International financial and management accounting lesson 13

13 CAPITAL RATIONING AND RISK FACTOR IN CAPITAL BUDGETING CONTENTS 13.0 Aims and Objectives 13.1 Introduction 13.2 Meaning of Capital Rationing 13.3 Objective of Capital Rationing 13.4 E

13

CAPITAL RATIONING AND

RISK FACTOR IN CAPITAL BUDGETING

CONTENTS

13.0 Aims and Objectives

13.1 Introduction

13.2 Meaning of Capital Rationing

13.3 Objective of Capital Rationing

13.4 Effect of Capital Rationing

13.5 Steps Involved in Capital Rationing

13.6 Risk Analysis in Capital Budgeting

13.6.1 Need for Risk Analysis in Capital Budgeting

13.6.2 General Techniques

13.6.3 Quantitative Techniques

13.7 Let us Sum up

13.8 Lesson End Activity

13.9 Keywords

13.10 Questions for Discussion

13.11 Suggested Readings

13.0 AIMS AND OBJECTIVES

After studying this lesson you will be able to:

 Explain the Meaning of Capital Rationing

 Discuss the objective and the effects of Capital Rationing

 Explain the steps involved in Capital Rationing

 Understand Risk Analysis in Capital Budgeting

 Understand the Techniques used for in Corporation of Risk Factor in Capital Budgeting decision

13.1 INTRODUCTION

The profitability of a capital project can be determined under any of the discounted cash flow techniques, such as the net present value method, profitability index method or internal rate of return method The acceptable criteria under these methods are: (i) In the case of net present value method, the net present value of the project must

be more than zero

(ii) In the case of profitability index method, the profitability index must be more than 1

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(iii) In the case of internal rate of return method, the internal rate of return should be more than the cost of capital

No doubt, if a concern has more funds it can accept and implement all profitable projects

13.2 MEANING OF CAPITAL RATIONING

Capital rationing means the allocation of the limited funds available for financing the capital projects to only some of the profitable projects in such a manner that the long-term returns are maximized In other words, it means the selection of only some of the profitable investment proposals or projects out of the several profitable investment proposals available

13.3 OBJECTIVE OF CAPITAL RATIONING

The main objective of capital rationing is, to ensure the selection of only those profitable investment proposals that will provide the maximum long-term returns In short, the objective of capital rationing is to maximise the value of the firm

13.4 EFFECT OF CAPITAL RATIONING

The effects of capital rationing are:

(i) When there is capital rationing, a firm will not be able to undertake all the profitable investment proposals It has to accept only some of the profitable investment proposals and reject the other profitable investment proposals

(ii) When there is capital rationing, it will be possible for the firm to maximize the wealth of the owners and to maximize the market value per share

13.5 STEPS INVOLVED IN CAPITAL RATIONING

Capital rationing involves two important steps They are:

a) Ranking of the different investment proposals: First, the different investment

proposals or capital projects available, should be ranked on the basis of their profitability (i.e., on the basis of their net present value or profitability index or the internal rate of return), in the descending order

b) Selection of some of the profitable investment proposals: Then, on the basis of

their profitability in the descending order, the selection of that combination of profitable investment proposals, which would provide the highest profitability, should

be made subject to the budget constraint for the period

Illustration 1: A firm has the following investment opportunities:

Proposal Initial outlay Rs Profitability index

The available fund amount is Rs 4,00,000

Which proposals the firm should accept?

241 Capital Rationing and Risk Factor in Capital Budgeting

Solution:

First Step: Ranking of the proposals in the descending order of their Profitability Index.

Second Step: Selection of the proposals: Here, the profitability index of all the proposals

is above unity, i.e., above one As such, all the proposals are profitable or acceptable

However, as the funds available are limited, there should be capital rationing and only the

most profitable combination of the proposals should be accepted

For determining the most profitable combination of proposals, first, we should determine

the net present value of the various acceptable proposals The net present value of each

of the various acceptable proposals can be computed with the help of the following

formula:

Net present value of a proposal = Initial capital cost of a project X Profitability index

of the proposal - 1

Accordingly, the net present value of each of the various investment proposals is:

Proposal Net Present value of the Proposal

1 3,00,000 x 1.20 – 1 i.e = Rs 60,000

2 1,50,000 (1.15 – 1) i.e = Rs 22,500

3 2,50,000 (1.10 – 1) i.e = Rs 25,000

After the ascertainment of the net present value of each of the various profitable proposals,

the selection of the combination which will yield the highest total net present value has

to be made Such a combination of proposals can be :

Various possible combination of proposals:

i) Proposal involving a capital outlay of Rs 3,00,000 and yielding a net present value

of Rs 60,000

ii) Proposals 2 and 3 involving capital outlay of Rs (1,50,000 + 2,50,000) 4,00,000 and

yielding total net present value of Rs (22,500+10,000) 32,500

iii) Proposals 2 and 4 involving capital outlay of Rs (1,50,000 + 2,00,000) 350,000 and

yielding a net present capital outlay of Rs (22,500 + 10,000) 32,500

Of the three possible combinations, the net present value of the first combination is the

highest So, this combination has to be selected

Note: It is assumed that the uninvested capital of Rs (4,00,000 - 3,00,000) 1,00,000 has

a net present value of zero

13.6 RISK ANALYSIS IN CAPITAL BUDGETING

13.6.1 Need for Risk Analysis in Capital Budgeting

If a capital budgeting decision is made on the assumption that the capital project or

investment proposal does not involve any risk (i.e., there is certainly regarding the future

estimate of cash inflows from capital project during its estimated life), then, there is no

question of risk analysis is capital budgeting

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However, in real saturation, the assumption that the investment proposal does not involve any risk does not hold good In real situation, owing to a number of reasons, such as technical, economic, political, cyclical fluctuation, financial, foreign exchange, taxation etc., the actual return from an investment proposal will be usually different from the estimated returns In other words, there is uncertainly regarding the future estimation of cash inflows from capital project In short, there is risk in capital budgeting or investment decision (Of course, the risk from one investment proposal to another Some proposals will be less risky and some may be more risky)

13.6.2 General Techniques

Risk Adjusted Discount Rate Method

Meaning and features of Risk Adjusted Discount Rate Method : Under the risk adjusted discount rate method, the future cash flow from capital projects are discounted at the risk adjusted discount rate and decision regarding the selection of a project is made on the basis

of the net present value of the project computed at the risk adjusted discount rate The risk adjusted discount rate is based on the assumption that investors expect a higher rate of return on more risky projects and a lower rate of return on less risky projects, and

so, a higher discount rate is used for discounting the cash flows of more risky project and

a lower discount rate is used for discounting the cash flows of less risky project

Merits of Risk-Adjusted Discount Rate Method

a) It is easy to understand and simple to calculated

b) The risk-premium rate included in the risk adjusted rate takes care of the risk element in the future cash flows of the project

c) It takes into account the risk averse attitude of investors

Demerits of Risk-Adjusted Discount Rate Method

a) The risk-premium rates, determined under this method, are arbitrary So, this method may not give objective results

b) It is the future cash flows which are subject to risk and not the discount rate So, the future cash flows must be adjusted and not the discount rate But, under this method, it is the discount rate that is adjusted and not risk, and not the future cash flows Thus, this method adjusts the wrong element

Certainty Equivalent Coefficient method:

Introduction: Certainty equivalent co-efficient method is a method which makes

adjustment against risk in the estimates of future cash inflows for a risky capital investment project

Features of certainty equivalent coefficient method: Under this method, adjustment

against risk is made in the estimates of future cash inflows of a risky capital project by adjusting (i.e reducing) to a conservative level the estimated cash flows of a capital investment proposal by applying a correction factor termed as certainty equivalent coefficient

The certainty equivalent coefficient is the ratio of riskless cash flow to risky cashflow Riskless cash flow means the cash flow which the management expects, when there is

no risk in investment proposal Risky cash flow means the cash flow which the management expects when there is risk in investment proposal

243 Capital Rationing and Risk Factor in Capital Budgeting

The certainty equivalent coefficient can be calculated with the help of the following

formula:

Riskless cash flow Certainty equivalent coefficient =

Risky cash flow Suppose the risky cash flow is Rs 20,000 and the riskless cash flow is Rs 14,000

14, 000 The certainty equivalent co - efficient is : = 0.7

20, 000

Steps involved in certainty equivalent coefficient method: The various steps involved

in the certainty equivalent coefficient method are:

1 First, the certainty equivalent coefficient has to be calculated for each year of a

project

2 Secondly, the risk-adjusted cash flow of a project for each year has to be calculated

The risk-adjusted cash flow of a year can be calculated as follows: Estimated cash

flow for the year X Certainty equivalent coefficient

Suppose the estimated cash flow of a project for a year is Rs 20,000 and the

certainty equivalent coefficient for the cash flow of that year is 7, the risk adjusted

cash flow for the year will be : 20,000 × 7 = Rs 14,000

3 Thirdly, we have to find out the present value of the capital project The present

value of the capital project can be found by adopting the following procedure First,

the risk-adjusted cash flow for each year should be multiplied by the present value

factor applicable to that year to get the present value of the risk-adjusted cash flow

of each year

4 Fourthly, we have to ascertain the net present value of the project The net present

value of the project will be :

Rs

Less Initial investment on the project

Net present value of the project

5 After the net present value of a project is computed, decision is taken as to the

selection of the project The selection of a project is, usually, made on the following

lines :

i) Generally, a project becomes acceptable, if it has a positive (i.e., +) net present

value

ii) If there are two or more mutually exclusive projects, generally, the project

whose net present value is higher (if there are only two projects) or highest

(if there are three or more projects) is selected

Merit of this method: This method is an improvement over the previous method, as it

provides for adjustment against risk

Demerit: Even this method is not strictly objective, as an element of subjectivity is

bound to arise while converting risky cash flows into riskless cash flows

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13.6.3 Quantitative Techniques

Sensitivity Analysis Meaning of Sensitivity Analysis: Sensitivity analysis is a way of analyzing the changes

in the net present value or the internal rate of return of a project to a given change in one

of the variables of capital investment proposal like the estimated cash inflows of the project, the rate of return or the estimated economic life of the project It indicates how sensitive is a projects" net present value to a change in any particular variable of investment proposal

Under the sensitivity analysis, usually, estimation of the cash inflows of a project is made under three assumptions or situations, viz, (i) pessimistic, (ii) most likely and (iii) optimistic outcomes associated with the project After estimating the cash inflows and determining the net present value of the project under the three different situations, conclusion is drawn about the riskiness of the project Under this analysis, it is usually concluded that the larger is the difference between the pessimistic and optimistic cash inflows and the resultant net present value, the more is the risk of the project and vice versa

Steps involved in the Technique of Sensitivity Analysis: The technique of sensitivity

analysis involves three steps They are:

a) Identification of all the variables which have influence on the project's net present value or internal rate of return

b) Determination of the mathematical relationship between the various variables which affect the project's net present value or internal rate of return

c) Analysis of the impact of the change in each of the variables on the project's net present value or internal rate of return

Advantages of the Techniques of Sensitivity Analysis: The technique of sensitivity

analysis has certain advantages They are:

a) It is a popular method of assessing the risk associated with a project

b) It shows how sensitive a project is to a change in any variable influencing the investment proposal

c) It is helpful to locate and assess the impact of risk on a project's profitability Disadvantages of the Technique of Sensitivity Analysis : The technique of sensitivity analysis is not free from drawbacks It suffers from the following drawbacks i) Unless the combined effect of changes in a set of inter-related variables is examined, the technique of sensitivity analysis will be useless Single variable sensitivity testing may lead to wrong conclusion

ii) Examination of the combined effect of changes in a set of variables is a very complex process

Probability Assignment Method Introduction: Under the probability assignment approach, probabilities are assigned to

the various cash inflow estimates and the expected monetary values for the various cash inflow estimates are ascertained On the basis of the sum total expected monetary values of the various cash flow estimates of each project, decision-making as to the selection of a project is made Generally, a project whose expected monetary value is greater or greatest is selected

245 Capital Rationing and Risk Factor in Capital Budgeting

Meaning of Probability: Probability means the degree of likelihood of occurrence of

even in future When an event is said to have '1' probability, it means that it is bound to

occur If an event is said to have '0' (zero) probability, It means that the event is not going

to occur

The probability of an event is determined on the basis of repeated observation of the

event under identical situations over a period of time

Probability may be objective or subjective: An objective probability is based on a

larger number of observations under independent and identical conditions repeated over

a period of time Objective probability is of little utility in a capital budgeting decision As

no two independent investment situations can be identical

A subjective probability is not based on a large number of observations under independent

and identical conditions repeated over a period of time It is based on the personal judgment

of the person concerned For this reason, a subjective probability is also known as

personalized probability In capital budgeting decisions, probabilities are of subjective

type

Steps involved in Probability Assignment Approach: The various steps involved in

the probability assignment approach are:

1 First, probabilities are assigned to a series of cash inflow estimates (i.e., cash

inflow estimates for different events) for each year

2 Second, the expected monetary value of each figure of the cash inflow estimate is

computed The expected monetary value of each figure of the cash inflow estimate

can be calculated as follows:

Each figure of cash flow estimate x probability assignment to each figure of cash

flow estimate

3 Third, the total monetary value of the project is computed by adding the monetary

values of the various figures of cash inflow estimates

4 Lastly, decision-making as to the selection of the project is made Generally, the

project whose total expected monetary value is higher or highest is preferred

Second Step: Decision-making as to the selection of the project : The expected monetary

value of Project A is more than project B So, Project A is preferable

Standard Deviation Approach

Introduction: Probability assignment approach is, no doubt, a good technique of risk

analysis in capital budgeting But it does not give precise results about the extend of

variability of cash inflows So, to overcome this drawback of probability assignment

method, standard deviation method or approach has been introduced

Standard deviation method is a statistical technique of risk measurement in capital

budgeting It is regarded as an improvement over the probability assignment method

Meaning and Features of Standard Deviation Approach: Standard deviation is the

square root of the squared deviations calculated from the mean This measure (i.e.,

standard deviation) is used to compare the variability of probable cash inflows of different

projects from their respective mean or expected values

This technique indicates that a project having a larger standard deviation will be more

risky as compared to a project having smaller standard deviation

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Steps involved in the calculation of Standard Deviation: A number of steps are

involved in the calculation of standard deviation They are:

1 First, we have to compute the mean value (i.e., the arithmetic average) of the projected cash inflows

2 Second, we have to square up the deviations between the mean value and the projected cash inflows

3 Third, we have to square up the deviations so arrived at This gives squared deviations

4 Fourth, we have to multiply the squared deviations by the assigned probabilities

This gives weighted squared deviations

5 Fifth, we have to total up the weighted squared deviations

6 Lastly, we have to find out the square root of the total weighted squared deviations

The resulting figure is the standard deviation

7 The formula for calculating standard deviation is: 2

pdcf Σ

Where, 'S' means standard deviation 'p' means probability assigned

'dcf' means deviation from the mean (i.e., the expected monetary value)

Advantage of Standard Deviation Approach: The main advantage of standard

deviation approach is that it gives a precise measure of risk associated with a project It indicates that a project having higher standard deviation is more risky as compared to a project having a lower standard deviation

Drawback of Standard Deviation Approach: No doubt, standard deviation approach

is an improvement over the probability assignment approach But it suffers from a drawback That is, it is only an absolute measure of dispersion or variation and not a relative measure of variation As a result, when the values of mean expected monetary value show wide variations in the case of two or more projects, the results shown by the standard deviation method may not be precise

Standard Deviation

Square Deviation

Square root of 30,50,000, i.e., 30,50,000 = 1,746.42

Note: In this case, the arithmetic mean of cash inflows is cash as follows:

Total cash inflows of five events

Rs

A 12,000

B 10,000

C 9,000

D 8,000

E 6,000 Total 45,000

Arithmetic mean or average : 45,000/5 = Rs 9,000

247 Capital Rationing and Risk Factor in Capital Budgeting

Comment: The standard deviation of Project B is more than that of Project A That

means the variability of cash flow is more in the case of Project B than in the case of

Project A So, Project B is more risky

Coefficient of Variation Approach

Coefficient of variation approach is a relative measure of dispersion It is considered

superior to standard deviation approach in capital risk evaluation associated with

investment proposals

Features of Coefficient Variation Approach: There may be cases where the standard

deviations of two investment projects are the same, but the expected monetary values of

probable cash flows of the two projects differ Again, there may be cases where the

expected monetary values of probable cash flows of two projects are the same, but the

standard deviations of the projects may be different In such cases or situations, the

coefficient of variation of each of the investment projects is computed to get a more

precise relative measure of risk

Coefficient of variation is found by dividing the standard deviation by the mean (i.e., the

arithmetic mean of the estimated cash inflows)

The formula for the calculation of coefficient of variation is:

Coefficient of variation S tan dard Deviation

Mean (i.e., the arithmetic mean of the estimate cash inflows)

=

Advantages of Coefficient of Variation Approach: The Coefficient of variation is a

relative measure It is quite useful for comparison where the projects involve different

cash outlays or different monetary values of cash inflows

The coefficient of variation suggests that, the more is the coefficient of variation of a

project, the greater is the risk associated with that project

Illustration 2

Taking the illustration given under standard deviation approach, calculate the coefficient

of variation and suggest which project is more risky

Solution:

The coefficient of deviation (i.e., variation) of the projects is :

Project A

Standard Deviation of the Project i.e 1688.19

= 0.21 Arithmetic mean of the estimated cash inflows of the project, i.e, Rs 8, 000

Project B

Standard Deviation of the Project i.e.1746.42

= 0.19 Arithmetic mean of the estimated cash inflows of the project, i.e Rs 9, 000

Comment:

The coefficient of deviation of Project B is more than that of project A That means,

Project B is more risky

In this context, It may be noted that with higher risk, the profitability of the project is also

higher As such, the selection of a project depends upon the capacity of the investor to

bear risk If the investor is not averse to risk, he may prefer project B and in case he is

averse to risk he may prefer Project A

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Decision Tree Analysis

Decision tree is a graphic display of relationship between a present decision and possible future events, future decisions and their sequences The sequences of events is mapped out over time in a format resembling branches of a tree

Steps involved in the Decision Tree Process: A number of steps are involved in the

decision tree process The major steps are :

1 Defining the investment opportunity or proposal

2 Identification of alternatives

3 Delineation of the decision tree

4 Forecasting cash flows and probability assignment

5 Computation of the expected monetary values

6 Evaluating or analyzing the results and choosing the best alternative

Advantages of the Technique of Decision Tree Analysis: The technique of decision

tree analysis has certain advantages They are:

a) This technique facilitates investment decisions in a scientific way

b) This technique gives an overall view of all the possibilities associated with a project, helps the management to take decisions keeping the entire picture in mind c) As this technique links the probable outcomes of a decision one after another in an inter-related manner along with probabilities assigned to each sequential outcome,

it is very useful in tackling investment situations requiring decisions to be taken in a sequence

Disadvantages of the Technique of Decision Tree Analysis: The technique of decision

tree analysis is not free from drawbacks It suffers from the following drawbacks: a) A prime decision may have a number of sequential decision points and each one of such decision points may have numerous decision branches or decision alternatives

Check Your Progress

1 What do you understand by capital rationing?

2 Mention the steps involved in the process of capital rationing

3 What is sensitivity analysis?

13.7 LET US SUM UP

Capital rationing means the allocation of the limited funds available for financing the capital projects to only some of the profitable projects in such a manner that the long-term return are maximised