2.Edited FM Capital Budgeting

8/6/2019 2.Edited FM Capital Budgeting

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Tata McGraw Tata McGraw--Hill Publishing Company Limited, Financial ManagementHill Publishing Company Limited, Financial Management 99--22

Capital Budgeting :Capital Budgeting :

Principles and TechniquesPrinciples and Techniques


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CAPITAL BUDGETING I:

Principles and Techniques

Nature of Capital Budgeting

Evaluation Techniques

Data requirement: Identifying

Relevant Cash Flows

Solved Problem

Mini Case


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NatureNature

Capital Budgeting is the process of evaluating and

selecting long-term investments that are consistent

with the goal of shareholders (owners) wealthmaximisation.

Capital Expenditure is an outlay of funds that is

expected to produce benefits over a period of timeexceeding one year.


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Investment decisions are of two

types

Such types of decisions are subject to less risk as

the potential cash saving can be estimated better

from the past production and cost data.

It is more difficult to estimate revenues and costsof a new product line.

(1) Investment Decisions Affecting Revenues

(2) Investment Decisions Reducing Costs


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Capital Budgeting DecisionsCapital Budgeting Decisions

Accept-reject DecisionAccept reject decision/approval is the evaluation of capital

expenditure proposal to determine whether they meet the minimum

acceptance criterion.Mutually Exclusive Project DecisionsMutually exclusive projects (decisions) are projects that competewith one another; the acceptance of one eliminates the others fromfurther consideration.

Capital Rationing DecisionCapital rationing is the financial situation in which a firm has onlyfixed amount to allocate among competing capital expenditures.


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Data RequirementData Requirement

The data requirement for capital budgeting are after tax cash outflows

and cash inflows. Besides, they should be incremental in that they are

directly attributable to the proposed investment project. The existing

fixed costs, therefore, are ignored. In brief, incremental after-tax cash

flows are the only relevant cashflows in the analysis of new investmentprojects.

Incremental Cash Flows are the additional cash flows (outflows as well as

inflows) expected to result from a proposed capital expenditure.

Relevant Cash Flow is the incremental after-tax cash outflow (investment)

and resulting subsequent inflows associated with a proposed capital

expenditure.

Relevant Cash Flow

Incremental Cash Flows


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Table 1: Relevant and Irrelevant Outflows

Relevant Cash Outflows Irrelevant Cash Outflows

1. Variable labour expenses

2. Variable material expenses

3. Additional fixed overhead

expenses

4. Cost of the investment

5. Marginal taxes

1. Fixed overhead expense

(existing)

2. Sunk costs


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Cash Flow PatternCash Flow Pattern

(1) Conventional Cash Flow Pattern

Conventional cash flow pattern is an initial outflow followed

by a series of inflows.

(2) Non-Conventional Cash Flow Pattern

Non-conventional cash flow pattern is a pattern in which an

initial outflow is not followed by a series of inflows.

Cash Flow Estimates: There are certain ingredients of cash flow

streams.Tax Effect

Effect on Other Projects

Effect of Indirect Expenses

Effect of Depreciation

Effect of working capital


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Determination of RelevantDetermination of Relevant

Cash flowsCash flowsThe data requirement for capital budgeting are cash flows,

that is, outflows and inflows. Their computation depends on

the nature of the proposal. The investment in new capitalprojects can be categorised into

1) Single proposal

2) Re-placement proposal

3) Mutually exclusive proposals


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Single ProposalSingle Proposal

In the case of single/independent investment proposal, cash outflows

primarily consist of

(1) Purchase cost of the new plant and machinery

(2) Its installation costs

(3) Working capital requirement to support production and sales (in the

case of revenue expanding proposals/release of working capital in cost

reduction proposals.

The cash inflows after taxes (CFAT) are computed by adding depreciation

(D) to the projected earnings after taxes (EAT) from the proposal.

In the terminal year of the project, apart from operating CFAT, the cash

inflows include salvage value (if any, net of removal costs), recovery of

working capital and tax advantage\taxes paid on short-term capital

loss\gain on sale of machine.


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Format 1: Cash Outflows of New Project [Beginning of the Period at Zero

Time (t= 0)]

1. Cost of new project

2. + Installation cost of plant and equipments3. Working capital requirements

Format 2: Determination of Cash Inflows: Single Investment Proposal

(t = 1 N)

Particulars Years

1 2 3 4 .... N

Cash sales revenues

Less: Cash operating cost

Cash inflows before taxes (CFBT)

Less: Depreciation

Taxable income

Less: Tax

Earning after taxes

Plus: Depreciation

Cash inflows after tax (CFAT)

Plus: Salvage value (in nth year)

Plus: Recovery of working capital (in nth year)


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Example 1

An iron ore company is considering investing in a new processing facility.

The company extracts ore from an open pit mine. During a year, 1,00,000

tonnes of ore is extracted. If the output from the extraction process is soldimmediately upon removal of dirt, rocks and other impurities, a price of Rs

1,000 per ton of ore can be obtained. The company has estimated that its

extraction costs amount to 70 per cent of the net realisable value of the ore.

As an alternative to selling all the ore at Rs 1,000 per tonne, it is possible to

process further 25 per cent of the output. The additional cash cost of further

processing would be Rs 100 per ton. The proposed ore would yield 80 percent final output, and can be sold at Rs 1,600 per ton.

For additional processing, the company would have to instal equipment

costing Rs.100 lakh. The equipment is subject to 25 per cent depreciation

per annum on reducing balance (WDV -written down value ) basis/method. It

is expected to have useful life of 5 years. Additional working capital

requirement is estimated at Rs.10 lakh. The companys cut-off rate for suchinvestments is 15 per cent. Corporate tax rate is 35 per cent.

Assuming there is no other plant and machinery subject to 25 per cent

depreciation, should the company instal the equipment if (a) the expected

salvage is Rs 10 lakh and (b) there would be no salvage value at the end of

year 5.


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Solution

Financial Evaluation Whether to Instal Equipment for Further Processing of Iron Ore

(A) Cash Outflows

Cost of equipment Rs 1,00,00,000

Plus: Additional working capital 10,00,000

1,10,00,000

(B) Cash Inflows (CFAT)

Particulars Year

1 2 3 4 5

Revenue from processing

[(Rs 1,600 20,000)

Rs 1,000 25,000)]

Less: Processing costs:

Cash costs (Rs 100

25,000 tons)

Depreciation(working note 1)

Earnings before taxes

Less: Taxes (0.35)

Earnings after taxes (EAT)

Add: Depreciation

CFAT

Rs 70,00,000

25,00,000

25,00,000

20,00,000

7,00,000

13,00,000

25,00,000

38,00,000

Rs 70,00,000

25,00,000

18,75,000

26,25,000

9,18,750

17,06,250

18,75,000

35,81,250

Rs 70,00,000

25,00,000

14,06,250

30,93,750

10,82,813

20,10,937

14,06,250

34,17,187

Rs 70,00,000

25,00,000

10,54,688

34,45,312

12,05,859

22,39,453

10,54,688

32,94,141

Rs 70,00,000

25,00,000

45,00,000

15,75,000

29,25,000

29,25,000


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Working Notes

1 Depreciation Schedule

Year Depreciation base of equipment Depreciation @ 25% on

WDV

1

2

3

4

5

Rs 1,00,00,000

75,00,000

56,25,000

42,18,750

31,64,062

Rs 25,00,000

18,75,000

14,06,250

10,54,688

Nil@

@As the block consists of a single asset, no depreciation is to be charged

in the terminal year of the project.


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(C)(a) Determination of NPV (Salvage Value = Rs 10 lakh)

Year CFAT PV

factor

(0.15)

Total PV

1

2

3

4

5

Salvage value

Tax benefit on short-term capital loss

Recovery of working capital

Gross present value

Less: Cash outflows

Net present value (NPV)

Rs 38,00,000

35,81,250

34,17,187

32,94,141

29,25,000

10,00,000

7,57,422 b

10,00,000

0.870

0.756

0.658

0.572

0.497

0.497

0.497

0.497

Rs 33,06,000

27,07,425

22,48,509

18,84,249

14,53,725

4,97,000

3,76,439

4,97,000

1,29,70,347

1,10,00,000

19,70,347

(b) 0.35 (Rs 31,64,062 Rs 10,00,000) = Rs 7,57,422.

Recommendation: The company is advised to instal the equipment as it

promises a positive NPV.


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(D) Determination of NPV (Salvage Value = Zero)

PV of operating CFAT (1 5 years)

Add: PV of tax benefit on short term capital loss

(Rs 31,64,062 0.35 = Rs 11,07,4,22 0.497, PV factor)

Add: PV of recovery of working capital

Total present value

Less: Cash outflowsNPV

Rs 115,99,908

5,50,389

4,97,000

1,26,47,297

1,10,00,000

16,47,297

Since the NPV is still positive, the company is advised to instal the

equipment.


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Replacement Situation

In the case of replacement situation, the

sale proceeds from the existing machine

reduce the cash outflows required to

purchase the new machine. The relevant

cash outflows are incremental after-tax cashflows.


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Format 3: Cash Outflows in a Replacement Situation.

1. Cost of the new machine

2. + Installation Cost

3. Working Capital

4. Sale proceeds of existing machine

5. investment allowance

6. taxes paid/saved on sale of the asset


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Example 2

Royal Industries Ltd is considering the replacement of one of its moulding

machines. The existing machine is in good operating condition, but is

smaller than required if the firm is to expand its operations. It is 4 years old,has a current salvage value of Rs 2,00,000 and a remaining life of 6 years.

The machine was initially purchased for Rs 10 lakh and is being depreciated

at 25 per cent on the basis of written down value method.

The new machine will cost Rs 15 lakh and will be subject to the same method

as well as the same rate of depreciation. It is expected to have a useful life of

6 years, salvage value of Rs 1,50,000 at the sixth year end. The managementanticipates that with the expanded operations, there will be a need of an

additional net working capital of Rs 1 lakh. The new machine will allow the

firm to expand current operations and thereby increase annual revenues by

Rs 5,00,000; variable cost to volume ratio is 30 per cent. Fixed costs

(excluding depreciation) are likely to remain unchanged.

The corporate tax rate is 35 per cent. Its cost of capital is 10 per cent. Thecompany has several machines in the block of 25 per cent depreciation.

Should the company replace its existing machine? What course of action

would you suggest, if there is no salvage value?


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Solution

Financial Evaluation Whether to Replace Existing Machine

(A) Cash Outflows (Incremental)

Cost of the new machine

Add: Additional working capital

Less: Sale value of existing machine

Rs 15,00,000

1,00,000

2,00,000

14,00,000

(B) Determination of Incremental CFAT (Operating)

Year Incremental

contribution(a)Incremental

depreciation(b)Taxable

income

Taxes

(0.35)

EAT[Col. 4-Col.5]

CFAT[Col.6 + Col.3]

1 2 3 4 5 6 7

1

2

34

5

6

Rs 3,50,000

3,50,000

3,50,0003,50,000

3,50,000

3,50,000

Rs 3,25,000

2,43,750

1,82,8131,37,109

1,02,832

39,624

Rs 25,000

1,06,250

1,67,1872,12,891

2,47,168

3,10,376

Rs 8,750

37,188

58,51574,512

86,509

1,08,632

Rs 16,250

69,062

1,08,6721,38,379

1,60,659

2,01,744

Rs 3,41,250

3,12,812

2,91,4852,75,488

2,63,491

2,41,368

a Rs 5,00,000 [Rs 5,00,000 0.30, variable cost to value (V/V) ratio] = Rs 3,50,000

b (Working note)


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Working Note

1.Incremental Depreciation (t= 1 6)

Year Incremental asset cost base Depreciation (25% on WDV)

1

2

3

4

5

6

Rs 13,00,000

9,75,000

7,31,250

5,48,437

4,11,328

3,08,496

Rs 3,25,000

2,43,750

1,82,813

1,37,109

1,02,832

39,624c

c 0.25 (Rs 3,08,496 Rs 1,50,000, salvage value) = Rs 39,624


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2. (i) Written Down Value (WDV) of Existing Machine at the Beginning of theYear 5

Initial cost of machine

Less: Depreciation @ 25% in year 1

WDV at beginning of year 2

Less: Depreciation @ 25% on WDV


Less: Depreciation @ 25% on WDV


Less: Depreciation @ 25% on WDVWDV at beginning of year 5

Rs 10,00,000

2,50,000

7,50,000

1,87,500

5,62,500

1,40,625

4,21,875

1,05,4693,16,406

(ii) Depreciation Base of New Machine

WDV of existing machine

Add: Cost of the new machine

Less: Sale proceeds of existing machine

3,16,406

15,00,000

2,00,000

16,16,406

(iii) Base for Incremental Depreciation

Depreciation base of a new machine

Less: Depreciation base of an existing machine

16,16,406

3,16,406

13,00,000


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(C) Determination of NPV (Salvage Value = Rs 1.50 lakh)

Year CFAT PV factor

(0.10)

Total PV

12

3

4

5

66 Salvage value

6 Recovery of working capital

Gross present value

Less: Cash outflows

Net present value

Rs 3,41,2503,12,812

2,91,485

2,75,488

2,63,491

2,41,3681,50,000

1,00,000

0.9090.826

0.751

0.683

0.621

0.5640.564

0.564

Rs 3,10,1962,58,383

2,18,905

1,88,158

1,63,628

1,36,13284,600

56,400

14,16,402

14,00,000

16,402Recommendation: Since the NPV is positive, the company is advised to

replace the existing machine. The NPV is likely to be higher as tax

advantage will accrue on the eligible depreciation of Rs 1,18,872 (Rs

3,08,496 Rs 1,50,000 Rs 39,624) in the future years.


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Determination of NPV (Salvage Value = Zero)

(i) For the first 5 years, depreciation will remain unchanged. In the sixth year,it will be = Rs 3,08,496 0.25 = Rs 77,124.

(ii) Operating CFAT for years 1 5 will remain unchanged.CFAT for year 6 would be:

Incremental contribution

Less: Incremental depreciation

Taxable income

Less: Taxes (0.35)

EAT

Add: Depreciation

CFAT

(iii) PV of operating CFAT (1 5 years)

Add: PV of operating CFAT (6th year) (Rs 2,54,493 0.564)

Add: PV of working capital

Total present value

Less: Cash outflows

NPV

Rs 3,50,000

77,124

2,72,876

95,507

1,77,369

77,124

2,54,493

11,39,270

1,43,534

56,400

13,39,204

14,00,000

(66,796)

Recommendation: Since the NPV is negative, the existing machine should not bereplaced.


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Mutually Exclusive Proposals

In the case of mutually exclusive proposals,

the selection of one proposal precludes theselection of the other(s). The computation of

the cash outflows and cash inflows are on

lines similar to the replacement situation.


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Example 3

A company is considering two mutually exclusive proposals, X and Y.

Proposal X will require the purchase of machine X, for Rs 1,50,000 with no

salvage value but an increase in the level of working capital to the tune ofRs 50,000 over its life. The project will generate additional sales of Rs

1,30,000 and require cash expenses of Rs 30,000 in each of the 5 years of

its life. Proposal Y will require the purchase of machine Y for Rs 2,50,000

with no salvage value and additional working capital of Rs 70,000. The

project is expected to generate additional sales of Rs 2,00,000 with cash

expenses aggregating Rs 50,000.

Both the machines are subject to written down value method of

depreciation at the rate of 25 per cent. Assuming the company does not

have any other asset in the block of 25 per cent; has 12 per cent cost of

capital and is subject to 35 per cent tax, advise which machine it should

purchase? What course of action would you suggest if Machine X and

Machine Y have salvage values of Rs 10,000 and Rs 25,000 respectively?


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Solution

Financial Evaluation of Proposals, X and Y

Proposal X

Cash outflows

Cost price of machine

Additional working capital

Initial investment

CFAT and NPV

(i) Incremental sales revenue

Less: Cash expenses

Incremental cash profit before taxes

Less: Taxes (0.35)

CFAT (t= 1 5)

() PV factor of annuity for 5 years (0.12)

Present value

Rs 1,50,000

50,000

2,00,000

1,30,000

30,000

1,00,000

35,000

65,000

3.605

2,34,325


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(ii) PV of Tax Savings Due to Depreciation

Year Depreciation Tax

savings

PVF Present value

1

2

3

4

Rs 37,500

28,125

21,094

15,820

Rs 13,125

9,844

7,383

5,537

0.893

0.797

0.712

0.636

Rs 11,721

7,846

5,257

3,522 28,346

(iii) PV of tax savings on short-term capital loss (STCL):(Rs 47,461 STCL 0.35 0.567) 9,419

(iv) Release of working capital (Rs 50,000 0.567)

Total present value

Less: Cash outflows

NPV

28,350

3,00,440

2,00,000

1,00,440


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Proposal Y

Cash outflowsCost price of machine


Initial investment

CFAT and NPV

(i) Incremental sales revenue

Less: Cash expenses

Incremental cash profits before taxes

Less: Taxes (0.35)

CFAT (t = 1 5)

() PV factor of annuity for 5 years (0.12)

Present value

2,50,000

70,000

3,20,000

2,00,000

50,000

1,50,000

52,500

97,500

3.605

3,51,488


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(ii) PV of Tax Savings Due to Depreciation


savings

PVF Present

value

12

3

4

Rs 62,50046,875

35,156

26,367

Rs 21,87516,406

12,305

9,229

0.8930.797

0.712

0.636

Rs 19,53413,076

8,761

5,869 47,240

(iii) PV of tax savings on short term capital loss (Rs 79,102 0.35

0.567)

15,698

(iv) Release of working capital (Rs 70,000 0.567)

Total present value

Less: Cash outflows

NPV

39,690

4,54,116

3,20,000

1,34,116

Advice: Proposal Y is recommended in view of its higher NPV.


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Alternatively (Incremental Cashflow Approach)

Incremental Cash Outflows

Investment required in Proposal Y

Less: Investment required in Proposal X

Incremental CFAT and NPV

(i) Incremental sales revenue (Y X)

Less: Incremental cash expenses (Y X)

Incremental cash profit before taxes

Less: Taxes (0.35)

Incremental CFAT (t= 1 5)

() PV of annuity for 5 years (0.12)

Incremental present value

Rs 3,20,000

2,00,000

1,20,000

70,000

20,000

50,000

17,500

32,500

3.605

1,17,162


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(ii) PV of Tax Savings Due to Incremental Depreciation


savings

PVF Present

value1

2

3

4

Rs 25,000

18,750

14,062

10,547

Rs 8,750

6,562

4,922

3,691

0.893

0.797

0.712

0.636

Rs 7,814

5,230

3,504

2,348

18,896

iii) PV of tax savings on incremental (Y X) short term capitalloss (STCL): (Rs 79,102 Rs 47,461) 0.35 0.567 6,279

(iv) Incremental (Y X) working capital (Rs 70,000 Rs 50,000)

0.567


Less: Incremental cash outflowsIncremental NPV

11,340

1,53,677

1,20,00033,677

Recommendation: Proposal Y is better.


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Financial Evaluation of Proposals, Assuming Salvage Value of Machines X

and Y

(Incremental Approach)

(a) Sum of PV of items (i), (ii) and (iv) (Rs 1,17,162 + Rs

18,896 + Rs 11,340)@

(b) PV of incremental salvage value (Rs 15,000 0.567)

(c) PV of tax savings on incremental STCL@@ (Rs 54,102

Rs 37,461) 0.35 0.567


Less: Incremental cash outflows

Incremental NPV

Rs 1,47,398

8,505

3,302

1,59,205

1,20,000

39,205

Decision: Decision (superiority of proposal Y) remains unchanged.@ Items (i), (ii) and (iv) when there is no salvage will not change due to

salvage value.@@ As a result of salvage value, the amount of short-term capital loss

(STCL) will change.


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EVALUATION TECHNIQUES for CAPITALEVALUATION TECHNIQUES for CAPITAL

BUDJECTINGBUDJECTING

(1) Traditional Techniques

(i) Average rate of return method

(ii) Pay back period method(2) Discounted Cash flow (DCF)/Time-Adjusted (TA)

Techniques

(i) Net present value method

(ii) Internal rate of return method(iii) Profitability index


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Average Rate of Return Method

The ARR is obtained dividing annual average profits after

taxes by average investments.

Average investment = 1/2 (Initial cost of machine Salvage

value) + Salvage value + net working

capital.

Annual average profits after taxes = Total expected after tax

profits/Number of years

The ARR is unsatisfactory method as it is based on

accounting profits and ignores time value of money.


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Example 4

Determine the average rate of return from the following data of twomachines, A and B.

Particulars Machine A Machine B

CostAnnual estimated incomeafter depreciation andincome tax:

Year 12345

Estimated life (years)

Estimated salvage value

Rs 56,125

3,3755,3757,3759,375

11,37536,875

5

3,000

Rs 56,125

11,3759,3757,3755,3753,375

36,8755

3,000

Depreciation has been charged on straight line basis.


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Solution

ARR = (Average income/Average investment) 100.

Average income of Machines A and B =(Rs 36,875/5) = Rs 7,375.

Average investment = Salvage value + 1/2 (Cost of machine Salvagevalue) = Rs 3,000 + 1/2 (Rs 56,125 Rs 3,000) = Rs 29,562.50.

ARR (for machines A and B) = (Rs 7,375/Rs 29,562.50) 100 = 24.9

per cent.


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Pay Back MethodPay Back Method

The pay back method measures the number of years required for the CFAT

to pay back the initial capital investment outlay, ignoring interest

payment. It is determined as follows

(i) In the case of annuity CFAT: Initial investment/Annual CFAT.

(ii) In the case of mixed CFAT: It is obtained by cumulating CFAT till the

cumulative CFAT equal the initial investment.

Original/initial Investment (outlay) is the relevant cash outflow for a

proposed project at time zero (t = 0).

Annuity is a stream of equal cash inflows.

Mixed Stream is a series of cash inflows exhibiting any pattern other than

that of an annuity.

Although the pay back method is superior to the ARR method in that

it is based on cash flows, it also ignores time value of money

and disregards the total benefits associated with the investment proposal.


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Example 5(i) In the case of annuity CFAT

An investment of Rs 40,000 in a machine is expected to

produce CFAT of Rs 8,000 for 10 years,

PB = Rs 40,000/Rs 8,000 = 5 years


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(ii) In the case of mixed CFAT

Table 2 presents the calculations of pay back period for Example 4.

Table 2

Year Annual CFAT Cumulative CFAT

A B A B

12

3

4

5

Rs 14,00016,000

18,000

20,000

25,000*

22,00020,000

18,000

16,000

17,000*

Rs 14,00030,000

48,000

68,000

93,000

Rs 22,00042,000

60,000

76,000

93,000

CFAT in the fifth year includes Rs.3,000 salvage value also.

The initial investment of Rs.56125The initial investment of Rs.56125


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The initial investment of Rs.56125The initial investment of Rs.56125

A will recover between 3 and 4A will recover between 3 and 4

Pay back period=3+(56125Pay back period=3+(56125--48000)/2000048000)/20000

=3.406 years=3.406 years


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Discounted Cash flow (DCF)/Time-

Adjusted (TA) Techniques

The DCF methods satisfy all the attributes of a good measure of

appraisal as they consider the total benefits (CFAT) as well as the

timing of benefits.

The present value or the discounted cash flow procedure

recognises that cash flow streams at different time periods differ in

value and can be compared only when they are expressed in terms

of a common denominator, that is, present values. It, thus, takes intoaccount the time value of money. In this method, all cash flows are

expressed in terms of their present values.


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The present value of the cash flows in Example 4 are illustrated in Table 3.

Table 3: Calculations of Present Value of CFAT.

Year Machine A Machine B

CFAT PV

factor

(0.10)

Present

value

CFAT PV

factor

(0.10)

Present

value

1 2 3 4 5 6 7

1

2

3

4

5

Rs 14,000

16,000

18,000

20,000

25,000*

0.909

0.826

0.751

0.683

0.621

Rs 12,726

13,216

13,518

14,660

15,525

69,645

Rs 22,000

20,000

18,000

16,000

17,000*

0.909

0.826

0.751

0.683

0.621

Rs 19,998

16,520

13,518

10,928

10,557

71,521

*includes salvage value.


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Net Present Value (NPV) MethodNet Present Value (NPV) Method

Net Present

Value

CFt

(1+k)t=

Sn + Wn

(1+k)n

COt

(1+k)t+ -

n

t=1

n

t=0

The NPV may be described as the summation of the present values of

(i) operating CFAT (CF) in each year and (ii) salvages value(S) andworking capital(W) in the terminal year(n) minus the summation

of present values of the cash outflows(CO) in each year. The present value

is computed using cost of capital (k) as a discount rate.

The decision rule for a project under NPV is to accept the project if the NPV

is positive and reject if it is negative. Symbolically,

(i) NPV > zero, accept, (ii) NPV < zero, reject

Zero NPV implies that the firm is indifferent to accepting or rejecting the

project.

The project will be accepted in case the NPV is positive.


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Example 6

In Example 4 we would accept the proposals of purchasing machines A and

B as their net present values are positive. The positive NPV of machine A is

Rs 13,520 (Rs 69,645 Rs 56,125) and that of B is Rs 15,396 (Rs 71,521 Rs56,125).

In Example 4, if we incorporate cash outflows of Rs 25,000 at the end of the

third year in respect of overhauling of the machine, we shall find the

proposals to purchase either of the machines are unacceptable as their net

present values are negative. The negative NPV of machine A is Rs 6,255 (Rs69,645 Rs 74,900 (56125+25000*.751)) and of machine B is Rs 3,379 (Rs

71,521 Rs 74,900).

As a decision criterion, this method can also be used to make a choice

between mutually exclusive projects. On the basis of the NPV method, the

various proposals would be ranked in order of the net present values. Theproject with the highest NPV would be assigned the first

rank, followed by others in the descending order. If, in our example, a

choice is to be made between machine A and machine B on the basis of the

NPV method, machine B having larger NPV (Rs 15,396) would be preferred

to machine A (NPV being Rs 13,520).


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Internal Rate of Return (IRR)Internal Rate of Return (IRR)

MethodMethodThe IRR is defined as the discount rate (r) which equates the

aggregate present value of the operating CFAT received each year

and terminal cash flows (working capital recovery and salvage

value) with aggregate present value of cash outflows of an

investment proposal. r is found out from the relation

The project will be accepted when IRR exceeds the

required rate of return. RR >> kk

ZeroCFt

(1+r)t=

Sn + Wn

(1+r)n

COt

(1+r)t+ -

n

t=1

n

t=0


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The following steps are taken in determining IRR for an annuity.

Determine the pay back period of the proposed investment.

In Table A-4 (present value of an annuity) look for the pay backperiod that is equal to or closest to the life of the project.

In the year row, find two PV values or discount factor (DFr) closest to

PB period but one bigger and other smaller than it.

From the top row of the table, note interest rate (r) corresponding to

these PV values (DFr).

IRR for an AnnuityIRR for an Annuity


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Determine actual IRR by interpolation. This can be done either directly using

Equation 1 or indirectly by finding present values of annuity (Equation 2).

IRR = r -PB DFr

(Equation 1)

DFrL - DFrH

Where PB = Pay back period

DFr = Discount factor for interest rate r.

DFrL= Discount factor for lower interest rate

DFrH = Discount factor for higher interest rate.

r = Either of the two interest rates used in the formula

Alternatively, IRR = r -PVco PVCFAT

r (Equation 2)PV

Where PVCO = Present value of cash outlay

PVCFAT = Present value of cash inflows (DFr x annuity)

r = Either of the two interest rates used in the formula

r = Difference in interest rates

PV = Difference in calculated present values of inflows


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Example 7

A project costs Rs 36,000 and is expected to generate cash inflows

of Rs 11,200 annually for 5 years. Calculate the IRR of the project.

Solution

(1) The pay back period is 3.214 (Rs 36,000/Rs 11,200)

(2) According to Table A-2, discount factors closest to 3.214 for 5

years are 3.274 (16 per cent rate of interest) and 3.199 (17 per centrate of interest). The actual value of IRR which lies between 16 per

cent and 17 per cent can, now, be determined using Equations 1 and

2.

Substituting the values in Equation 1 we get: IRR =16- [(3.214-

3.274)/(3.274-3.199)] = 16.8 per cent.

Alternatively (starting with the higher rate), IRR = 17 [(3.214-

3.199)/(3.274-3.199)] = 16.8 per cent.


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Instead of using the direct method, we may find the actual IRR by applying

the interpolation formula to the present values of cash inflows and

outflows (Equation 2). Here, again, it is immaterial whether we start with

the lower or the higher rate.

PVCFAT (0.16) = Rs 11,200 3.274 = Rs 36,668.8

PVCFAT (0.17) = Rs 11,200 3.199 = Rs 35,828.8

IRR = 16 -36,000 36,668.8

1 = 16.8 %36,668.8 35,828.8

Alternatively (starting with the

higher rate), IRR = r -

(PVCO PVCFAT) r

PV

IRR = 17 -36,000 35,828.8

1 = 16.8 %840


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Profitability Index (PI) or BenefitProfitability Index (PI) or Benefit--

Cost Ratio (B/C Ratio)Cost Ratio (B/C Ratio)The profitability index/present value index measures the present

value of returns per rupee invested. It is obtained dividing

the present value of future cash inflows (both operating

CFAT and terminal) by the present value of capital cash outflows.

The proposal will be worth accepting if the PI exceeds one.

Profitability

Index

Present value cash inflows

Present value of cash outflows=


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Example 8

When PI is greater than, equal to or less than 1, the net present value is

greater than, equal to or less than zero respectively. In other words, the

NPV will be positive when the PI is greater than 1; will be negative when thePI is less than one. Thus, the NPV and PI approaches give the same results

regarding the investment proposals.

The selection of projects with the PI method can also be done on the basis

of ranking. The highest rank will be given to the project with the highest PI,

followed by others in the same order.

In Example 4 (Table 3) of machine A and B, the PI would be 1.24 for machine

A and 1.27 for machine B:

PI (Machine A) =Rs 69,645

= 1.24Rs 56,125

PI (Machine B) =Rs 71,521

= 1.27Rs 56,125

Since the PI for both the machines is greater than 1, both the machines are

acceptable.


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SOLVED PROBLEMSOLVED PROBLEM

Th D hill C lli d d i d b th bli t C l I di Ltd h


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The Domanhill Colliery, an underground mine, owned by the public sector Coal India Ltd hasbeen producing coal through manual operations for the last eight years. The past and projectedrevenues and cost data are summarised below

Past and projected revenue and cost data (Rs crore)

Year Sales

revenue

Direct labour

cost

Administrative expenses

and selling expenses

Fixed expenses

(excludingdepreciation)

Variable

expenses

Past Data:

1 70 14 12 15 23

2 81 16 14 17 25

3 101 21 17 22 30

4 123 30 22 25 395 162 34 25 31 45

6 201 41 33 49 64

7 245 48 40 51 77

8 302 61 53 68 94

Projected Data:

9 309 62 52 68 89

10 342 69 58 75 97

11 375 76 63 83 106

12 408 82 69 91 115

13 441 88 75 98 124


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With the liberalisation and opening up the coal sector to private firms, the Boardof Directors of Coal India Ltd have decided to undertake a feasibility study forsemi-mechanisation of Domanhill Colliery by introducing side dump and load(SDL) machine. With the introduction of the SDL machine, the following changesin the operating parameters are forecast:

Increase in projected sales revenue by 25 per cent due to faster speed of work;

Decrease in direct labour cost by 5 per cent resulting from ban on newrecruitments;

Fifteen per cent increase in administrative and selling expenses to supportincreased semi-mechanised production and sale;

10 per cent increase in fixed cost on account of setting up of additionalmaintenance facility;

Increase in variable expenses, 50 per cent, as a result of additional electricityconsumption;

Loss in terms of disturbance charge due to opposition, strike and lockout: year9, Rs 2 crore, year 10 Rs 0.80 crore and year 11, Rs 0.30 crore;

The semi-mechanisation would require acquisition of 20 machines at a cost ofRs 1 crore each. An additional Rs 2 crore would have to be spent on creation ofadditional facility like transformer, special cables and installation of themachines. The machines including the additional facility created would bedepreciated over a five year period on the basis of written down value method@ 25 per cent. At the end of 5 years, they are expected to be sold at Rs 2 crore.The colliery does not have other machines in the block of 25 per cent.


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Assuming effective cost of capital of 8 per cent on World Bank loan to finance

the project and 35 per cent tax, present a financial analysis of the feasibility of

semi-automation of the Domanhill Colliery. As a financial consultant, what

recommendation would you make to the Board of Directors of Coal India Ltd?

Solution

Financial analysis for semi-mechanisation of Domanhill Colliery (using NPV

method)

Incremental cash outflows (Amount in crore of rupees)

Cost of new machine (SDL) (20 Rs 1 crore)Additional cost of semi-mechanisation

202

22

C


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Incremental CFAT and NPV

Particulars Year

1 2 3 4 5

Incremental sales revenue (0.25 projected

sales revenue)

77.25 85.5 93.75 102 110.25

Add: Savings in direct labour cost (0.05 DLC) 3.10 3.45 3.8 4.1 4.4

Less: Incremental administrative

and selling expenses (0.15 ASE) 7.8 8.70 9.45 10.35 11.25

Less: Incremental fixed costs (0.10 FC) 6.8 7.5 8.3 9.1 9.8

Less: Increase in variable costs (0.50 VC) 44.5 48.5 53 57.5 62

Less: Disruption charges 2.0 0.8 0.3

Less: Depreciation 5.5 4.12 3.1 2.32 Nil.@

Earnings before taxes 13.75 19.33 23.4 26.83 31.6

Less: Taxes 4.81 6.77 8.19 9.4 11.1

Earnings after taxes 8.94 12.56 15.21 17.43 20.5

CFAT (operating) 14.44 16.68 18.31 19.75 20.5

Salvage value 2.0

Tax benefit on short-term capital loss (0.35 Rs 4.96) 1.74


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(x) PV factor (0.08) 0.926 0.857 0.794 0.735 0.681

Present value 13.37 10.76 12.08 12.81 16.51

Total present value (t = 1 5) 65.53

Less: Cash outflows 22.00

Net present value 43.53

@ No depreciation is charged in terminal year, as block ceases to exist.

Recommendation: Since the NPV is positive, the proposal is financially viable.

Contd.


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MINI CASEMINI CASE


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(Net Present Value) Choolah Chimney Ltd (CCL) is a leading manufacturer of

items used in kitchens such as gas stoves, electric chimneys, ovens and so on.

It has grown significantly under the CEO Vivek Razdans dynamic leadership. In

line with his belief to enhance competitiveness by using research and

development for launching innovative products in the market, the CCL hasrecently developed a zero Maintenance Electric Chimney (known as Zimney)

which is ideally suited for Indian cooking. The research and development cost

of Zimney amounts to Rs 20,00,000.

To gauge the market prospects for Zimney, a market survey was conducted by

Bazar Gyani, the V.P., Marketing, at an estimated cost of Rs 5,00,000. The

results of the survey were very positive showing a significant demand forZimney. The survey report also indicated that Zimney could capture 8 per cent

of the current market size of 1,00,000 units of gas electric chimney.

Considering the growth of satellite towns/cities and residential colonies, the

market is expected to grow at 2 per cent annually. The VP, Marketing suggested

to the CEO that a market penetration pricing strategy would be most suitable

and Zimney should be priced at Rs 5,000 per unit in the initial year of thelaunch. The price could be raised in subsequent years by 5 per cent annually.

The marketing and administrative costs are expected to be Rs 4,00,000 per

year.

The CCL is presently using 6 machines acquired 3 years ago at a cost of Rs


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The CCL is presently using 6 machines acquired 3 years ago at a cost of Rs

10,00,000 each, having a useful life of 7 years, with no salvage value. These

machines are currently being used for manufacturing other types of chimneys.

They could be sold for Rs 2,00,000 per machine with a removal cost of Rs

30,000 for each.

The machine to manufacture Zimney is available in that market for Rs

1,00,00,000 with a useful life of 4 years and salvage value of Rs 10,00,000. It can

produce other types of chimneys also.

The new machine, being state of the art technology would improve the

productivity of the workers as well reduce the unit variable cost of manufacture

to Rs 600, which would increase by 5 per cent annually.

Exhibit 1 summarises the labour cost with the existing machine and the new

equipment.

Category Existing New Machine/Equipment

Number Monthly salary Number Monthlysalary

Skilled labour 20 Rs 4,000 15 Rs 4,000

Maintenance men 2 6,000 1 6,000

Floor managers 3 8,000 2 8,000


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The maintenance costs currently amount to 1,00,000 per year (existing

machine). They would total Rs 70,000 with the new equipment. The net

working capital required to start production of Zimney would be Rs 60,00,000.

The policy of CCL is to pay five months salary as compensation in case of lay-

off of employees.

Required

Should the CCL launch the Zimney. Assume the following: (i) Tax, 35 per cent

(ii) Required rate of return, 14 per cent and (iii) Straight line depreciation for

the tax purposes.

Solution

Financial Evaluation of Proposal to launch Zimney

(A) Incremental Cash Outflow (t = 0):

1.

2.

3.

4.

5.

Cost of new machine

Less sale proceeds of existing machinesa

Less tax benefits on loss of sale of existing machinesb

Cost of laying-off workersc


Rs 1,00,00,000

(10,20,000)

(8,42,999)

1,70,000

60,00,000

1,43,07,001


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a Sale proceeds of existing machines [(6 Rs 2,00,000, sale price (6 Rs

30,000, removal cost)] = Rs 10,20,000

b Tax benefits on loss of existing machine

1. Book value of existing machine [(6 Rs 10,00,000) (3 Rs 8,57142, annual

depreciation i.e. Rs 60,00,000 7)] = Rs 60,00,000 Rs 25,71,428 = Rs

34,28,571.

2. Loss on sale of existing machine [book value, Rs 34,28,571 Rs 10,20,000,

sale proceeds] = Rs 24,08,571.

3. Tax benefit (Rs 24,08,571 (A) 0.35) = Rs 8,42,999.

c Cost of lay-off:

1. Skilled labour 5 Rs 4,000 5 (months) = Rs 1,00,000

2. Floor manager = 1 Rs 8,000 5 = 40,000

3. Maintenance person = 1 Rs 6,000 5 = 30,000

1,70,000

(B) Incremental Cash Inflows: (t = 1 4):


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(B) Incremental Cash Inflows: (t = 1 4):

YearYear

Particulars 1 (Rs) 2 (Rs) 3 (Rs) 4 (Rs)

1. Sales revenuea 4,00,00,000 4,28,40,000 4,58,81,640 4,91,34,408

2. Add savings in

maintenance costb30,000 30,000 30,000 30,000

3. Add savings in labour

costc4,08,000 4,08,000 4,08,000 4,08,000

4. Less variable costd (52,00,000) (55,40,800) (59,05,796) (62,96,663)

5. Less incremental

depreciatione (13,92,858) (13,92,858) (13,92,858) (13,92,858)

6. EBT 3,38,45142 3,63,44,342 3,90,20,986 4,18,82,887

7. Less tax (0.35) (1,18,45,799) (1,27,20,519) (1,36,57,346) (1,46,59,010)

8. EAT 2,19,99,342 2,36,23,822 2,53,63,640 2,72,23,876

9. Add incremental

depreciation 13,92,858 13,92,858 13,92,858 13,92,858

10. CFAT 2,33,92,200 2,50,16,680 2,67,56,498 2,86,16,734

11. Release of working

capital 60,00,000

12. Total 2,33,92,200 2,50,16,680 2,67,56,498 3,46,16,734

a Sales revenue : Year 1 (0 08 1 00 000 Rs 5 000) = Rs 4 00 00 000


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a Sales revenue : Year 1 (0.08 1,00,000 Rs 5,000) = Rs 4,00,00,000

2 (0.08 1,02,000 Rs 5,250) = 4,28,40,000

3 (0.08 1,04,040 Rs 5,512) = 4,58,81,640

4 (0.08 1,06,120 Rs 5,787) = 4,91,34,408

b Savings in maintenance cost (Rs 1,00,000, existing Rs 70,000 proposed) = Rs 30,000c Savings in labour cost:

1 Existing:Skilled labour (20 Rs 4,000 12 months) Rs 9,60,000

Floor manager (3 Rs 8,000 12) 2,88,000

Maintenance (2 Rs 6,000 12) 1,44,000 Rs 13,92,000

2 New: Skilled labour (15 Rs 4,000 12) 7,20,000

Floor manager (2 Rs 8,000 12) 1,92,000

Maintenance (1 Rs 6,000 12) 72,000 9,84,000

4,08,000

d Variable cost and general administrative costs:

Year 1 [(0.08 1,00,000 Rs 600) + Rs 4,00,000] = Rs 52,00,000

2 [(0.08 1,02,000 Rs 630) + Rs 4,00,000] = 55,40,000

3 [(0.08 1,04,040 Rs 661) + Rs 4,00,000] = 59,05,796

4 [(0.08 1,06,120 Rs 694) + Rs 4,00,000] = 62,96,663

e Incremental depreciation:

1. New equipment (Rs 1,00,00,000 Rs 10,00,000) 4 Rs 22,50,000

2. Existing (Book value, Rs 34,28,571 0) 4 8,57,142

13,92,858


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(C) Computation of NPV

Year Incremental

cash inflows

PV factor

(0.14)

Total PV

1 Rs 2,33,92,200 0.877 Rs 2,05,14,959

2 2,50,16,680 0.769 1,92,37,826

3 2,67,56,498 0.675 1,80,60,636

4 3,46,16,734 0.592 2,04,93,106

Total 7,83,06,527

Less Incremental cash outflow 1,43,07,001

NPV 6,39,99,526

Decision: The Chola Chimney should launch the Zimney

Note: The research and development cost of Zimney (Rs 20,00,000) and

expenses incurred on market survey (Rs 5,00,000) are sunk cost and,

therefore, irrelevant for analysis.


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Table A-1 : The Present Value of One Rupee

Year 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909

2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826

3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751

4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683

5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621

6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564

7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513

8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467

9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424

10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386

11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350

12 0.887 0.789 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319

13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290

14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263

15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239


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Table A-1: The Present Value of One Rupee (Contd.)

Yea

r

11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833

2 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694

3 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579

4 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482

5 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402

6 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335

7 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279

8 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233

9 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194

10 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162

11 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135

12 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112

13 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093

14 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078

15 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065


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Table A-2 : The Present Value of an Annuity of One Rupee

Year 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.9092 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736

3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487

4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170

5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791

6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355

7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868

8 6.728 7.326 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335

9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759

10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145

11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495

12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.81413 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103

14 13.004 12.106 11.296 10.563 9.899 9.295 8.746 8.244 7.786 7.367

15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.560 8.061 7.606


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Table A-2: The Present Value of an Annuity of One Rupee (Contd.)

Year 11% 12% 13% 14% 15% 16% 17% 18% 9%1 20%

1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.850 0.833

2 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528

3 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106

4 3.102 3.037 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589

5 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991

6 4.231 4.111 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326

7 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605

8 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837

9 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031

10 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192

11 6.207 5.938 5.687 5.453 5.234 5.029 4.836 4.656 4.487 4.327

12 6.492 6.194 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439

13 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533

14 6.982 6.628 5.303 6.002 5.724 5.468 5.229 5.008 4.802 4.611

15 7.191 6.811 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675


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Format 1: Cash Outflows of New Project [Beginning of the Period at Zero Time

(t= 0)] a) No salvage

1. Cost of new machine 50000

2. + Installation cost 100003. + Working capital requirements 40000

4. tax saving due to investment allowance 6250 (5000*25%)*50%

Format 2: Determination of Cash Inflows: Single Investment Proposal

(t = 1 10)

Particulars Years1 2 3 4 .... 10

Cash sales revenues 42000 42000 42000 42000 . 42000

Less: Cash operating cost 32000 32000 32000 32000 .. 32000

Less: Depreciation 6000 6000 6000 6000 . 6000

Taxable income 4000 4000 4000 4000 .. 4000

Less: Tax (50%) 2000 2000 2000 2000 2000Earning after taxes 2000 2000 2000 2000 .. 2000

Plus: Depreciation 6000 6000 6000 6000 .. 6000

Cash inflows after tax (CFAT) 8000 8000 8000 8000 8000

Plus: Recovery of working capital (in10th year) 40000

48000

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