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10-10-11

Chapter 10Chapter 10

Capital Budgeting II: Capital Budgeting II: Additional AspectsAdditional Aspects


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10-10-22

CAPITAL BUDGETING II: ADDITIONAL ASPECTS

NPV, IRR, Profitability Index Methods – A Comparison

Inflation and Capital budgeting

Project Selection Under Capital Rationing

Solved Problems

Mini Case


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NPV Vs. IRR Methods

The NPV and IRR methods would in certain situations give the same accept-reject decision. But they may also differ in the sense that the choice of an asset under certain circumstances may be mutually contradictory. The comparison of these methods, therefore, involves a discussion of

(1) the similarities between them, and

(2) their differences, as also the factors which are likely to cause such differences.

NPV and IRR: Similarities

The two methods-IRR and NPV- would give consistent results in terms of acceptance or rejection of investment proposals in certain situations.

Conventional Investment A conventional investment is one in which the cash flow pattern is such that an initial investment (outlay or cash outflow) is followed by a series of cash inflows. Thus, in the case of such investments, cash outflows are confined to the initial period.

Independent Proposals The independent proposals refer to investments the acceptance of which does not preclude the acceptance of others so that all profitable proposals can be accepted and there are no constraints in accepting all profitable projects.


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The reason why both the methods are equivalent and support or reject a proposal is simple. According to the NPV method, the decision rule is that a project will be accepted if it has a positive NPV, that is, NPV exceeds zero. The IRR method would support projects in whose case the IRR is more than the required rate of return (r exceeds k). When the NPV = zero or the IRR = k, the project may be accepted or rejected. The projects which have positive net present values will also have an IRR higher than the required rate of return.

Thus, Fig. 1 portrays NPV as (i) positive; (ii) zero; and (iii) negative corresponding to three situations (a) IRR > K; (b) IRR = K; (c) IRR < K.

Figure 1 shows the relationship between the NPV of a project and the discount rate. If there is no K, or discount rate is zero (a very unreal situation), NPV is maximum. As the value of K increases, the NPV starts declining. At 12 per cent rate of discount, the NPV is zero. This is the IRR also because by definition it is that rate of discount which reduces the NPV to zero. Assuming cost of capital to be 8 per cent, we find that NPV is positive by amount (a) and the project is acceptable and so is it under IRR as its value is > K (0.12 > 0.08). If we assume K to be 16 per cent, the project is unacceptable as the NPV is negative by amount (b) and so is it under IRR as IRR < K (0.12 < 0.16). The two approaches lead to identical results with regard to the accept-reject decision.


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Net

pre

sen

t va

lue

Discount rate (K)

Figure 1 : NPV and Discount rate

(a)

(+)

04 8 12 16 20

(b)

(-)

x

y


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NPV and IRR Methods: Differences

However, in certain situations they will give contradictory results such that if the NPV method finds one proposal acceptable, IRR favours another. This is so in the case of mutually exclusive investment projects. If there are alternative courses of action, only one can be accepted. Such alternatives are mutually exclusive. The mutual exclusiveness of the investment projects may be of two types: (i) technical, and (ii) financial.

Technical Exclusiveness The term technical exclusiveness refers to alternatives having different profitabilities and the selection of that alternative which is the most profitable. Thus, in the case of a purchase or lease decision the more profitable out of the two will be selected.

Financial Exclusiveness The mutual exclusiveness may also be financial. If there are resource constraints, a firm will be forced to select that project which is the most profitable rather than accept all projects which exceed a minimum acceptable level (say, k). The exclusiveness due to limited funds is popularly known as capital rationing.

The different ranking given by the NPV and IRR methods can be illustrated under the following heads:

1. Size-disparity problem;

2. Time-disparity problem; and

3. Unequal expected lives.


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1. Size-disparity problem

Size disparity arises when the initial investment in mutually exclusive projects is different.

Example 1

Particulars Project A Project B Project B-A

Cash outlaysCash inflows at the end of year, 1IRR (%)kNPV

(Rs 5,000)6,250

25

681.25

10

(Rs 7,500)9,150

22

817.35

(Rs 2,500)2,900

16

Thus, the two methods rank the projects differently. Project A has a higher IRR (0.25) than project B (0.22) but the NPV of project B (Rs 817.35) is more than that of A (Rs 681.25). The important question is which method, in such a situation, gives better results? The answer should be related to the effect of the decision on the maximisation of the shareholders’ wealth. The IRR method is not compatible with the goal of wealth maximisation. It is concerned with the rate of return on investment or yield rather than the total yield on the investment. In the above example, assuming 10 per cent to be the required rate of return, the firm would be left with Rs 750 [Rs 6,250 – (Rs 5,000 + 0.10 × Rs 5,000)] after one year in case project A is accepted and Rs 900 [Rs 9,150 – (Rs 7,500) + 0.10 × Rs 7,500] in case project B is accepted. The NPV method suggests that project B is better. This recommendation is consistent with the goal of the firm of maximising shareholders’ wealth.


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Incremental Approach

The conflict between the NPV and IRR in the above situation can be resolved by modifying the IRR so that it is based on incremental analysis. According to the incremental approach, when the IRR of two mutually exclusive projects whose initial outlays are different exceeds the required rate of return, the IRR of the incremental outlay of the project requiring a bigger initial investment should be calculated. This involves the following steps:

1) Find out the differential cash flows between the two proposals.

2) Calculate the IRR of the incremental cash flows.

3) If the IRR of the differential cash flows exceeds the required rate of return, the project having greater investment outlays should be selected, otherwise it should be rejected.

In Example 1, the IRR of the differential cash outlay of Project B is 16 per cent. The required rate of return is 10 per cent. Thus, project B is better than project A in spite of the fact that IRR in the latter is lower because it offers the benefits offered by project A plus a return in excess of the required return on Rs 2,500, that is, differential cash outlays.


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2. Time-disparity Problem

Time-disparity arises when the cash flow pattern of mutually exclusive projects is different.

Example 2

Year Cashflows

Project A Project B

01234IRR (%)NPV (0.08)

Rs 1,05,00060,00045,00030,00015,000

20 23,970

Rs 1,05,00015,000 30,00045,00075,000

16 25,455

We find on the basis of a comparison of the internal rate of returns that project A is better, but the NPV method suggests that project B is better. Since the cost of capital is 8 per cent, given the objective of the firm to maximise wealth, project B is definitely better.Under the time-disparity problem it is the cost of capital which will determine the ranking of projects. If we take k = 0.10, we shall find project A is better as its net present value would be Rs 19,185 compared to Rs 18,435 of B. Its IRR is also more than that of B. Both the methods give identical prescription. But it does not imply that the IRR is superior to the NPV method, as the NPV is giving the same ranking as the IRR. In the event of conflicting rankings, the firm should rely on the rankings given by the NPV method.


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3. Projects With Unequal Lives

Another situation in which the IRR and NPV methods would give a conflicting ranking to mutually exclusive projects is when the projects have different expected lives. This is shown in Example 3.

Example 3

There are two projects A and B. A has a service life of one year, while B’s useful life is five years. The initial cash outlay for both the projects may be assumed to be Rs 20,000 each. The cash proceeds from project A (at the end of the first year) amount to Rs 24,000. The cash generated by project B at the end of the fifth year is likely to be Rs 40,200. Assume that the required rate of return is 10 per cent. Compute the NPV and the IRR of the two projects.

SolutionIRR and NPV of Projects A and B

Project IRR (per cent) NPVA 20 Rs 1,816B 15 4,900

Obviously, the ranking given by the IRR and NPV methods is different. According to the IRR method, the recommendation would favour project A while the NPV method would support project B. The conflict in the ranking by the two methods in such cases may be resolved by adopting a modified procedure. There are two approaches to do this:


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(1) Common time horizon approach

Common time horizon approach makes a comparison between projects that extends over multiples of the lives of each.

Example 4

Particulars Project A Project B

Initial outlay Rs 10,000 Rs 20,000

Cash inflows after taxes

Year-end 1 8,000 8,000

2 7,000 9,000

3 Nil 7,000

4 Nil 6,000

Service life (years) 22

Required rate of return 0.10


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Solution

Project A

Year Cash flows PV factor Total present value

012334NPV

Rs 10,0008,0007,000

(10,000)a

8,0007,000

1.0000.9090.8260.8260.7510.683

(Rs 10,000)7,2725,782

(8,260)6,0084,7815,583

a Machine replaced at the end of year 2.

Project B


01234

Rs 20,0008,0009,0007,0006,000

1.0000.9090.8260.7510.683

Rs 20,0007,2727,4345,2574,098

Net present value 4,061

Decision Project A should be preferred to project B because of its larger NPV. If we had compared the two projects without incorporating the consequences of replacing the machine at the end of year 2, the decision would have been the reverse, because the net present value of project A then would be Rs 3,054 [Rs 7,272 + Rs 5,782 – Rs 10,000].


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(2) Equivalent annual value, (EANPV)/cost approach (EAC).

The EANPV/EAC is a better approach. The EANPV is determined

dividing the NPV of cash flows of the project by the annuity factor

corresponding to the life of the project at the given cost of capital.

The EAC is obtained dividing the total PV of cash outflows by the

relevant annuity factor. While the maximisation of EANPV is the

decision-criterion in the case of revenue-expanding proposals, the

minimisation of EAC is the guiding criterion for cost reduction

proposals.


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Example 5 (Revenue-expanding Investment Proposal)

A firm is considering to buy one of the following two mutually exclusive

investment projects:

Project A: Buy a machine that requires an initial investment outlay of Rs

1,00,000 and will generate the CFAT of Rs 30,000 per year for 5 years.

Project B: Buy a machine that requires an initial investment outlay of Rs

1,25,000 and will generate the CFAT of Rs 27,000 per year for 8 years.

Which project should be undertaken by the firm? Assume 10 per cent as cost

of capital.

Solution

(i) Determination of NPV of Projects A and B

Project Years CFAT PV factor (0.10) Total PV NPV

A

B

1-5

1-8

Rs 30,000

27,000

3.791

5.335

Rs 1,13,730

1,44,045

Rs 13,730

19,045


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Example 6

(Cost-reduction Investment Proposal) A firm is considering to instal a large stamping machine. Two machines currently being marketed will do the job satisfactorily. Machine A costs Rs 50,000 and will require cash running expenses of Rs 15,000 per year. It has a useful life of 6 years and is expected to yield Rs 2,000 salvage value at the end of its useful life. Machine B costs Rs 65,000 but cash running expenses are expected to be Rs 12,000. This machine is expected to have a useful life of 10 years with salvage value of Rs 5,000. Assume both the machines would be depreciated on straight line basis for tax purposes.

If the corporate tax rate is 35 per cent and cost of capital is 10 per cent, which machine should be bought by the company?

(ii) Determination of EANPV:

EANPV (A) = Rs 13,730/3.791 = Rs 3,621.74

EANPV (B) = Rs 19,045/5.335 = Rs 3,569.82

On the basis of NPV criterion, Project B is preferred. However, on the basis of EANPV, project A becomes more desirable, with higher EANPV. In fact, acceptance of project A would be a right decision.

)1(capital ofcost givenat project the of life to ingcorrespond annuity ofPV

project the of valuepresent Net EANPV


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Solution

Equivalent Annual Costs of Machines A and B

Particulars Costs PV factor (0.10)

Adjusted PV

Machine A Machine B Machine A Machine B

0 (Initial cost)(Operating cost): 1-6 years (A) 1-10 years (B)

Less: Salvage value: 6th year (A) 10th year (B)Present value of total costsDivided by annuity PV factor for 10 per cent corresponding to the life of the project (capital recovery factor)Equivalent annual cost (EAC)

Rs 50,000

6,950—

2,000`

Rs 65,000

5,700

5,000

1.000

4.3556.145

0.5640.386

Rs 50,000

30,267.25________80,267.25

1,128.00 —

79,139.25

4.355

18,172

Rs 65,000

35,026.501,00,026.50

— 1,930

98,096.50

6.145

15,963.63

Recommendation Since Machine B has a lower equivalent annual cost, it is preferred investment.


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Working Notes

Determination of Operating Costs

Particulars Machine A Machine B

Cash running cost Rs 15,000 Rs 12,000

Less: Tax shield @35 per cent (assuming profitable

operations)

5,250 4,200

Less: Tax advantage on depreciation charged every year:

Machine A (Rs 8000 × 0.35) 2,800 —

Machine B (Rs 6,000 × 0.35) — 2,100

Effective operating cash outflows 6,950 5,700


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Reinvestment Rate Assumption

The conflict between the NPV and IRR methods is mainly ascribed to the

different reinvestment rate assumptions of intermediate cash inflows

accruing from projects. The IRR method implicitly assumes that the cash

flows generated from the projects are subject to reinvestment at IRR. In

contrast, the reinvestment rate assumption under the NPV method is the

cost of capital. The assumption of the NPV method is conceptually superior

to that of the IRR as the former has the virtue of having a uniform rate

which can consistently be applied to all investment proposals.

The IRR can be modified (to overcome the deficiency of the reinvestment

rate assumption) assuming the cost of capital to be the reinvestment rate.

Implicit investment rate

Implicit investment rate is the rate at which interim cash flows can be

invested.


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Under the IRR method, both projects have a rate of return of 100 per cent. If Rs 100 were invested for one year at 100 per cent, it would grow to Rs 200, and if invested for two years, to Rs 400. Since both the projects have the same IRR, the firm should be indifferent regarding their acceptability, if only one of two projects is to be picked up as both the projects are equally profitable. For this to be true, it is necessary that Rs 200 received at the end of year 1 in case of project A should be equal to Rs 400 at the end of year 2. In order to achieve this, it necessarily follows that the firm must be able to reinvest the first year’s earnings at 100 per cent. If not, it would be unable to transform Rs 200 at the end of the first year into Rs 400 at the end of the second. And if it cannot transform Rs 200 into Rs 400 in a year’s time, the two projects A and B cannot be ranked equal. There is no reason to believe that a firm can find other investment opportunities at precisely the required rate.

In contrast, the present value method does not pose any problem. Let us calculate the present value of Example 7, assuming cost of capital (k) as 10 per cent.

The superficiality of the reinvestment rate under the IRR method can be demonstrated by comparing the following two investment projects.

Project Initial investment Cash inflows

Year 1 Year 2

A Rs 100 Rs 200 0

B 100 0 Rs 400


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The PV method indicates that project B is preferable to project A as its net present value is greater. The reinvestment rate in the PV method seems more realistic and reasonable. It assumes that earnings are reinvested at the same rate as the market cost of capital.

However, the IRR can be modified assuming the cost of capital to be the reinvestment rate. The intermediate cash inflows will be compounded by using the cost of capital. The compounded sum so arrived at and the initial cost outflows can be used as the basis of determining the IRR.

Thus, the assumption regarding the reinvestment rate of the cash inflows generated at the intermediate stage is theoretically more correct in the case of NPV as compared to the IRR.

Example 7

Year Project A Project B

Cashflows PV factor Total PV Cashflows PV factor Total PV

1 Rs 200 0.909 Rs 181.80 0 — —

2 0 — ____________ Rs 400 0.826 Rs 330.40

181.80 330.40

Less: Initial outlay 100.00 100.00

Net present value 81.80 230.40


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Computational Problems

IRR method also suffers from computational problems. These may be discussed with reference to two aspects.

Computation in Conventional Cash Flows

It has been shown while computing the IRR that the calculation of the IRR involves a trial-and-error procedure as a result of which complicated computation has to be done. In conventional proposals having a constant cash inflow stream (i.e. annuity) the computation, is not so tedious.

Computation in Non-conventional Flows

The problem of computation of IRR gets accentuated when cash flow patterns are non-conventional. The complications in such cases are

a) that the IRR is indeterminate, and

b) there may be multiple IRRs


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Indeterminate IRR

For the following pattern of cash flows of an investment proposal, the IRR cannot be determined.

Example 8

CO0 = Rs 1

CFAT1 2

CO2 2

Where subscripts 0, 1, 2 refer to respective time periods, CFAT = cash inflows, CO = cash outflows

The required equation to solve the IRR is:

Clearly, the value of IRR is intermediate. On the other hand, the NPV of this project, given k as 10 per cent, can be easily ascertained. This would be negative (Rs –0.834), as shown below:

1r toleads which ,r1

2

r1

21 2

2


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Clearly, the value of IRR is intermediate. On the other hand, the NPV of this project, given k as 10 per cent, can be easily ascertained. This would be negative (Rs –0.834), as shown below:


012

Rs (1)+2(2)

1.0000.9090.826

Rs 1.0001.818

(1.652)(0.834)

Multiple Rates of IRR

Another serious computational deficiency of IRR method is that it can yield multiple internal rates of return. This is illustrated in Example 9.

Example 9

Initial cost

Net cash flow

Net cash flow

Year 0

1

2

(Rs 20,000)

90,000

(80,000)


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Let (1 + r) be = X and divide both sides of equation by Rs 10,000, 2 = [(9/X) – (8/X)2] = 0

Multiplying by X 2, we can transform the equation into the quadratic form, 2X 2 – 9X + 8 = 0

Such an equation with a variable to the second power has 2 roots which can be identified as:

where a = coefficient of the variable raised to the second power

b = coefficient of the variable raised to the first power

c = constant or coefficient of the variable raised to the zero power

Substituting the values for a, b, and c into the quadratic formula produces value for X of 1.21. Since X = (1 + r), the internal rates for this project are 21.9 and 228 per cent.

2r1

000,80Rs

r1

90,000 Rs 20,000 Rs :isequation required The

(2)2a

4acbbX

2


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Thus, the project yields a dual IRR. This kind of problem does not arise when the NPV method is used. The problem with the IRR is that if two rates of return make the present value of the project zero, (21.9 and 228 per cent respectively in our example), which rate should be used for decision-making purposes?

To conclude the discussion relating to the comparison of NPV and IRR methods, the two methods would give similar accept-reject decisions in the case of independent conventional investments. They would, however, rank mutually exclusive projects differently in the case of the

1) Size-disparity problem,

2) Time-disparity problem, and

3) Unequal service life of projects.

The ranking by the NPV decision criterion would be theoretically correct as it is consistent with the goal of maximisation of shareholders’ wealth.


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Net Present Value Vs. Profitability Index

In most situations, the NPV and PI, as investment criteria, provide the same accept and reject decision, because both the methods are closely related to each other. Under the PI method, the investment proposal will be acceptable if the PI is greater than one; it will be greater than one only when the proposal has a positive net present value. Likewise, PI will be less than one when the investment proposal has negative net present value under the NPV method. However, while evaluating mutually exclusive investment proposals, these methods may give different rankings.

Thus, project A is acceptable under the NPV method, while project B under the PI method. Which project should the firm accept? The NPV technique is superior and so project A should be accepted.

Example 10

Year Project A Project B

012Present value of cash inflow (0.10)NPVPI

(Rs 50,000)40,00040,00069,44019,440

69,440/50,000 = 1.39

(Rs 35,000)30,00030,00052,08017,080

52,080/35,000 = 1.49


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Project Selection Under Capital Project Selection Under Capital RationingRationing

The capital rationing situation refers to the choice of investment proposals under financial constraints in terms of a given size of capital expenditure budget. The objective to select the combination of projects would be the maximisation of the total NPV. The project selection under capital rationing involves two stages: (1) identification of the acceptable projects. (2) selection of the combination of projects. The acceptability of projects can be based either on profitability index or IRR. The method of selecting investment projects under capital rationing situation will depend upon whether the projects are indivisible or divisible. In case the project is to be accepted/rejected in its entirety, it is called an indivisible project; a divisible project, on the other hand, can be accepted/rejected in part. These are illustrated in Examples 11 and 12 respectively.


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Example 11 (Divisible Project)

A company has Rs 7 crore available for investment. It has evaluated its options and has found that only 4 investment projects given below have positive NPV. All these investments are divisible. Advise the management which investment(s)/projects it should select.

Project Initial investment (Rs crore)

NPV (Rs crore) PI

X 3.00 0.60 1.20

Y 2.00 0.50 1.25

Z 2.50 1.50 1.60

W 6.00 1.80 1.30

Solution

Ranking of the Projects in Descending Order of Profitability Index

Project and (rank) Investment outlay (Rs crore)

Profitability index NPV (Rs crore)

Z (1) 2.50 1.60 1.50

W (2) 6.00 1.30 1.80

Y (3) 2.00 1.25 0.50

X (4) 3.00 1.20 0.60

Accept Project Z in full and W in part (Rs 4,50,000) as it will maximise the NPV.


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Example 12 (Indivisible Project) A company working against a self-imposed capital budgeting constraint of Rs 70 crore is trying to decide which of the following investment proposals should be undertaken by it. All these investment proposals are indivisible as well as independent. The list of investments along with the investment required and the NPV of the projected cash flows are given as below:

Project Initial investment (Rs crore)

NPV (Rs crore)

ABCDE

1024322218

618203020

Which investment should be acquired by the company?

Solution

NPV from investments D, E and B is Rs 68 crore with Rs 64 crore utilised leaving Rs 6 crore to be invested in some other investment outlet. No other investment package would yield an NPV higher than this amount. The company is advised to invest in D, E and B projects.

Trial and error process is an integral part of selecting optimal investment packages/set in capital ratinoning situation. Consider Example 13.


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Example 13 Sound Limited has a financial resource constraint of a maximum of Rs 65 lakh in the current year. It has evaluated a large number of investment projects but has discarded all except those listed below. All the listed investment proposals are independent. The selected list of investments provide investment outlays, gross present value, NPV and present value index.

Project Investment outlay

NPV Gross present value

Present value index

ABCDEFGHIJKLMNO

Rs 21,85,00019,10,00015,50,00013,00,00011,45,000

9,40,0006,75,0005,35,0004,65,0004,30,0004,10,0003,50,0002,75,0002,45,0001,90,000

1,26,05,000

Rs 15,07,50010,70,000

2,15,0002,75,000

15,80,0004,25,0006,20,0003,90,0006,10,0004,77,5002,95,0003,05,0001,07,5002,05,0003,00,000

83,82,500

Rs 36,92,50029,80,00017,65,00015,75,00027,25,00013,65,00012,95,000

9,25,00010,75,000

9,07,5007,05,0006,55,0003,82,5004,50,0004,90,000

2,09,87,500

1.691.561.141.212.381.451.921.732.312.111.721.871.391.842.58

Which investments should be acquired by Sound Limited?


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Solution First, we should arrange the investment projects in descending order of present value (PI) index. The optimal investment portfolio/set will be one which yields the maximum NPV. The investment projects are accordingly listed below.

Project PI Investment outlays of NPV of

Project Cumulative Project Cumulative

OEIJGLNHKABFMDC

2.582.382.312.111.921.871.841.731.721.691.561.451.391.211.14

Rs 1,90,00011,45,000

4,65,0004,30,0006,75,0003,50,0002,45,0005,35,0004,10,000

21,85,00019,10,000

9,40,0002,75,000

13,00,00015,50,000

Rs 1,90,00013,35,00018,00,00022,30,00029,05,00032,55,00035,00,00040,35,00044,45,000

66,30,0001

63,55,000

Rs 3,00,00015,80,000

6,10,0004,77,5006,20,0003,05,0002,05,0003,90,0002,95,000

15,07,50010,70,000

4,25,0001,07,5002,75,0002,15,000

Rs 3,00,00018,80,00024,90,00029,67,50035,87,50038,92,50040,97,50044,87,50047,82,500

— 58,52,5002

1 Not feasible at this stage; cumulative investment outlays exceed Rs 65 lakh.2 Investment outlay as well as NPV consist of projects (from O to H) plus project B.


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Project Investment outlays of NPV of

Project (s) Cumulative Project (s) Cumulative

O to H — Rs 40,35,000 — Rs 44,87,500

A Rs 21,85,000 62,20,000 Rs 15,07,500 59,95,000

M 2,75,000 64,95,000 1,07,500 61,02,500

Such a substitution exercise involves a trial and error approach. Thus, the optimal investment package consists of 10 projects (O, E, I, J, G, L, N, H, A and M) requiring a total investment outlay of Rs 64.95 lakh, yielding a total NPV of Rs 61,02,500.

In case the company is guided simply by the PI index, then it selects the first nine projects (numbered from O through K) plus project B. This investment package yields an NPV of Rs 58,52,500.


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Fallout of Capital Rationing

Capital rationing limits the amount to be spent on capital expenditure decisions. The firm may impose such a limit primarily for two reasons: (i) there may be a paucity of funds and(ii) corporate managers/owners may be conservative and may not like to invest more than a specified/stated sum in capital projects at one point of time; they may like to accept projects with a greater margin of safety, measured by NPV.

Whatever might be the reasons for capital rationing, it usually results in an investment policy that is less than optimal. The reason is that capital rationing does not allow the business firm to accept all profitable investment projects which could add to net present value and, thus, add to the wealth of shareholders.

Another notable consequence is that capital rationing may lead to the acceptance of several small investment projects (promising higher return per rupee of investment) rather than a few large investment projects. Acceptance of such a package of investment projects is likely to have a bearing on the risk complexion of the business firm (perhaps it may decrease).

Finally, selection criterion of investment projects under capital rationing (based on one-period analysis) does not reckon intermediate cash inflows expected to be provided by an investment project.


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10-10-3434

INFLATION AND CAPITAL BUDGETING

The capital budgeting results would be unrealistic if the impact of inflation is not correctly factored in the analysis. The cash flow estimates will not reflect the real purchasing power. In other words, cash flows would be shown at inflated sums and, to that extent, cause distortion in capital budgeting decisions. Therefore, cash flows should be adjusted to accommodate the inflation factor so that the capital budgeting decisions reflect the ‘true’ picture. This Section dwells on the procedure for adjusting data for inflation. Consider Example 14.

Example 14

Proposal X requires an initial capital outlay of Rs 2,00,000, with no salvage value, and will be depreciated on a straight line basis for tax purposes. The earnings before depreciation and taxes (EBDT) during its 5 year life are:

Year 1 2 3 4 5

EBDT Rs 70,000 Rs 76,000 Rs 80,000 Rs 60,000 Rs 52,000


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10-10-3535

Determination of NPV (When There is No Inflation)

(Amount in thousand rupees)

Year EBDT Depreciation

(200 ÷ 5)

Taxable income

(Col. 2 – 3)

EAT (Col. 4 ×

0.65)

CFAT (Col. 5 +

3)

PV factor

Total PV (Col. 6 ×

7)

1 2 3 4 5 6 7 8

1 70 40 30 19.5 59.5 0.893 53.13

2 76 40 36 23.4 63.4 0.797 50.53

3 80 40 40 26.0 66.0 0.712 46.99

4 60 40 20 13.0 53.0 0.636 33.71

5 52 40 12 7.8 47.8 0.567 27.10

Gross present value 211.46

Less: Cash outflows 200.00

Net present value 11.46

Since the net present value is positive, the project is worth accepting in a non-

inflationary scenario.


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10-10-3636

Determination of CFAT in Inflationary Situation


Year EBDT

Compound factor at 0.15

Revised EBDT

(Col. 2 × 3)

Depreciation

Taxable income

(Col. 4 – 5)

EAT (Col. 6 ×

0.65)

CFAT (Col. 7 +

5)

1 2 3 4 5 6 7 8

1 70 1.150 80.50 40 40.50 26.32 66.32

2 76 1.322 100.47 40 60.47 39.31 79.31

3 80 1.521 121.68 40 81.68 53.09 93.09

4 60 1.749 104.94 40 64.94 42.21 82.21

5 52 2.011 104.57 40 64.57 41.97 81.97

In an inflationary situation, EBDT are expected to grow at 15 per cent. As per Table A-1 (showing compound sum of one rupee), EBDT can be determined (reflecting 15 per cent compound rate of growth). As amount of depreciation remains unchanged, taxable profits as well as taxes would go up as exhibited below:


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10-10-3737

Since CFAT are inflated sums, they are to be deflated at the rate of inflation (15 per cent) to determine real cash flows. The relevant calculations are as follows:

Determination of Real Cash Flows


Year CFAT Discount/deflated factor at 0.15 as per

Table A – 3

Real cash inflows (CFAT) (Col. 2 × 3)

1 2 3 4

1 66.32 1/1.15 = 0.870 57.70

2 79.31 1/ (1.15)2 = 0.756 59.96

3 93.09 1/(1.15)3 = 0.658 61.25

4 82.21 1/(1.15)4 = 0.572 47.02

5 81.97 1/(1.15)5 = 0.497 40.74

The real cash flows are substantially lower than nominal cash flows. This is due to the fact that increased income (as depreciation charges do not change) is subject to higher amount of taxes. The corporate tax rate is more than twice (35 per cent) the inflation rate (15 per cent). The NPV and real cash inflows are shown in the following tables.


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10-10-3838

NPV of Real CFAT

(Amount in Rs thousands)

Year Real CFAT PV factor at 12% Total PV (Col. 3 x 4)

1 2 3 4

12345Gross present valueLess: Cash outflowsNet present value

57.7059.9661.2547.0240.74

0.8930.7970.7120.6360.567

51.5347.7943.6129.9023.10

195.93200.00

(4.07)

IRR of Real CFAT

(Amount in Rs thousands)

Year Real CFAT PV factor at 11% Total PV (Col. 3 x 4)

1 2 3 4

12345Gross present valueIRR (%)

57.7059.9661.2547.0240.74

0.9010.8120.7310.6590.593

51.9948.6944.7730.9924.16

200.60 11.00


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10-10-3939

Since the NPV is negative under inflationary situations, the investment proposal is not acceptable. Similar conclusions follow based on the internal rate of return method. The IRR based on real CFAT is 11 per cent—lower than the cost of capital (12 per cent).

Thus, inflation results both in lower cash flows and lower real rates of return. Example 14 highlights that firms (conscious of protecting the real purchasing power of their owners) may go for unprofitable investment projects, affecting the shareholders wealth adversely. It underlines the significance of incorporating the inflation factor in evaluating capital budgeting decisions, in particular for business firms interested in real returns.

Consistency warrants that the real cost of capital should be used to discount real cash inflows after taxes and the nominal cost of capital should be employed for nominal CFAT. This point is illustrated in Example 15.


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10-10-4040

Example 15

The investment data of Prudent Company Ltd launching a new product and with 12 per cent cost of capital, is as follows:

Particulars Amount

InvestmentCFAT: Year 1

2345

Rs 7,00,0005,00,0004,00,0002,00,0001,00,0001,00,000

Assuming an inflation rate of 5 per cent, determine NPV of the project by using both the nominal rate of discount and the real rate of discount.

Solution

NPV Using Nominal Rate of Discount

Year CFAT PV factor at 0.12 Total PV

12345Total present value Less: Cash outflowsNet present value

Rs 5,00,0004,00,0002,00,0001,00,0001,00,000

0.8930.7970.7120.6360.567

Rs 4,46,5003,18,8001,42,400

63,600 56,700

10,28,0007,00,0003,28,000


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10-10-4141

Table 1: Real Cash Flows

Year CFAT Deflation factor at 0.05 Real CFAT

1 Rs 5,00,000 1/(1.05) = 0.952 Rs 4,76,000

2 4,00,000 1/(1.05)2 = 0.907 3,62,800

3 2,00,000 1/(1.05)3 = 0.864 1,72,800

4 1,00,000 1/(1.05)4 = 0.823 82,300

5 1,00,000 1/(1.05)5 = 0.784 78,400

The nominal rate of discount (n) is obtained by compounding the real rate (r) and inflation rate (i). In equations terms, it is

(l + n) = (l + r) (l + i) (3)

or (l + r) = (l + n)/(l + i). (4)

Substituting the values,

(l + r) = 1.12/1.05 = 1.0667

or r = 0.0667 or 6.67 per cent.

Since the discount rate now to be used is the real discount rate, the CFAT should also be adjusted for inflation so that they too are expressed in real terms. In operational terms, CFAT will be deflated by the inflation rate (5 per cent). While Table 1 shows real/deflated CFAT, NPV of real CFAT is provided in Table 2.


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10-10-4242

Table 2: NPV Using Real Rate of Discount

Year Real CFAT PV factor at 6.67%a Total PV

1 Rs 4,76,000 0.938 Rs 4,46,488

2 3,62,800 0.879 3,18,901

3 1,72,800 0.824 1,42,387

4 82,300 0.772 63,536

5 78,400 0.724 56,761

Total present value

10,28,073

Less: Cash outflows

7,00,000

Net present value 3,28,073b

a Based on interpolation as per Table A – 3. b Difference in NPV of Rs 73 (Rs 3,28,073 – Rs 3,28,000) between the two

discount rates (nominal and real) is on account of rounding off the values. Both the approaches provide the same answer.


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10-10-4343

SOLVED PROBLEMSSOLVED PROBLEMS


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10-10-4444

Solved Problem 1

Avon Chemical Company Ltd is presently paying an outside firm Re 1 per gallon to dispose of the waste material resulting from its manufacturing operations. At normal operating capacity the waste is about 40,000 gallons per year.

After spending Rs 40,000 on research, the company discovered that the waste could be sold for Rs 15 per gallon if it was processed further. Additional processing would, however, require an investment of Rs 6,00,000 in new equipment, which would have an estimated life of 5 years and no salvage value. Depreciation would be computed by the reducing balance method @ 25 per cent. There are no other assets in the 25 per cent block.

Except for the costs incurred in advertising Rs 20,000 per year, no change in the present selling and administrative expenses is expected if the new product is sold. The details of additional processing costs are as follows: variable—Rs 5 per gallon of waste put into process; fixed (excluding depreciation)—Rs 30,000 per year.

In costing the new product, general factory overheads will be allocated at the rate of Re 1 per gallon.

There will be no losses in processing, and it is assumed that all of the waste processed in a given year will be sold in that very year. Waste that is not processed further will have to be disposed off at the present rate of Re 1 per gallon. Estimates indicate that 30,000 gallons of the new product could be sold each year.

The management, confronted with the choice of disposing off the waste, or processing it further and selling it, seeks your advice. Which alternative would you recommend? Assume that the firm’s cost of capital is 15 per cent and it pays, on an average, 35 per cent tax on its income.


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10-10-4545

Solution

Cash outflows:

Cost of additional investment Rs 6,00,000

(i) Present value of cash inflows (excluding depreciation), t = 1 – 5

Particulars Amount

Increase in sales revenue (30,000 × Rs 15) Rs 4,50,000

Cost saving: reduction in disposal costs (30,000 × Re 1) 30,000

Less: Incremental costs: 4,80,000

Variable (30,000 × Rs 5) Rs 1,50,000

Fixed, manufacturing or processing 30,000

Advertising 20,000 2,00,000

Earnings before taxes 2,80,000

Less: Taxes 98,000

CFAT 1,82,000

× PVIFA (×)3.352

Total present value 6,10,064


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10-10-4646

(ii) PV of tax shield due to depreciation

Year Depreciation Tax advantage PV factor Total PV

1 Rs 1,50,000 Rs 52,500 0.870 Rs 45,675

2 1,12,500 39,375 0.756 29,767

3 84,375 29,531 0.658 19,431

4 63,281 22,148 0.572 12,669

1,07,542

(iii) PV of tax advantage due to short-term capital loss: [0.35 × (Rs 1,89,844) × 0.497] = Rs 33,023.

(iv) Determination of NPV

Gross present value [(i) + (ii) + (iii)] Rs 7,50,629

Less: Cost of additional investment 6,00,000

NPV 1,50,629

Note: Rs 40,000 spent on research is irrelevant cost and so is the allocated share of factory overheads.

Recommendation: Since the NPV is positive, the company is advised to purchase new equipment.


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10-10-4747

Solved Problem 2

An educational institute is planning to install airconditioners for its new computer centre. It has received proposals from 2 manufacturers. The first proposal is for the installation of 6 window airconditioners @ Rs 25,000 each. The other is for the installation of split airconditioners of an equal capacity costing Rs 2,00,000. The useful life of window airconditioners is 6 years and that of split airconditioners is 10 years. The cash operating costs associated with each proposal are given below:

Year Proposal 1 Proposal 2

1 2 3 4 5 6 7 8 910

Rs 20,00020,00020,00025,00025,00025,000

Rs 18,00018,00018,00022,00022,00022,00026,00026,00026,00026,000

The salvage value of the window airconditioners at the end of 6 years is expected to be Rs 10,000 and that of the split airconditioners Rs 15,000. Advise the educational institute which proposal should be selected by it if its opportunity cost of funds is 10 per cent.


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10-10-4848

Solution Equivalent Annual Cost

Proposal 1

Particulars Year Cost PV factor (at 10%)

PV

Purchase cost 0 Rs 1,50,000 1.000 Rs 1,50,000

Operating costs 1 20,000 0.909 18,180

2 20,000 0.826 16,520

3 20,000 0.751 15,020

4 25,000 0.683 17,075

5 25,000 0.621 15,525

6 25,000 0.564 14,100

Salvage value 6 (10,000) 0.564 (5,640)

Total PV Rs 2,40,780

Equivalent Annual Cost (EAC) = (Total present value of the project / PV of annuity corresponding to the life of the project at the given cost of capital.Rs 2,40,780/4.355 = Rs 55,288.17


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10-10-4949

Proposal 2

Particulars Year Cost PV factor (at 10%) PV

Purchase costOperating costs

Salvage ValueTotal PV

01234567891010

Rs 2,00,00018,00018,00018,00022,00022,00022,00026,00026,00026,00026,000

(15,000)

1.0000.9090.8260.7510.6830.6210.5640.5130.4670.4240.3860.386

Rs 2,00,00016,36214,86813,51815,02613,66212,40813,33812,14211,02410,036(5,790)

Rs 3,38,174

Equivalent Annual Cost (EAC) = Rs 3,32,384/6.145 = Rs 55,032.38

Recommendation The educational institution should go for split airconditioners as their equivalent annual cost is lower.


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10-10-5050

MINI CASEMINI CASE


10-10-5151

10-10-5151

(Replacement Situation) Gurgaon Chemicals supplies chemicals and dyes to various units in and around NCR Delhi. The onsite delivery of chemicals and dyes every month is 2,000 units. The unit sale price is Rs 100. The cost per unit is Rs 50. It is using a tempo which can carry a maximum of 80 units. The total distance covered in one tripe is 400 kms. The cost of diesel in the NCR Delhi is Rs 25.5 per litre. The average consumption of diesel is 8 kms per litre.

Due to increase in demand for dyes for industrial use, Gurgaon Chemicals has an opportunity to make and deliver 2,500 units per month. To cater to the increased demand, the company is contemplating buying a mini truck with a capacity to carry 165 units. The required mini truck is available from Eicher for Rs 14,00,000. The tempo being currently used has a book value of Rs 6,00,000. It can be sold for Rs 4,00,000. The salary of the tempo driver is Rs 6,000 per month. If the mini truck is acquired, Grugaon Chemicals would have to increase his monthly salary to Rs 8,000. The consumption of diesel by the truck would average 5 kms per litre. The maintenance cost of the mini truck would be Rs 8,500 compared to Rs 6,200 maintenance cost of the tempo. Gurgaon Chemical uses straightline method of depreciation for tax purposes. The tempo has a remaining useful life of 5 years. The mini could truck serve the need of the Gurgaon Chemicals for the next 5 years. The applicable tax rte is 35 per cent.

Nitin Jain, the CEO of Gurgaon Chemicals, has asked the CFO, Rahul Joshi, to examine the financial viability of the proposal to replace the tempo by the mini truck and make appropriate recommendation in this regard. Assume a required rate of return of 14 per cent.


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10-10-5252

Solution: Financial Analysis of Replacement of Tempo by Mini Truck

(A) Incremental cashoutflow (t = 0)

Cost of mini truck Rs 14,00,000

Less sale value of tempo 4,00,000

Less tax advantage on loss on sale of tempo:

Current book value Rs 6,00,000

Sale value 4,00,000

Loss on sale 2,00,000

Tax advantage x 0.35 70,000 Rs 9,30,000


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10-10-5353

(B) Increment cashoutflows (t = 1 – 5)

Incremental revenue1 (500 units x 12 months x Rs 100 6,00,000

Less incremental costs:Cost of additional units2 2,40,000Diesel charges3 (15,300)Maintenance cost4 2,300Driver’s salary5 24,000Depreciation6 1,60,000 4,71,000

Earnings before taxes 1,29,000

Less taxes (0.35) 45,150

EAT 83,850

Add depreciation 1,60,000

CFAT (t = 1 – 5 years) 2,43,850

PVIFA5.14 x 3.433

Total PV 8,37,137

NPV (B – A) (92,863)1 [ 500 units (2,500 units – 2,000 units) x 12 months x Rs 100]2 (500 units x 12 x Rs 50) 3 Diesel charges


10-10-5454

10-10-5454

3 Diesel charges

Truck Tempo

Mileage km/lit 5 8

Kms per trip 400 400

Trips/month (2,500 units ÷ 165 units per trip) 15 -

(2,000 units ÷ 80 units per trip) - - 25

Kms annually (12 months x 15 x 400) 72,000 -

(12 months x 25 x 400) - 1,20,000

Diesel consumed (72,000 ÷ 5) 14,400 -

(1,20,000 ÷ 8) - 15,000

Total cost (14,400 x Rs 25.5) Rs 3,67,700

-

(15,000 x Rs 25.5) - Rs 3,82,000

Savings in diesel cost (Rs 3,82,500 – Rs 3,67,200) = (Rs 15,300)

4 Maintenance cost (Rs 7,500 – Rs 6,200)5 Drivers salary [(Rs 8,000 – Rs 6,000) x 12 months)


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10-10-5555

6 Depreciation:

Depreciation on truck (Rs 14,00,000 ÷ 5) Rs 28,000

Depreciation on tempo (Rs 6,00,000 ÷ 5) 1,20,000

1,60,000

Recommendation

The proposal to acquire the mini truck and dispose off the tempo is

financially viable. The CEO may approve it and initiate follow-up

action.

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