Capital Budgeting (Contd...)

8/8/2019 Capital Budgeting (Contd...)

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Lesson 13

Chapter 4

Capital Budgeting

Unit 2

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After studying this lesson, you should be able to:

Describe and be able to use the IRR technique for evaluating capital

investments.

Understand the acceptance criteria for IRR. Explain some potential difficulties of several methods.

Compare IRR with NPV.

Understand and explain the use and role of capital rationing.

INTERNAL RATE OF RETURN (IRR)

The other important discounted cash flow technique of evaluation of capital budgetingproposals is known as IRR technique. The IRR of a proposal is defined as the discount

rate, which produces a zero NPV i. e., the IRR is the discount rate which will quite the

present value of cash inflows with the present value of cash outflow. The IRR is also

known as Marginal Rate of Return orTime Adjusted Rate of Return. Like the NPV, the

IRR is also based on the discounting technique. In the IRR technique, the future cash

inflows are discounted in such a way that their total present value is just equal to the

present value of total cash outflows. The time-schedule of occurrence of the future cash

flows is known but the rate of discount is not. Rather this discount rate is ascertained, by

the trial and error procedure. This rate of discount so calculated, which equates the

present value of future cash inflows with the present value of outflows, is known as the

IRR.


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Calculation:

Symbolically, the IRR is equal to the value of 'r' in the Equation

COo =nn

n

r

WCSV

r

CF

r

CF

R

CF

r

CF

or

CFo

)1()1()1()1()1()1(2

2

2

2

2

1

+

++

+

+

+

+

+

+

+

+

+

Where COO = cash outflow at time 0,

CFi = cash inflow at different point of time,

N = life of the project, andr = rate of discount (yet to be calculated)

SV&WC = salvage value and working capital at the end of the n years

The above Equation can also be written as

CO0 = nii

n

i r

WCSV

ri

CF

)1()(1 +

++

+=

Or o = 01 )1()(

COr

WCSV

ri nii

n

i

+

++

+=

CF

It may be noted in the Equation that this equation to be solved to ascertain the

value of 'r'. Unfortunately, the value of 'r' can only be ascertained by the trial and error

procedure together with linear interpolation.

Successive application of different discount rates to all cash flows must be made

until a close approximation of a zero NPV is found. With some experience, an analyst

will find that usually no more than two trials are necessary, because the first result will

show the direction of any refinement needed. A positive NPV indicates the need for a

higher discount rate, while a negative NPV calls for lowering the discount rate.

The specific procedure to find out the value of r implies finding out the net present

value of the proposal at two different assumed values of 'r' within which the IRR is

expected to lie. Thereafter, the two rates are interpolated to make the net present value

equal to zero.


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The detailed procedure for the calculation of IRR can be explained in two different

situations i. e.,

(i) When future cash flows are equal and take a form of annuity, and

(ii) When future cash flows are unequal. Both the situations have been taken up as

follows:

Case A: When future cash flows are equal:

A firm is evaluating a proposal costing Rs. 1,00,000 and having annual inflows of Rs.

25,000 Occurring at the end of each of next six years: There is no salvage value. The IRR

of the proposal may be calculated as follows:

Step 1:

Make an approximation of the IRR on the basis of cash flows data. A rough approxima-

tion may be made with reference to the payback period. The payback period in the given

case is 4 years. Now, search for a value nearest to 4 in the 6th year row of the PVAF

table. The closest figures are given in rate 12% (4.111) and the rate 13% (3.998). This

means that the IRR of the proposal is expected to lie between 12% and 13%.

Step 2:In order to make a precise estimate of the IRR, find out the NPV of the project for both

these rates as follows:

At 12%, NPV = (Rs. 25,000 x PVAF (12%, 6y) - Rs.l,00,000

=(Rs.25,000 x 4.111}-Rs.l,00,000

= Rs.2,775.

At 13%, NPV = (Rs. 25,000 x, PVAF (I3%, 6y) - Rs.l,00,000

= (Rs.25,000 x 3.998}-Rs 1,00,000

= Rs. -50.


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Step 3:

Find out the exact IRR by interpolating between 12% and 13%. It may be noted that IRR

is the rate of discount at which the NPV is zero. At 12%, the NPV is Rs. 2,775 and at

13% the NPV is Rs. -50. Therefore, the rate at which the NPV is zero will be higher than

12% but less than 13%. By interpolating difference of 1 %(13% - 12%), over NPV

difference of Rs. 2,825 [Rs: 2,775 -(-50)],

IRR = 12% +950,99775,02,1

000,00,1775,02,1

= 12.98%

So, the IRR of the project is 12.98%. The IRR can also be ascertained by starting

from 13%.

In such as case, the IRR is

IRR= 13% -950,99775,02,1

950,99000,00,1

= 12.98%

Case B: When future flows are not equal:

In case when the project is expected to generate an uneven stream of cash flows, the

calculation of the IRR is complicated. In order to minimize the number of calculations,

IRR can be calculated as follows.

I will explain this with the help of an example.

Example

Suppose a firm is evaluating a proposal costing Rs. 1,60,000 and expected to generate

cash inflows of Rs. 40,000, Rs. 60,000, Rs. 50,000, Rs. 50,000 and Rs. 40,000 at the end


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of each of next 5 years respectively. There is no salvage value thereafter. In this case,

there is an uneven stream of cash inflows and the IRR can be approximated as follows.

Step 1:

Find out the average annual cash inflow to get a Fake annuity.

Year

1

2

3

4

5

Cash inflows

(Rs.) CF

40,000

60,000

50,000

50,000

40,000

Total 2,40,000

= 2,40,000 /5 = Rs. 48,000.

Step 2:

Divide the initial outlay with the average cash inflows 1,60,000/48,000 = 3.33 yrs

Step 3:

Now, search for a value nearest to 3.33 in 5 years row of the PVAF table. The closest

figures given in table are at 15% (3.352) and at 16% (3.274). This means that the IRR of

the proposal is expected to lie between 15% and 16%.

Step 4:


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Find out the NPV of the proposal for both of these approximate rates as follows.

Year

1

2

3

4

5

Cash inflow

40,000

60,000

50,000

50,000

40,000

PVF (16%,5y)

.862

.743

.641

.552

.476

PVF (15%,5Y)

.870

.756

.658

.572

.497

PV (16%)

34,480

44,580

32,050

27,600

19,040

1,57,750

PV (15%)

34,800

45,360

32,900

28,600

19,880

1,61,540

At 16%, NPV = Rs. 1,57,750 - Rs. 1,60,000

= Rs. -2,250

At 15%, NPV = Rs. 1,61, 540-Rs. 1,60,000

=Rs.l, 540.

Step 5:

Find out the exact IRR by interpolating between 15% and 16%. At 15% the NPV is Rs.

1,540 and at 16% the NPY is Rs. -2,250. Therefore, the rate at which NPV is zero will be

more than 15%-but less than 16%. By interpolating the difference of 1% (i.e. 16% -

15%rover the NPV difference of Rs. 3,790 [i.e. Rs_ 2,250 - (- 1,540)],

IRR= 15% +750,57,1540,61,1

000,60,1540,61,

1

= 15.40%

So, the IRR of the project is 15.40%. The IRR can also be ascertained by starting from

16%. In such a case, the IRR is


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IRR = 16% -750,57,1540,61,1

750,57,1000,60,

1

= 15.40%

The Decision Rule:

In order to make a decision on the basis of IRR technique; the firm has to determine, in

the first instance, its own required rate of return. This rate, k, is also known as the cut-off

rate or the hurdle rate. A particular proposal may be accepted if its IRR, r, is more than

the minimum rate i. e., k, otherwise rejected. However, if the IRR is just equal to the

minimum rate, k, then the firm may be indifferent. In case of ranking of mutually

exclusive proposals, the proposal with the highest IRR is given the top priority while the

project with the lowest IRR is given the lowest priority. Proposals whose IRR is less than

the minimum required rate, k, may altogether be rejected.

This decision rule is based on the fact that the NPV of the project is zero if its

cash flows are discounted at the minimum' required rate i. e., k. If the proposal can give a

return higher than this minimum required rate, then it is expected to contribute to the

wealth of the shareholders. It may be noted however, that the IRR, r, of the proposal is

internal to the project while the minimum required rate, k, is external to the project.

The Critical Evaluation:

Besides the NPV technique, the IRR technique is the other important discounted cash

flow technique of evaluation of capital budgeting proposals. The IRR technique has been

compared with the NPV technique at a later stage.

However, the merits of the IRR technique can be summarized as follows:

i. The IRR technique takes into account the time value of money and the cash flows

occurring at different point of time are adjusted for time value of money to make

them comparable.


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ii. It is a profit-oriented concept and helps selecting those proposals which are

expected to earn more than the minimum required rate of return. So, the IRR

technique helps achieving the objective of maximization of shareholders wealth.

iii. The IRR of a proposal is expressed as a percentage and is compared with the cut-

off rate, which is also expressed as a percentage. Thus, the IRR has an appeal for

those who want to analyze proposal in terms of its percentage return.

iv. Like NPV technique, the IRR technique is also based on the consideration of all

the cash flows occurring at any time. The salvage value, the working capital used

and released etc. are also considered.

v. The IRR technique is based on the cash flows rather than the accounting profit.

Thus, it can be stated that the IRR technique possesses all the ingredients of a sound

evaluation technique. Still it has, on the other hand, some draw backs, as follows:

a) As far as the calculation of IRR is concerned, it involves a tedious and

complicated trial and error procedure.

b) An important drawback of the IRR technique is that it makes an implied

assumption that the future cash inflows of a proposal are reinvested at a rate equal

to the IRR. Say, in case of mutually exclusive proposals, say A and B having IRR

of 18% and 16%, the IRR technique makes an implied assumption that the future

cash inflows of project A will be reinvested at 18% while the cash inflows of

project B will be reinvested at 16%. It is imaginary to think that the same firm

will have different reinvestment opportunities depending upon the proposal

accepted.

c) Since, the IRR is a scaled measure, it tends to be biased towards the smaller

projects which are much more likely to yield high percentage returns over the

larger projects.

Example

A company is considering a new project for which the investment data are as

follows:


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Capital outlay Rs 2,00,000

Depreciation 20% p.a.

Forecasted annual income before charging depreciation, but after all other charges

are as follows:

Year 1 Rs 1,00,000

2 1,00,000

3 80,000

4 80,000

5 40,000

4,00,000

On the basis of the available data, set out calculation, illustrating and comparing the

following methods of evaluating the return:

(a) Payback method.

(b) Rate of return on original investment, and

(c) IRR.

Solution:

Since there is no tax, the annual income before depreciation and after other charges is

equivalent to Cash flows (CF).

(a) Capital outlay of Rs.2,00,000 is recovered in the first two years, Rs. 1,00,000

(year 1) + Rs 1,00,000 (year 2), therefore, the payback period is two years.

(b) Rate of return on original investment:

Year CF (Rs) Depreciation (Rs) Net income (Rs)


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1

2

3

4

5

1,00,000

1,00,000

80,000

80,000

40,000

40,000

40,000

40,000

40,000

40,000

60,000

60,000

40,000

40,000

2,00,000

Average Income = Rs. 2,00,000/5 = Rs. 40,000

Average incomeRate of Return =

Original investmentx 100

Rs 40,000=

Rs 2,00,000x 100 = 20%

(c) Calculation of IRR:

Total CF Rs 4,00,000Average CF =

No. of years=

5= 80,000

Cash outflows Rs 2,00,000PB value =

Average CF=

Rs 80,000= 2.5 years

Factors closest to PB value of 2.5 corresponding to 5 years (life of the project) are 2.532

(28%) and 2.436 (30%). Since the actual cash flow stream is higher in initial years than

average cash flows, higher discount rate of 33% may also be tried along with 30%.

Year CF (Rs.) PVF at Total PV (Rs.)

30% 33% 30% 33%


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1

2

3

4

5

1,00,000

1,00,000

80,000

80,000

40,000

0.769

0.592

0.455

0.350

0.269

0.752

0.565

0.425

0.320

0.240

76,900

59,200

36,400

28,000

10,760

75,200

56,500

34,000

25,000

9,600

2,11,260 2,00,900

The IRR of a project is the rate of discount at which the NPV is 0. Since the NPV

at 33% is Rs. 900 only (i.e., Rs. 2,00,900 Rs. 2,00,000), the IRR is 33% (approx).

Example

A firm whose cost of capital is 10% is considering two mutually exclusive projects X and

Y, the details of which are:

Year Project X Project Y

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

Cash inflows 1 10,000 50,000

2 20,000 40,000

3 30,000 20,000

4 45,000 10,000

5 60,000 10,000

Compute

i. Net Present Value at 10%,

ii. Profitability Index, and

iii. Internal Rate of Return for the two projects.

Solution

Calculation of NPV:


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CF (Rs.) PVF (10%,n) Total PV (Rs.)Year

1

2

3

4

5

X

10,000

20,000

30,000

45,000

60,000

Y

50,000

40,000

20,000

10,000

10,000

0.909

0.826

0.751

0.683

0.621

X

9,090

16,520

22,530

30,735

37,260

Y

45,450

33,040

15,020

6,830

6,210

Total PV

Less cash outflow

NPV

PI = (PV of inflows/PV of outflows)

1,16,135

70,000

46,135

1.659

1,06,550

70,000

36,550

1.522

Calculation of IRR:

Initial cash outlaysPayback value =

Average cash inflows

Rs 70,000Payback value =

Rs 33,000= 2.121

Rs 70,000Payback value =

Rs 26,000= = 2.692

The PVAF table indicates that for project X, the PV Factor closest to 2.121 against 5

years is 2.143 at 37% and Project Y, the PV factor closest to 2.692 is 2.689 at 25%. In the

case of Project X, since CF in the initial years are considerable smaller than the average

cash flows, the IRR is likely to be much smaller than 37%. In the case of Project Y, CF in

the initial years are considerably larger than the average cash flows, the IRR is likely to


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be much higher than 25 %. So, Project X may be tried at 27% and 28% and the Project Y

may be tried at 36% and 37%

Project X


1

2

3

4

5

10,000

20,000

30,000

45,000

60,000

27%

0.787

0.620

0.488

0.384

0.303

28%

0.781

0.610

0.477

0.373

0.291

27%

7,870

12,400

14,640

17,280

18,180

28%

75,200

56,500

34,000

25,000

9,600

70,370 68,565

Since the NPV is Rs. 370 (i.e., Rs. 70,370 70,000) only, at 27%, the IRR is 27%

approx.


1

2

3

4

5

50,000

40,000

20,000

10,000

10,000

36%

0.735

0.541

0.398

0.292

0.215

37%

0.730

0.533

0.389

0.284

0.207

36%

36,750

21,640

7,690

2,920

2,150

37%

36,500

21,320

7,780

2,840

2,070

71,420 70,510

Since the NPV @ 37% is Rs. 510 (i.e., 70,510 70,000) only, the IRR is likely to be

slightly more than 37% the results of the above calculations may be summarized as

follows:


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Project X Project Y

NPV 46,

PI 1.659 1.522

IRR 27% 37%

Example

A Company is considering the replacement of its existing machine, which is obsolete and

unable to meet the rapidly rising demand for its product. The company is faced with two

alternatives:

(i) To buy Machine A which is similar to the existing machine or

(ii) To go in for Machine B which is more expensive and has much greater

capacity.

The cash flow at the present level of operations under the two alternatives are as follows:

Cash flows (in lacs of Rs.) at the end of year:

0 1 2 3 4 5

Machine A -25 5 20 14 14

Machine B -40 10 14 16 17 15

The companys cost of capital is 10%. The finance manager tries to evaluate the

machines by calculating the following:

1. Net Present Value;

2. Profitability Index;

3. Payback period; and

4. Discounted Payback period.


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PV of cash inflow = 37.35 53.58

PV of Cash outflow 25.00 40.00

= 1.494 1.339

Calculation of Pay Back Period:

Cash inflows Cumulative cash inflowsYear

0

1

2

3

4

5

Machine A

-25

5

20

14

14

Machine B

-40

10

14

16

17

15

Machine A

-

-

5

25

39

53

Machine B

-

10

24

40

57

72

In both cases, the Pay Back Period is 3 Years.

Calculation of Discounted Payback Period:

Cash inflows Cumulative cash inflowsYear

0

1

2

3

4

5

Machine A

-25.00

4.15

15.00

9.52

8.68

Machine B

-40.00

9.10

11.62

12.00

11.56

9.30

Machine A

4.15

19.15

28.67

37.35

Machine B

9.10

20.72

32.72

44.28

53.58

Machine A Machine B

Outflow -25.00 -40.00


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In 3 years Pay back were 19.15 32.72

Unrecouped outflow 5.85 7.28

In 4the year Net Present value 9.52 11.56

5.85 7.28

Thus Pay back = 3 + = 3 +

9.52 11.56

= 3.614 years = 3.629 years

Conclusion:

1. NPV

2. Profitability Index

3. Payback Period

4. Discounted Payback

Machine A

12.35

1.494

3 years

3.164 years

Machine B

13.58

1.339

3 years

3.629 years

Choice

B

A

Indifferent

A

Because of rising demand of Companys product, Machine B should be the choice

as it has higher capacity and its NPV is also higher.


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NNooww iiss tthhee ttiimmee ttoo tteesstt yyoouurr uunnddeerrssttaannddiinngg::

MULTIPLE CHOICE QUESTIONS

1) The relevant cash flows of a capital budgeting project are:

(a) The total cash flows of the company.

(b) The added net income associated with the new project.

(c) The incremental after-tax cash flows that occur, given the decision to proceed

with the new project.

(d) The incremental added outflows, which occur if we proceed with the project.

2) Cash flows that have preceded the decision to proceed with the project or that

have been connected to be:

(a) Sunk.

(b) Irrelevant.

(c) Prior.

(d) Important in the evaluation of the project.

3) Which of the following is not generally included in the initial outlay of a capital

budgeting project?

(a) Funds for added net working capital

(b) The sale of the old facility the new project is replacing

(c) The sale of the new facility at the end of its useful life

(d) The cost of installation of the new facility

4) Morton Corp. is considering additional production facilities and expects inventory to

increase by Rs4 million, accounts receivable by Rs3 million, and accounts payable by


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Rs2 million. If other working capital accounts stay the same, what amount of added net

working capital should be considered as part of the initial outlay of this project?

(a) Rs9 million

(b) Rs5 million

(c) Rs7 million

(d) Rs1 million

5) While depreciation is not an operating cash flow, it is relevant in a capital budgeting

evaluation of operating cash flows because:

(a) Depreciation impacts the pre-tax operating cash flows but not the after-tax cash

flows.

(b) Depreciation, a non-cash expense, impacts the pre-tax operating cash flows, the

taxes paid, and the after-tax cash flows.

(c) Depreciation influences operating income before depreciation.

(d) A large amount of depreciation impresses investors and favorably impacts the

stock price of the company.

6) An added annual depreciation amount of Rs 60,000 associated with a project under

evaluation will increase operating cash flows by ______ for a company with a 40% tax

rate.

(a) Rs 60,000

(b) Rs 24,000

(c) Rs 36,000

(d) Not enough information is available.

7) A company is considering replacing extrusion equipment on its production line. The

old equipment can be sold for Rs 80,000 and has a book value of Rs 70,000. If it has a

40% tax rate, what is the total incremental cash flow related to selling the old equipment?


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(a) Rs 80,000

(b) Rs70, 000

(c) Rs 84, 000

(d) Rs 76, 000

8) Thomas Corp. is considering the purchase of a new machine that will generate an

additional Rs 100,000 in revenue and cost savings of Rs 20,000 per year. The first year

depreciation on the machine is Rs30,000. What are the after-tax operating cash flows for

the first year? Thomas has a tax rate of 40%.

(a) Rs 90, 000

(b) Rs 84, 000

(c) Rs 54, 000

(d) Rs 120, 000

9) In a capital budgeting project evaluation, the financing costs are considered when:

(a) Estimating the annual operating cash flows.

(b) Estimating the discount rate used in the NPV method.

(c) Estimating the initial outlay.

(d) Estimating the final terminal value payoff.

10) Morgan Corp. is studying the incremental cash flows of a pending replacement

investment. In Year 1, the new investment will increase cash revenues by Rs 40,000 per

year and reduce cash labor expenses by Rs 20,000. The added MACRS depreciation

expense is Rs 15, 000 and Morgan Corp. has a 40% tax rate. What is the incremental

after-tax cash flow for Year 1?

(a) Rs 15, 000

(b) Rs 45, 000


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(c) Rs 60, 000

(d) Rs 42, 000

Now we will move on to TRUE/FALSE exercises

1. The Raymond Company will spend Rs 25,000 to study the feasibility of building a

retail store at the junction of two interstate highways. If the store is built, the constructioncosts will be Rs1.5 million. The incremental start-up cost is Rs1.525 million.

(a) True(b) False

2. Initial costs for a project often include an investment in net working capital.

(a) True

(b) False

3. An increase in accounts payable is a cash outflow that is included in the net

working capital requirement for a project.

(a) True

(b) False

4. A tax decrease is a positive cash inflow.

(a) True(b) False

5. Lane International currently has depreciation expenses of Rs 953,000 a year. They

are considering building a new Rs5 million building that would be depreciated straight-

line over 30 years. The marginal tax rate of the firm is 35%. The new building would

provide an incremental positive cash flow from depreciation every year in the amount ofRs 58, 333.

(a) True(b) False

6. Fancy Shoes For You is considering adding a new line of ladies shoes called Jis

Right. Sales of Jis Right shoes are estimated at 11,000 pair a year at an average price of

Rs 42 per pair. Sales of existing shoe lines are expected to decline by Rs 1,81,000 a yearif Jis Right shoes are added to the selection. The incremental increase in sales is Rs

1,70,000.


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(a) True

(b) False

7. The payments on loans and the payment of dividends are called operational cash

flows and are included in the incremental cash flows of a project.

(a) True

(b) False

8. Project shutdown costs include the after-tax proceeds from the sale of project assets

and the recovery of the investment in net working capital.

(a) True

(b) False

9. Eddie has an old truck that he uses for hauling trash from his shop to the garbagedump. The transmission just went out and so Eddie had to install a new one at a cost of

Rs650. On top of that, the engine is now starting to run rough and Eddie is afraid it mayneed a serious overhaul. In frustration, Eddie decides to trade the truck on a newer model

priced at Rs 4,500. The dealer will give Eddie Rs500 as a trade-in value for the old truck.

Eddie is trying to evaluate the purchase of the newer truck. In his analysis, Eddie shouldignore the Rs650 he paid to replace the transmission.

(a) True(b) False

10. A project that contains a real option has less value than a project that does not

contain such an option.

(a) True

(b) False

11. When analyzing real options a probability of occurrence is assigned to each

possible course of action.

(a) True

(b) False

12. Martha Rae is considering selling a piece of equipment that her firm owns. There

is 15% probability the equipment will sell for Rs 45, 000, a 40% probability it will sellfor Rs 33,000 and a 45% probability that she can sell it for Rs 25,000. Martha should use

a selling price of Rs 25, 000 in her analysis as she tries to decide whether or not to place

an ad to sell this equipment.


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(a) True(b) False

13. Installation and delivery costs for new equipment should be included in the initial

investment cash flow amount.

(a) True

(b) False

14. The Precision Company is analyzing the installation of new computer software to

manage their daily workflow. The cost of the software, including staff training, is Rs49,000. The software is expected to have no effect on sales but should reduce labor costs

by Rs 20, 000 a year for the next several years. Software is charged as an expense when

purchased. The marginal tax rate is 32%. The net incremental operating cash flow in Year2 of the project is an increase of Rs13, 600.

(a) True

(b) False

Answers to multiple choices;

1(c), 2(a), 3(c), 4(b), 5(b), 6(b), 7(d), 8(b), 9(b), 10(d).

Answers to True/False

1(F), 2(T), 3(F), 4(T), 5(T), 6(F), 7(F), 8(T), 9(T), 10(F), 11(T), 12(F), 13(T), 14(T)

Capital Budgeting (Contd...)

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