lesson-18 capital budgeting

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Accounting and Finance forManagers LESSON

18 CAPITAL BUDGETING

CONTENTS18.0 Aims and Objectives

18.1 Introduction

18.2 Aim of Capital Budgeting

18.3 Methods of Capital Budgeting

18.3.1 Pay Back Period Method

18.3.2 Accounting or Average Rate of Return

18.3.3 Discounted Cash Flows Method

18.4 Present Value Method

18.5 Capital Rationing

18.6 Divisible Project

18.7 Indivisible Project

18.8 Risk Analysis in Capital Budgeting

18.9 Let us Sum up

18.10 Lesson-end Activity

18.11 Keywords

18.12 Questions for Discussion

18.13 Suggested Readings

18.0 AIMS AND OBJECTIVES

After studying this lesson you will be able to:

(i) decide why capital budgeting is most important decision of the financial management

(ii) describe various objectives and methods of capital budgeting

(iii) distinguish between divisible and indivisible projects.

18.1 INTRODUCTIONThe capital budgeting is one of the important decisions of the financial management of theenterprise. The decisions pertaining to the financial management of the firm are following:

Decisions of Financial Management

Financing Investment Dividend Liquidity

Long Term Investment Short Term Investment

Capital Budgeting Working Capital Management

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Capital BudgetingWhy the capital budgeting is considered as most important decision over the others?

The capital budgeting is the decision of long term investments, which mainly focuses theacquisition or improvement on fixed assets. The importance of the capital budgeting isonly due to the benefits of the long term assets stretched to many number of years in thefuture. It is a tool of analysis which mainly focuses on the quality of earning pattern ofthe fixed assets.

The capital budgeting decision is a decision of capital expenditure or long term investmentor long term commitment of funds on the fixed assets.

Charles T. Horngreen “A long-term planning for making and financing proposed capitaloutlays”.

18.2 AIM OF CAPITAL BUDGETING

To make rational investment: The study of capital budgeting on capital expendituresevades not only over capitalization but also under capitalization. The long-term investmentnormally demands heavy volume of investment which is met out by the firm either throughexternal or internal source of financing. Hence, the amount of capital raised by the firmshould neither greater nor lesser than the investment.

Locking up of capital: The amount invested is requiring longer gestation to recover.The longer gestation is connected with future horizon in getting back the investment.The future is uncertain unlike the present. If the longer is the gestation in the future leadsto greater risk involved.

Effect on the profitability of the enterprise: The profitability of the enterprise is mainlydepending on the proper planning of the capital expenditure.

Nature of Irreversibility: The improper/ unwise capital expenditure decision cannot beimmediately corrected as soon as it was found. Once it is invested is invested whichcannot be reversed. The poor investment decision will require the firm either to keep itas an idle in the form of investment or to unnecessarily meet out fixed commitmentcharge of the capital which excessively raised more than the requirement.

18.3 METHODS OF CAPITAL BUDGETING

The methods are the nothing but the instruments of the capital budgeting to study thequality of the investments/fixed assets. The investments are studied by the firms in thefollowing angles:

l Based on the number of years taken for getting back the investment – Pay BackPeriod Method

l Based on the profits accrued out of the investment – Accounting Rate of Return/Average Rate of Return

l Based on the timing of benefits – Present value of future benefits of the investment–Discounted cash flow methodsv Based on the comparison in between the cash outlay and receipts discounted

with the help of minimum rate of return - Net present value methodv Based on the identification of maximum rate of return, in between the initial

cash outlay and discounted expected future receipts - Internal Rate of returnmethod

v Based on the ration in between the present values of cash inflows and outflows– Present value index method

Check Your Progress

(1) Capital budgeting means a study of

(a) Budgeting of long-term capital

(b) Budgeting of short-term capital

Contd....

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Accounting and Finance forManagers

(c) Budgeting of short-term assets

(d) Worthiness of long-term assets

(2) Capital budgeting tools are classified into(a) Yearly basis

(b) On the basis of return

(c) On the basis of present value of money

(d) (a), (b) & (c)

(3) Selection criterion are classified into(i) Acceptance of the investment proposal

(ii) Rejection of investment proposal

(iii) Neither can be accepted nor rejected

(a) (i) only(b) (ii) only(c) (iii) only

(d) (iv), (ii) & (iii)

The classification of methods are generally in two categories:

l Traditional methodsv Pay Back Period methodv Accounting Rate of Return

l Discounted cash flow methodsv Net present value methodv Internal Rate of Return methodv Present value index methodv Discounted pay back period method

18.3.1 Pay Back Period Method

What is pay back period?

The pay back period is the period taken by the firm to get back the investment. The payback period is nothing but number of years/months/days required by the firm to get backits investment invested in the project.

To find out the pay back period, the following are two important covenants required:

l Initial outlay / Initial investment/ Original investment

l Cash inflows

How the pay back period is calculated?The pay back period is calculated by way of establishing the relationship between thevolume of investment and the annual earningsWhile calculating the pay back period, the nature of annual earnings should be identified.The nature of the annual earnings can be classified into two categories:

l Cash flows are equivalent or constant

l Cash flows are not equivalent or constant

If the cash flows are equivalent, How the pay back period is to be calculated ?

The cost of the project is Rs.1,00,000. The annual earnings of the project is Rs.20,000.Calculate the pay back period.

Years 5 20,000 .Rs

1,00,000 Rs.

Earnings Annual Average

Investment Initialperiodback Pay

==

=

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Capital BudgetingIt is obviously understood that, Rs.20,000 of annual earnings (cash inflows) requires 5years time period to get back the original volume of the investment.

If the cash flows are not equivalent, How the pay back period is to be calculated ?

The cost of the project is Rs.1,00,000. The annual earnings of the project are as follows

The ultimate aim of determining the cumulative cash inflows to find out how manynumber of years taken by the firm to recover the initial investment.

The next step under this method is to determine the cumulative cash flows

The uncollected portion of the investment is Rs,10,000. This Rs.10,000 is collected fromthe 4th year Net income / cash inflows of the enterprise. During the 4th year the totalearnings amounted Rs.20,000 but the amount required to recover is only Rs.10,000. Forearning Rs.20,000 one full year is required but the amount required to collect it back isamounted Rs.10,000. How many months the firm may require to collect Rs.10,000 outof the entire earnings Rs.20,000?

Pay back period consists of two different components

l Pay back period for the major portion of the investment collection in full course -E.g.: 3 years

l Pay back period for the left /uncollected portion of the investment

For the second category years 5.0 20,000 .Rs

10,000 .Rs ==

Total pay back period= 3 Years +.5 year = 3.5 years

Criterion for selection: If two or more projects are given for appraisal, considered to bemutually exclusive to each other for selection, the pay back period of the projects shouldtabulated in accordance with the ascending order. The project which has lesser payback period only to be selected over the other projects given for scrutiny.

Why lesser pay back has to be chosen?

The reason behind is that the project which has lesser pay back period got faster recoveryof the initial investment through cash inflows/Net income.

Selection criterion

Lesser the pay back period is better for acceptance of the project

Illustration 1: A project costs Rs.2,00,000 and yields and an annual cash inflow ofRs.40,000 for 7 years. Calculate pay back period

First step is identify the nature of the annual cash inflows

Year 1st 2nd 3rd 4th 5th Net Income Amount Rs

40,000 30,000 20,000 20,000 20,000

Year Annual Net Incomes Rs

Cumulative cash flows Rs.

1. 40,000 40,000

2. 30,000 70,000

3. 20,000 90,000

4. 20,000 1,10,000

5. 20,000 1,30,000

3 years full time required to recover the major portion of investment Rs.90,000

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In this problem, the annual cash inflows are equivalent throughout life period of theproject

Pay Back Period = years540,000 .Rs

2,00,000 .Rs

InflowsCash Annual

Investment Initial ==

Illustration 2: Calculate the pay back period for a project which requires a cash outlayof Rs.20,000 and generates cash inflows of Rs 4,000 Rs.8,000 Rs. 6,000 and Rs. 4,000in the first, second, third, and fourth year respectively

First step is to identify the nature of the cash inflows

The cash inflows are not equivalent/constant

Year Cash Inflows CumulativeRs Cash Inflows

Rs1. 4,000 4,0002. 8,000 12,0003. 6,000 18,0004. 4,000 22,000

Cost of the project is to be recovered Rs.20,000. The project takes 3 full years timeperiod to recover the major portion of the initial investment which amounted Rs.18,000out of Rs.20,000

The remaining amount of the initial investment is recovered only during the fourth year.The left portion Rs.2,000 has to be recovered only from the fourth year cash inflows ofRs.4,000.

Pay Back Period = Pay Back period of the major portion + Pay Back period of theremaining portion

Pay Back period of the major portion = 3 years

Pay Back period of the remaining portio: For the entire earnings of Rs.4,000, thefirm consumed one full year/12 months time period. How many number of monthsrequired to recover Rs.2,000 ?

months 6 months 125.04,000 .Rs

2,000 .Rs =×=

Total pay back period = 3 years + 6 months = 3 years 6 months

Illustration 3: A project cost of Rs.10,00,000 and yields annually a profit of Rs.1,60,000after depreciation and depreciation at 12% per annum but before tax 50% calculate payback period.

Pay Back PeriodinflowCash Annual

Investment Initial=

In this problem, the initial investment is given which amounted Rs.5,00,000.

The annual cash inflow is not given directly; to determine the cash inflow; what is meantby the cash inflow ?

Cash inflow = Profit after tax + Depreciation

Profit Before taxation =Rs.1,60,000

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Capital Budgeting(-)Taxation = Rs. 80,000

Profit after taxation = Rs. 80,000

(+)Depreciation 12% on = Rs. 10,00,000= Rs. 1,20,000

Annual Cash Inflow = Rs. 2,00,000

Pay Back Period = Rs.10,00,000 = 5 years

= Rs.2,00,000

Illustration 4: A company proposing to expand its production can go in either for anautomatic machine costing Rs.2,24,000 with an estimated life of 5 ½ years or an ordinarymachine costing Rs.60,000 having an estimated life of 8 years. The annual sales andcosts are estimated as follows:

Particulars Automatic Machine OrdinaryRs Machine Rs

Sales 1,50,000 1,50,000

CostsMaterial 50,000 50,000

Labour 12,000 60,000

Variable overheads 24,000 20,000

Compute the comparative profitability of the proposals under the pay back period method.Ignore Income Tax (I.C.W.A.Final)

The first step is to find out the Annual profits of the two different machines

The next step is to find out the pay back period of the two different machines respectively

Profitability Statement

Automatic Machine Rs Ordinary Machine Rs

Sales 1,50,000 1,50,000

Less : Material 50,000 50,000

Labour 12,000 60,000

Variable overheads 24,000 20,000

Annual profit 64,000 20,000

Pay Back Period

Particulars Automatic Machine Rs Ordinary Machine Rs

Cost of the Machine 2,24,000 60,000

Annual Profit 64,000 20,000

Pay Back Period Rs.2,24,000 Rs 60,000

Initial Investment Rs.64,000 Rs 20,000

Annual profit = 3½ years = 3 years

The pay back period method highlights that the ordinary machine is more ideal than theautomatic machine due to lesser pay back period i.e., 3 years. It means that the ordinarymachine is bearing the faster rate in getting back the investment invested than theautomatic machine.

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The another method to discuss is post pay back impact of the two different machines

Post pay back profit is the profit of the two different machines after the recovery of theinitial investment. The machine which has greater post pay back profit construe.

Post Pay Back Profit

Particulars Automatic Machine Rs Ordinary Machine Rs

Annual Profit R.No.1 64,000 20,000

Estimated Life R.No.2 5½ years 8 years

Pay Back Period R.No.3 3½ years 3 years

Post Pay Back Period

R.No. 4=R.No.2-R.No.3 2 years 5 years

Post Pay Back Profit = Rs.64,000×2 years = Rs.1,28,000

R.No5=R.No.1×R.No.4 = Rs.20,000×5years = Rs.1,00,000

Post pay back profit of the Automatic machine is higher than the Ordinary machine ;which amounted Rs.1,28,000.. It means that the profit of the automatic machine afterthe recovery of the initial investment is greater than that of the ordinary machine.

Illustration 5: A company has to choose one of the following two mutually exclusiveprojects. Investment required for each project is Rs 30,000. Both the projects have to bedepreciated on straight line basis The tax rate is 50%.

Year Profit Before Depreciation

Project A Rs Project B Rs

1. 8,400 8,400

2. 9,600 9,000

3. 14,000 8,000

4. 14,000 10,000

5. 4,000 20,000

Calculate pay back period

First step is to find out the depreciation under the straight line method

The next step is to determine the pay back period of the both projects A and B respectively

The next step is to compare both pay back periods of two different projects.

The depreciation under the straight line method is as follows

For Project A

000,6.Rsyears 5

30,000 .Rs

Project theof Life


For Project B

000,6.Rsyears 5

30,000 .Rs

Project theof Life


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Capital BudgetingProject A

1. 8,400 6,000 2,400 1,200 1,200 6,000 7,200 7,200

2. 9,600 6,000 3,600 1,800 1,800 6,000 7,800 15,000

3. 14,000 6,000 8,000 4,000 4,000 6,000 10,000 25,000

4. 14,000 6,000 8,000 4,000 4,000 6,000 10,000 35,000

5. 4,000 6,000 -(2000) 0 -(2000) 6,000 4,000 39,000

Pay back period = Pay back period of a major portion + Pay back period for remaining

Pay back period of the major portion= the firm has recovered a major portion of theinitial investment of Rs.25,000 within 3 full years out of Rs.30,000

The second half of the equation is that pay back period for the remaining i.e., Rs.5000 ofinitial investment which is to be recovered during the fourth year out of Rs.10,000

If Rs.10,000 earned throughout the year /12 months, how many months taken by thefirm in recovering Rs.5,000 out of Rs10,000

months 6months 125.000,10.Rs

5,000 .Rs =×==

Pay back period (Project A) = 3.6 years

The next stage to find out the pay back period of the project B

Project B

1. 8,400 6,000 2,400 1,200 1,200 6,000 7,200 7,200

2. 9,000 6,000 3,000 1,500 1,500 6,000 7,500 14,700

3. 8,000 6,000 2,000 1,000 1,000 6,000 7,000 21,700

4. 10,000 6,000 4,000 2,000 2,000 6,000 8,000 29,700

5. 20,000 6,000 14,000 7,000 7,000 6,000 13,000 42,700

Pay back period of the project B= 4 years + 13,000 Rs.

300 .Rs

= 4 years +.02 × 365 days = 4 years + 8 days = 4 years and 8 days

Pay back period of the project B is greater than that of the earlier Project A. It meansthat the Project A is bearing the faster rate in getting back the investment invested.

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Merits

l It is a simple method to calculate and understand

l It is a method in terms of years for easier appraisal

Demerits:

l It is a method rigid

l It has completely discarded the principle of time value of money

l It has not given any due weight age to cash inflows after the pay back period

l It has sidelined the profitability of the project.

18.3.2 Accounting or Average Rate of Return:

Under this method, the profits are extracted from the book of accounts to denominatethe rate of return. The profits which are extracted are nothing but after depreciation andtaxation and not cash inflows.

Selection criterion of the projects:

Highest rate of return of the project only is given appropriate weightage.

The Accounting rate of return can be computed as follows

Accounting Rate of Return (ARR)= 100Investment Original

Return Annual ×

Accounting Rate of Return (ARR)= 100Investment Average

Return Annual Average ×

Average annual return= Average profit after depreciation and taxation of the entire lifeof project i.e. for many number of years

Average Investment = Opening Investment + Closing Investment

2

=2

Scrap–Investment Opening

Illustration 6

Calculate the average rate of return for Projects X and Y from the following

Project X Project Y

Investments Rs.40,000 Rs.60,000

Expected Life 4 years 5 years

Projected net income ( after interest, depreciation and taxes)

Year Project X Rs Project Y Rs

1. 4,000 6,000

2. 3,000 6,000

3. 3,000 4,000

4. 2,000 2,000

5. ——- 2,000

12,000 20,000

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Capital BudgetingIf the required rate of return is 10% which project should be undertaken?

Average Rate of Return = 100Investment Original

Income Annual Average ×

The first step is to find out the average annual income of the two different projectsX and Y

Average Annual Income = Project theof Life

Project t the throughouincome Total

Average Annual Income( Project X) = 3,000 .Rsyears 4

12,000 .Rs =

Average Annual Income ( Project Y) = 4,000 .Rsyears 5

20,000 .Rs =

The next step is to find out the Average rate of return :

Average rate of return ( Project X) = %5.7100000,40.Rs

3,000 .Rs =×

Average rate of return ( Project Y) = %33.810060,000 .Rs

000,5.Rs =×

Both the projects are lesser than the given required rate of return. These two projectsare not advisable to invest only due to lesser accounting rate of return.

Illustration 7

The alpha limited is considering the purchase of a machine to replace a machine whichhas been in operation in the factory for the last 5 years.

Ignoring interest pay but considering tax at 50% of net earnings suggest which on thetwo alternatives should be preferred. The following are the details

Particulars Old Machine New Machine

Purchase price Rs.80,000 Rs,1,20,000

Economic life of the machine 10 years 10 years

Machine running hours per annum 2,000 2,000

Units per hour 24 36

Wages running per hour 3 5.25

Power per annum 2,000 3,500

Consumable stores per annum 6,000 7,500

Other charges per annum 8,000 9,000

Material cost per unit .50 .50

Selling price per unit 1.25 125

First step is to consider that few assumptions to proceed the problem without any technicaldifficulties.

First assumption is that there is no closing stock i.e. what ever goods produced are soldout in the market.

Second assumption is that the volume of the sales is expected to be remain throughoutthe life of the period.

Third assumption is that the depreciation charged by the firm is on the basis of straightline method.

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Steps involved in the computation of the accounting rate of return

The first is to compute the total number of units expected to produce

Total number of units of production = Total machine hours per annum × Units per hour

For old machine = 2,000 Hrs× 24= 48,000 units

For new machine = 2,000 Hrs × 36= 72,000 units

The second step is to determine the volume of annual sale of units:

Total volume of sales = Total number of units × Selling price per unit

For old machine = 48,000 units × Rs 1.25= Rs.60,000

For new machine = 72,000 units× Rs.1.25= Rs.90,000

According to the second assumption, the volume of sales is known as unaffectedthroughout the life period of the projects.

The next step is to find out the volume of the wages

Total wages = wages per hour × Machine running hours

For old machine = Rs.3× 2000 Hrs= Rs.6,000

For new machine = Rs5.25× 2000 Hrs=Rs.10,500

The next step is to find out the total material cost

Total material cost per unit = Total number of units × Material cost per unit

For old machine = 48,000× .5= Rs.24,000

For new machine = 72,000× .5=Rs.36,000

The last step is to find out the depreciation

Depreciation under straight line method asset theof period life Economic

investment Initial=

For old machine = Rs.8,000

For new machine = Rs.12,000

The next step is to draft the profitability statement of the enterprise under the head oftwo different machine viz old and new. To find out the annual income of the enterpriseunder two different machines

Profitability Statement

The Average rate of return

100Investment Average

Return Annual Average

100Investment Original

Return Annual Average

×=

×=

Old Machine New Machine Particulars Rs Rs Rs Rs

Sales 60,000 90,000 Less Direct Material

24,000

36,000

Wages 6,000 10,500 Power 2,000 4,500 Consumable stores 6,000 7,500 Other charges 8,000 9,000 Depreciation 8,000 12,000 54,000 79,500 Profit before tax 6,000 10,500 Tax at 50% 3,000 5,250 Profit after tax 3,000 5,250

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Capital Budgeting

Merits

l It is simple method to compute the rate of return

l Average return is calculated from the total earnings of the enterprise through outthe life of the firm

l The entire rate of return is being computed on the basis of the available accountingdata

Demerits

l Under this method, the rate of return is calculated on the basis of profits extractedfrom the books but not on the basis of cash inflows

l The time value of money is not considered

l It does not consider the life period of the project

l The accounting profits are different from one concept to another which leads togreater confusion in determining the accounting rate of return of the projects

18.3.3 Discounted Cash Flows Method

The discounted cash flows method is the only method nullifies the drawbacks associatedwith the traditional methods viz Pay back period method and Accounting rate of returnmethod. The underlying principle of the method is time value of money. The value of 1Re which is going to be received on today bears greater value than that of 1 Re expectedto receive on one month or one year later. The main reason is that "Earlier the benefitsbetter the principle". It means that the benefits whatever are going to be accrued duringthe present will be immediately reinvested again to maximize the earnings, so that theearlier benefits are weighed greater than the later benefits. The later benefits are expectedto receive only during the future which is connected with the future i.e., future is uncertain.It means that there is greater uncertainty involved in the receipt of the benefits connectedwith the future.

Why the time value of money concept is inserted on the capital budgeting tools?

The main reason is that the capital expenditure is expected to extend the benefits formany number of years. The 1 Re is expected to receive one year later cannot be treatedat par with the 1 Re of 2 years later. This is the only method considers the profitability aswell as the timing of benefits. This method gives an appropriate qualitative considerationto the benefits of various time periods.

Particulars Old Machine New Machine Average Rate of Return On the basis of original investment

Rs3,000 × 100 Rs.80,000 =3.75%

Rs.5,250 Rs.1,20,00 =4.375%

Average Rate of Return On the basis of average investment

Rs.3,000 × 100 Rs.40,000 =7.5%

Rs.5,250 Rs.60,000 =8.75%

Discounted cash flows method

Net Present value method Internal Rate of Return method Present value Index Method

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The time value of money principle is used for an analysis to study about the quality of theinvestments in receiving the future benefits.

There are general classifications which are as follows

l Net present value method

l Present value index method

l Internal rate of return method

18.4 PRESENT VALUE METHOD

Under this method, the initial outlay or initial investment available in terms of presentvalue is compared with the present value of future earnings of the enterprise.

Why the present value of the future earnings are found out?

The ultimate reason to find out the present value future earnings is that the comparisonin between inflows and outflows should be meaningful as well as effective. The presentvalue of the initial outlay cannot be converted into the future value for comparison, evenotherwise the conversion takes place, the comparison cannot be meaningful. To bemeaningful comparison, the future earnings are converted into the present value whichis known as discounting process through the discount rate. The rate at which the futureearnings are discounted is known as required rate of return.

Selection criterion of Net present value method

If the present value of future cash inflows are greater than the present value of initialinvestment ; the proposal has to be accepted.

If the present value of future cash inflows are lesser than the present value of initialinvestment ; the proposal has to rejected.

Initial Outlay <Present value of Benefits=> +ve NPV:- Project can be accepted

Initial Outlay>Present value of Benefits=>-ve NPV:-Project can be rejected

What is present value index?

The major lacuna of the Net present value method is unable to rank the projects oneafter the another, only due to the volume of the investment involved. To rank the projectsmeaningfully, the present value index method is adopted. The present value index of theinvestment can be calculated with the help of following formula:

Present value index methodoutflowscash theof valueesentPr

inflowscash theof valueesentPr=

Selection criterion

If the present value index is greater than one, accept the proposal; otherwise vice versa

Present value index>1:- Accept the investment proposal

Present value index<1:-Reject the investment proposal

What is internal rate of return method?

IRR is the rate at which initial investment is equal to the Present Value of future case in-flows. Under this method, while matching, these two are known but the rate which istaken for equation not given or known. The rate of discounting for matching should bedetermined through trial and error method.

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Capital BudgetingOnce the Internal rate of return is found out, the found IRR should be compared with therequired rate of return.

Decision criterion

If the IRR is more than the Required rate of return, the project has to be accepted

If the IRR is less than the Required rate of return, the project has to be rejected

Check Your Progress

(1) The utility of discounting principle is

(a) To determine the future value of the cash inflow

(b) To convert the Present value of Initial outlay into Future value

(c) To determine the present value of the future cash inflows for comparison withthe Initial Outlay

(d) None of the above

(2) Why Discounted cash flows method is considered to be a superior than theTraditional method ?

(a) Simple to understand

(b) Accuracy

(c) Time value of money

(d) Easy to calculate

Illustration 8

Project ABC Ltd. costs Rs 1,00,000. It produces the following cash flows

Advise either the project to be accepted or not.

The investment proposal has to be accepted only due to positive Net present value.

It means that the present value of the cash inflows are greater than the present value ofthe outlay. It means the discounted future earnings are greater than the present initialinvestment outlay.

Illustration 9

The Alpha Co Ltd., is considering the purchase of a new machine. Two alternativemachines (A and B) have been suggested, each having an initial coast of Rs.4,00,000and requiring of Rs.20,000 an additional working capital at the end of 1st year. Earningsafter taxation are expected to be follows

Year 1 2 3 4 5 Cash Inflows Rs 40,000 30,000 10,000 20,000 30,000 Present value of Re1 at 10%

.909 .826 .751 .683 .621

Year Cash inflows Rs

Present value factor @10%

Present value of cash inflows Rs

1. 40,000 .909 36,360 2. 30,000 .826 24,780 3. 10,000 .751 7,510 4. 20,000 .683 13,660 5. 30,000 .621 18,630

Total Present value of cash inflows 1,00,940 Total present value of cash outlay 1,00,000 Net present value 940(+ve)

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(CA Final Nov, 1972)

The profitability statement of Two machines -Alpha company

In the above problem, among the given machines, the firm is required to chose only onemachinery. To chose the ideal machinery among the given two, the net present valueshould be ranked.

The Machine B has been considered as preferable over the machine A due to higher netpresent value. The ranking of the machines do not indulge any difficulties. Why it so ?The main reason is that both machines are having equivalent volume of investmentoutlay. Out of the same initial outlays, we can rank that both machines one after theanother based upon the net present value.

Illustration 10

The initial cost of an equipment is Rs. 50,000. Cash inflows for 5 years are estimated tobe Rs.20,000 per year. The management's desired minimum rate of return is 15%.Calculate Net present value and Excess present value index.

At the end of every year, the firm expects to earn Rs.20,000. The amount expects toearn Rs.20,000 on every year is nothing but future value of money. The future value ofmoney should be converted into the present value for having comparison with the initialinvestment.

On every Rs.20,000 expected to receive forms a series of future cash inflows whichshould be converted into present value.

This conversion process i.e the process of converting the future value into present valueis known as discounting process. For discounting, the rate which is used for the processpronounced as discount rate or minimum rate of return. The conversion process can bedone in two different ways.

Discounting process :- PV= FV/ (1+r)n

For first year cash inflow Rs.20,000:-

PV=20,000/(1.15)=20,000×.870 =Rs.17,400

For second year cash inflow Rs.20,000;-

PV=20,000/(1.15)2 =20,000×.756 =Rs.15,120

Cash inflows Year Machine A Rs Machine B Rs

Present value factor 10%

1. 40,000 1,20,000 .91 2. 1,20,000 1,60,000 .83 3. 1,60,000 2,00,000 .75 4. 2,40,000 1.,20,000 .68 5. 1,60,000 80,000 .62

Machine A Machine B Year Present value factor@ 10%

Cash Inflow

Rs

Present Value

Rs

Cash Inflow

Rs

Present Value

Rs

1. .91 40,000 36,400 1,20,000 1,09,200 2. .83 1,20,000 99,600 1,60,000 1,32,000 3. .75 1,60,000 1,20,000 2,00,000 1,50,000 4. .68 2,40,000 1,63,200 1.,20,000 81,600 5. .62 1,60,000 99,200 80,000 49,600

Present value cash inflows 5,18,400 5,23,200 Present value cash outflows= Rs.4,00,000+ 20,000 X.91

4,18,200 4,18,200

Net present value 1,00,200 1,05,000

261

Capital BudgetingFor third year cash inflow Rs.20,000:-

PV=20,000/(1.15)3=20,000×.658 =Rs.13,160

For fourth year cash inflow Rs.20,000:-

PV=20,000/(1.15)4=20,000×.572 =Rs.11,440

For fifth year cash inflow Rs.20,000:-

PV=20,000/(1.15)5=20,000×.497 =Rs.9,940

Rs.67,060

OR

Alternately, the discounting can be done as follows

Being Rs.20,000 is nothing but as common cash inflow throughout 5 years of theproject, considered to be a series of cash inflows

Rs.20,000(.870+.756+.658+.572+.497) =Rs.67,060

Net present value = Present value of cash inflows - Present value of cash outlay

=Rs.67,060- Rs.50,000= Rs.17,060

The net present value of the project is +ve. Hence, the project can be accepted.

Illustration 11

A project costs Rs.36,000 and is expected to generate cash inflows of Rs.11,200 annuallyfor 5 years. Calculate the IRR of the project.

First step is to find out the fake pay back quotient

Pay back 214.311,200 .Rs

36,000 Rs.

return average Annual

Investment Initial ===

The next step is to locate the pay back quotient in the table M-4. The present value of 1Re should be computed for 5 number of years.

The location of the pay back quotient is in between the values of table M-4

The value 3.214 which lies in between 3.274 of 16% and 3.199 of 17%

The next step in the IRR calculation is that locating the maximum rate of return whichequates the initial outlay with the cash inflows of various time periods.

While equating the initial outlay with discounted cash inflows at certain percentage willderive the original rate of return. The process may be started from two different anglesviz

l Low discount rate

l High discount rate

The computation of IRR can be had through either low discount rate or high discountrate. This is further extended to different methods of calculation., which are as follows

l On the basis of values extracted from the table

l On the basis of volume

262


Calculation on the basis of discount rate table value

On the basis of Lower % of discount rate

=Lower discount rate

+

Discount rate difference ×

%8.16%2.%17199.3274.3

199.3214.3%1%17

rate)discount Higher -discount Lower(

rate)discount Higher -quotientBack Pay(

=−=−−×−=

Alternately, on the basis of volume, the methodology to be adopted for the determinationof IRR

The cash inflows of Rs.11,200 for 5 years are discounted @ 16% which amountedRs.36,668.8. Like wise the cash inflows of the same should be discounted at the rate of17% which amounted Rs.35,828.8

The next step is to find out the IRR. The IRR can be found out either on the basis oflower discounted cash inflows or higher discounted cash inflows.

On the basis of discounted cash inflows at lower rate @16%

=16% + 1% × )840(

)8.668(%%16

35.828.8)-36.668.8 .Rs(

36,000) .Rs8.668.36.Rs( ×+=−

=16%+.796=16.796%

On the basis of discounted cash inflows at higher rate @ 10%

(840)

(172)1%-17%

35,828.8)-36.668.8 .Rs(

35.828.8) Rs.-36,000 .Rs( =

== 17% -.204=16.796%

Merits of DCF methods

l It is only the best method incorporates the timing of benefits - time value of money

l It considers the economic life of the project

l It is a best method for both even and uneven cash inflows

Demerits of DCF methods

l It involves with tedious method of computation

l It is very difficult to locate or identify the exact discounting factor

l It never performs functions of discounting to the tune of accounting concepts.

(+) (-)

On the basis of discounted cash inflows – Lower rate –

Rs.36.668.8

Rs.36,000-Origin value- @ IRR

On the basis of discounted cash inflows – Higher

rate-Rs.35.828.8

Lower discount Rate 3.274

Origin value i.e., unknown IRR -3.214

Higher discount rate 3.199

263

Capital BudgetingIllustration 12

XYZ company is considering an investment proposal to install new drilling controls at acost of Rs.1,00,000. The facility has a life expectancy of 5 years and no salvage value.The tax rate is 35%. Assume the firm uses straight line depreciation and the same isallowed for tax purposes. The estimated cash flows before depreciation and tax formthe investment proposal are as follows:

Calculate the following

1. Pay back period

2. Average rate of return

3. Net present value at 10 percent discount rate

4. Profitability index at 10 percent discount rate

The first and foremost step is to find out the Cash Flows After Taxation

For finding out the Cash flows after taxation, the amount of depreciation i.e non recurringexpenditure should be appropriately considered for calculation. The depreciation has tobe computed in accordance with the stipulation given in the problem. The depreciationcharged by the firm is nothing but straight line method.

Straight line method of depreciation

20,000 .RsYears 5

000,00,1.Rs

machine theof period life Economic

valueScrap-Investment Initial

==

=

The depreciation has to be deducted initially from the cash flows before taxation, afterthe deduction of taxation, the earnings after taxation should be added with the depreciationwhich was already deducted in order to find out the total cash flows after taxation. Thepurpose of deducting the depreciation is nothing but an amount to be charged under theProfit & Loss account against the total revenue. Being as a non-recurring expenditurenot created any outflow cash resources. When there is no cash outflow, the amount ofdepreciation should be added finally to derive CFAT(Col 7)

Table

1. Pay back period method: Under this, method most important step is to identifythe nature of the cash flows after taxation. Are they uniform ? No, they are noteven cash flows. Hence, the cumulative cash flows after taxation has to be foundin order to find out the pay back period of the investment.

Year Cash flows Before Tax Rs 1. 20,000 2. 21,384 3. 25,538 4. 26,924 5. 40,770

Year Col 1

CFBT Rs

Col 2

Depreciation Rs

Col 3

Profits Before Tax

Rs Col 4=Col2-

Col3

Taxes (.35) Col 5

Earnings After tax

Rs Col6=Col4

-Col5

Cash flows after tax Rs

Col7= Col6+Col3

1. 20,000 20,000 Nil Nil Nil 20,000 2. 21,384 20,000 1,384 484 900 20,900 3. 25,538 20,000 5,538 1,938 3,600 23,600 4. 26,924 20,000 6,924 2,423 4,500 24,500 5. 40,770 20,000 20,770 7,270 13,500 33,500

22,500 1,22,500

264


Pay back period= Pay back period for the major portion of the investment

+

Pay back period for the remaining portion unrecovered

= 4 year + year .328year 4 33,500 .Rs

11,000 .Rs +=

= 4.328 years

2. Average rate of return (ARR):

100Investment Average

Income AverageARR ×=

Average Income is the average of earnings after taxation of the entire duration.

Why earnings after taxation has to be taken into consideration ? Why not the cashflows after taxation to be taken for consideration ?

The main purpose of considering the earnings after taxation is that the amountextracted from the book of accounts and taken for the computation of ARR, andimmediately after the payment of taxation.

Average investment is the average of opening and closing investment. If thedepreciation charge given is nothing but straight line method, automatically finalvalue of the asset will become equivalent to zero. The closing balance of the asset/investment is zero.

How the closing balance of the investment could be adjudged as equivalent tozero?

Table of Depreciation

At the end of the year, the closing balance amounted Rs.0 after charging thedepreciation year after year constantly in volume

%9100000,50.Rs

4,500 Rs.return of rate Average

500,4.Rsyears5

22,500 Rs. Income Average

50.000 Rs. 2

0 Rs.1,00,000 Rs.

2

balance Closingbalance Opening Average

=×=

==

=

+=

+=

Year Cash flows After Tax Rs Cumulative CFAT Rs 1. 20,000 20,000 2. 20,900 40,900 3. 23,600 64,500 4. 24,500 89,000 5. 33,500 1,22,500

Year Opening balance of the year Rs Closing balance of the year Rs 1. 1,00,000 80,000

2. 80,000 60,000

3. 60,000 40,000

4. 40,000 20,000

5. 20,000 0

265

Capital Budgeting3. Net present value method:

Under this method, the future cash flow after taxation should be discounted at therate 10%

The net present value is negative due to excessive investment more that of thepresent value of future earnings of the enterprise. Under this method, the investmentis not advisable to procure for the firm's requirements.

4. Profitability Index

The profitability index method is more useful in the case of more number ofinvestments, having uneven investment outlays, but this problem comes with onlyone investment proposal It is much easier to assess even in the case of Netpresent value method.

Profitability Index (PI) 100,000 .Rs

704,90.Rs

outflowscash of valueesentPr

inflowscash of valueesentPr ==

=.90704

The present value index quotient is less than that of the norms which should begreater than one but it secures only 90704. It means that the present value earningsare not sufficient to meet the initial cost of the machine.

Check Your Progress

(1) Why the depreciation is added at the end of computation to derive the cashflow ?

(a) Being as recurring charge

(b) Being considered as tax shield

(c) Being as non recurring charge


(2) Why "0" value is taken as closing balance of the investment for the computationof Average investment ?

(a) No value for the closing balance

(b) No value due to the application of straight line method of depreciation

(c) No scrap value at the end of the life of the asset


18.5 CAPITAL RATIONING

The capital rationing means that selection of investment proposals with reference tocapital budget by considering the financial constraints. The selection of the investmentproposals should be to the tune of required NPV which the firm wants to earn during thefuture. Under the capital rationing, there are two stages involved viz

Year Cash flows after tax Present value factor @ 10% Total Present Value Rs 1. 20,000 .909 18,180 2. 20,900 .826 17,263 3. 23,600 .751 17,724 4. 24,500 .683 16,734 5. 33,500 .621 20,803

Total Present value 90,704 Less Initial outlay 1,00,000 Net present value ( 9,296)

266


(i) Identification of the investment proposals

(ii) Selection of investment proposals

The selection of the investment proposals are on the basis of Discounted cash flowsmethod. The selection of the investment proposals are subject to two different categoriesviz indivisible and divisible. The investment which is wholly accepted or rejected due todecision criterion which is known as indivisible project but the divisible projects are ableto either accept or reject in parts.

18.6 DIVISIBLE PROJECT

A company has Rs. 7 Crore available for investment. It has evaluated its options and hasfound that only 4 projects given below have positive NPV. All these investment aredivisible Advise the management which investments projects it should select.

Out of the available Rs. 7 Cr, the first two projects selected on the basis of Profitabilityindex viz Z and W. The total amount of investment required to invest in both the projectsamounted Rs 8.50 Cr but the financial constraint is Rs.7 Cr. By considering the constraint,the first project fully accepted and the part of the next project W accepted for theremaining amount of corpus available by considering to maximize the NPV of the projectas a whole.

18.7 INDIVISIBLE PROJECT

A company working against a self imposed capital budgeting constraint of Rs 70 Cr istrying 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 ofinvestments along with the investment required and the NPV of the projected cashflows are given below

The D, E and B are the project for making an investment which jointly amounted Rs 64Cr and the remaining the Rs 6 cr to be invested into the project.

18.8 RISK ANALYSIS IN CAPITAL BUDGETING

In capital budgeting decisions, the risk component of the investment is not taken intoconsideration. The risk which is nothing but the business risk of the investment variesfrom one to another, to be considered in the real world situations. The risk which isnothing but the variability in between the actual returns and expected returns. The risk inthe investment has to be incorporated in the discount rate for studying the worth of theproject. To incorporate the risk in the discount rate, the meaning of the term risk should

Project Initial Investment Rs Cr NPV Rs Cr PI Z 2.50 1.50 1.60 W 6.00 1.80 1.30 Y 2.00 .50 1.25 X 3.00 .60 1.20

Project Initial Investment Rs Cr NPV Rs Cr A. 10 6 B. 24 18 C. 32 20 D. 22 30 E. 18 20

Project Initial Investment Rs Cr NPV Rs Cr PI X 3.00 .60 1.20 Y 2.00 .50 1.25 Z 2.50 1.50 1.60 W 6.00 1.80 1.30

267

Capital Budgetingbe known and distinguished from the uncertainty. The risk situation is one in which theprobabilities of one particular event are known but the uncertainty is the situation inwhich the probabilities are not known. In the case of risk situation, the future losses canbe foreseen unlike the uncertainty situation.

The incorporation of the risk factor in the discount rate in accordance with the variabilityof the returns. If the variability of the returns are more, the investor may prefer higherreturn in the form of risk premium for risky project unlike in the case of governmentsecurities. The government securities are not having any variability in the returns whichrequire the risk free return to discount only in order to know the worth of the investmentbut the risky projects are to be discounted only with the help of higher discount rates.

There quite number of techniques available for incorporating the risk component in thecapital budgeting are follows:

Sensitivity analysis

Standard deviation

Coefficient of variation and so on.

18.9 LET US SUM UP

The capital budgeting is the decision of long term investments, which mainly focuses theacquisition or improvement on fixed assets. The importance of the capital budgeting isonly due to the benefits of the long term assets stretched to many number of years in thefuture. It is a tool of analysis which mainly focuses on the quality of earning pattern ofthe fixed assets. The methods are the nothing but the instruments of the capital budgetingto study the quality of the investments/fixed assets. The pay back period is the periodtaken by the firm to get back the investment. The pay back period is nothing but numberof years / months/days required by the firm to get back its investment invested in theproject. The capital rationing means that selection of investment proposals with referenceto capital budget by considering the financial constraints. The selection of the investmentproposals should be to the tune of required NPV which the firm wants to earn during thefuture. Under the capital rationing, there are two stages involved viz

(i) Identification of the investment proposals

(ii) Selection of investment proposals

18.10 LESSON-END ACTIVITY

Elucidate the advantages and disadvantages of the traditional methods of capital budgeting.

18.11 KEYWORDS

Capital budgeting: A study on Long term investment decision in terms of quality ofbenefits

Pay back period: It is a time period during which the initial investment is recovered

ARR: Accounting rate of return - It is being calculated in accordance with the financialstatements

PV: Present value

IO: Initial outlay which is nothing but initial investment

NPV: Net present value which is the difference in between the Initial investment andPresent value of future cash inflows

IRR: Internal rate of return which is nothing but highest rate of return expected to earn

268


PI: Profitability Index is the ratio in between the present value of future cash inflowsand present value of initial

18.12 QUESTIONS FOR DISCUSSION

1. Define capital budgeting.

2. Highlight the importance of capital budgeting.

3. "Success of the firm relies upon the rational capital budgeting decisions"- Discuss.

4. What are two different classification of capital budgeting tools?

5. Illustrate the Pay back period method with an example.

6. Explain the process of computing the Accounting rate of return and their meritsand demerits.

7. List out the various methods of discounted cash flows.

8. Explain the meaning of IRR and the process of calculating the IRR.

9. List out the merits and demerits of the Discounted cash flows method.

18.13 SUGGESTED READINGS

M.P. Pandikumar “According & Finance for Managers” Excel Books, New Delhi.

R.L. Gupta and Radhaswamy, “Advanced Accountancy”.

V.K. Goyal, “Financial Accounting”, Excel Books, New Delhi.

Khan and Jain, “Management Accounting”.

S.N. Maheswari, “Management Accounting”.

S. Bhat, “Financial Management”, Excel Books, New Delhi.

Prasanna Chandra, “Financial Management – Theory and Practice”, Tata McGrawHill, New Delhi (1994).

I.M. Pandey, “Financial Management”, Vikas Publishing, New Delhi.

Nitin Balwani, “Accounting & Finance for Managers”, Excel Books, New Delhi.

lesson-18 capital budgeting

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