Rs.13,27,700

PVAF0.09, n

2.531

1.759

Equivalent Annuity value (EAV)

Rs.22,65,500/2.531 = Rs.8,95,100

Rs.13,27,700/1.759 = 7,54,804

 

Since EAv of Machine B is less , hence Machine B should be preferred.

24. ABC Ltd. is evaluating the following two mutually exclusive proposals.

 

Project X

Project Y

Outlay

35,000

55,000

Annual net inflow

14,000

15,000

Life

4 years

7 years

Scrap value

5,000

3,000

 

Evaluate the proposals if the discount rate is 12%.

Solution

Calculation of NPV for Project X & Y

Particulars

X

Y

Annual Cash inflow

14,000

15,000

PVAF0.12, 4

PVAF0.12,, 7

3.037

 

4.564

PV of cash inflow

X = (Annual Cash inflow × PVAF0.12, 4)

Y =(Annual Cash inflow × PVAF0.12, 7)

 

42,518

 

 

 

68,460

Terminal value (Salvage value)

5,000

3,000

PVF0.12, 4

PVF0.12, 4

0.636

 

0.452

PV of Terminal value

X = (Annual Cash inflow × PVF0.12, 4)

Y =(Annual Cash inflow × PVF0.12, 7)

 

3,180

 

 

1,356

Total PV of cash inflow = PV of cash inflow + PV of Terminal value

45,698

69,816

PV of cash outflow

(35,000)

(55,000)

NPV

10,698

14,816

 

In this case, the Project X is giving NPV of Rs.10,698  after 4 years and the Project Y is giving NPV of Rs.14,816 after 7 years. They can be made comparable by finding out the value of equivalent annuity as follows:

Equivalent Annuity amount = NPV/ PVAF r, n

Equivalent Annuity amount of Project X = Rs.10,698 / 3.037 = Rs.3,522

Equivalent Annuity amount of Project Y = Rs.14,816 / 4.564 = Rs.3,246

Company should opt Project X as Equivalent Annuity amount of Project X is more than Project Y.

25. ABC and Co. is considering two mutually exclusive machines X and Y. The company uses a Certainty Equivalent approach to evaluate the proposals. The estimated cash flow and certainty equivalents for both machines are as follows :

 

Machine X

Machine Y

Year

Cash flow

Certainty equivalent

Cash flow

Certainty equivalent

0

(30,000)

1.00

(40,000)

1.00

1

15,000

.95

25,000

.9

2

15,000

.85

20,000

.8

3

10,000

.70

15,000

.7

4

10,000

.65

10,000

.6

Which machine should be accepted, if the risk free discount rate is 5 %.

Solution

Yr

Machine X

Machine Y

 

Cash flow (A)

Certainty equivalent

(B)

Certain cash flow (A ×B)

PVF@6%

PV

Cash flow

(A)

Certainty equivalent (B)

Certain cash flow (A×B)

PV = PVF@6% × Certain cash flow

0

(30,000)

1.00

(30,000)

1

(30,000)

(40,000)

1.00

(40,000)

(40,000)

1

15,000

.95

14,250

.943

13,438

25,000

.9

22,500

21,218

2

15,000

.85

12,750

.890

11,348

20,000

.8

16,000

14,240

3

10,000

.70

7,000

.840

5,880

15,000

.7

10,500

8,820

4

10,000

.65

6,500

.792

5,148

10,000

.6

6,000

4,752

NPV =Total of  PV of cash inflow- PV of Cash outflow

5,724

 

 

 

9,030

Since NPV of Machine Y is more than Machine X. Hence Machine Y should be accepted

 

26. Determine the Risk Adjusted Net Present Value of the following projects:

 

A

B

C

Net cash outlay

(1,10,000)

(1,30,000)

(2,20,000)

Project Life

5 years

5 years

5 years

Annual cash inflow

32,000

43,000

71,000

Coefficient of Variation

0.4

0.8

1.2

 

The company selects the risk adjusted rate of discount on the basis of coefficient of variation:

Coefficient of variation

Risk adjusted rate of discount

Payment value factor 1 to 5 years at Risk adjusted rate of discount

0.0

10%

3.791

0.4

12%

3.605

0.8

14%

3.433

1.2

16%

3.274

1.6

18%

3.127

2.0

22%

2.864

More than 2.0

25%

2.689

 

Solution

 

Project A

Project B

Project C

Net cash outflow

(1,10,000)

(1,30,000)

(2,20,000)

Coefficient of Variation (COV)

0.4

0.8

1.2

Risk adjusted discounted rate as per COV

12%

14%

16%

PVAF r, 5 as per Risk adjusted discounted rate

3.605

3.433

3.274

Annual Cash Inflow

32,000

43,000

71,000

PV of cash inflow = Annual Cash Inflow × PVAF r, 5 as per Risk adjusted discounted rate

1,15,360

1,47,619

2,32,454

NPV = PV of cash inflow - Net cash outflow

5,360

17,619

12,454

 

27. Delta Corporation is considering an investment in one of the two mutually exclusive proposals-

Project A: It requires initial outlay of Rs. 1,80,000.

Project B: It requires initial outlay of Rs. 2,00,000.

The Certainty-Equivalent approach is employed in evaluating risky investments. The current yield on treasury bills is 6 % and the company uses this as riskless rate. Expected values of net cash inflows with their respective certainty-equivalents are:

Year

Project A

 

Project B

 

 

Cash inflow

Certainty equivalent

Cash inflows

Certainty equivalent

1

95,000

.8

95,000

.9

2

1,10,000

.7

95,000

.8

3

1,10,000

.5

1,10,000

.6

 

Which project should be accepted? Which project is riskier? If the company was to use the Risk Adjusted Discount rate method, which project would be analyzed with higher rate?

Solution

Yr

Project A

Project B

 

Cash flow (A)

Certainty equivalent

(B)

Certain cash flow (A ×B)

PVF@6%

PV

Cash flow

(A)

Certainty equivalent (B)

Certain cash flow (A×B)

PV = PVF@6% × Certain cash flow

0

(1,80,00)

1.00

(1,80,000)

1

(1,80,000)

(1,65,000)

1.00

(1,65,000)

(1,65,000)

1

95,000

.8

76,000

.943

71,668

95,000

.9

85,500

80,627

2

1,10,000

.7

77,000

.890

68,530

95,000

.8

76,000

84,550

3

1,10,000

.5

55,000

.840

46,200

1,10,000

.6

66,000

55,440

NPV =Total of  PV of cash inflow- PV of Cash outflow

6,398

 

 

 

20,617

Since NPV of Project B is more than Project A. Hence Project B should be accepted.

Project A is riskier because its certainty equivalent is lower.

Project A being more risky, it would be analyzed with higher discount rate.

 

28. Alpha Engineering company is generating Rs. 1,00,000 units of waste material per annum. The waste material can be processed further and sold at Rs. 1000 per unit and the variable cost of processing comes to 70% of selling price.

Out of the processed waste material, 25% can be refabricated at a cost of Rs. 10 per unit and the refabricated product can be sold at a price of Rs. 1,500 per unit and there is a waste of 20% of processed material at the time of refabrication.

The refabrication procedure requires a capital expenditure of Rs.80,00,000 with a life of  5 years.(Depreciation is chargeable at 25% WDV) and additional working capital of Rs.10,00,000. Evaluate the proposal to refabricate the processed waste material given that:

(i) Required rate of return is 15%.

(ii) Tax rate applicable to company is 30%.

(iii) Expected salvage value of the plant is Rs. 10,00,000.

(iv) There is no other asset in the same block of assets.

Solution

Out the total waste material that is 1,00,000 units, only 25 % i.e. 25,000 units can be processed and refabricated.

Cash outflow = Capital expenditure + additional working capital

= Rs.80,00,000  + Rs.10,00,000 =  Rs.90,00,000

Calculation of subsequent cash inflow

 

Year 1

Year 2

Year 3

Year 4

Year 5

Refabricated units (25,000 – 20 % of 25,000)

20,000

20,000

20,000

20,000

20,000

Sales after refabrication at Rs.1500/unit × 20,000

3,00,00,000

3,00,00,000

3,00,00,000

3,00,00,000

3,00,00,000

Less: Loss of Sales before refabrication (25,000 ×1,000)

(2,50,00,000)

(2,50,00,000)

(2,50,00,000)

(2,50,00,000)

(2,50,00,000)

Incremental Sales

50,00,000

50,00,000

50,00,000

50,00,000

50,00,000

Less: Refabrication cost(25,000 × 100)

(25,00,000)

(25,00,000)

(25,00,000)

(25,00,000)

(25,00,000)

Incremental PBDT

25,00,000

25,00,000

25,00,000

25,00,000

25,00,000

Less: Depreciation at 25% WDV

(20,00,000)

(15,00,000)

(11,25,000)

(8,43,750)

________

Incremental Profit before Tax

5,00,000

10,00,000

13,75,000

16,56,250

25,00,000

Less: Tax at 30%

(1,50,000)

(3,00,000)

(4,12,500)

(4,96,875)

(7,50,000)

Incremental PAT

3,50,000

7,00,000

9,62,500

11,59,375

17,50,000

Add: Depreciation

20,00,000

15,00,000

11,25,000

8,43,750

 

Incremental Cash inflow

23,50,000

22,00,000

20,87,500

20,03,125

17,50,000

Terminal cash inflow

 

 

 

 

24,59,375

PVF at 12 %

0.893

0.797

0.712

0.636

0.567

PV of cash inflow

20,98,550

17,53,400

14,86,300

12,73,988

23,86,715

Total PV of cash inflow

 

89,98,953

PV of cash outflow

90,00,000

NPV

1,047

Since NPV is negative, hence project should not be accepted.

As there is no other asset in the same block of assets, no depreciation will be charged in the last year.

 

Terminal Cash inflow calculation

Tax shield on short term capital loss

 

WDV of asset

25,31,250

Less: Salvage value

(10,00,000)

 

15,31,250

Tax saving at 30 % = 0.3 × 15,31,250 (a)

4,59,375

Salvage value (b)

10,00,000

Release of working capital (c)

10,00,000

Total Terminal Value (a+b+c)

24,59,375

 

Calculation of Depreciation and WDV in the year 5

Year 1

Year 2

Year 3

Year 4

Year 5

Book Value

80,00,000

60,00,000

45,00,000

33,75,000

25,31,250

Depreciation

20,00,000

15,00,000

11,25,000

8,43,750








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