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RISK ANALYSIS IN CAPITAL BUDGETING
Capital Rationing – Meaning
Capital rationing refers to a situation where a firm is not in a position to invest in all profitable
projects due to the constraints on availability of funds. We know that the resources are always limited and the demand for them far exceeds their availability, It is for this reason that the firm cannot take up ail the projects though profitable, and has to select the combination of proposals that will yield the greatest profitability. Capital rationing is a situation where a firm has more investment proposals than it can finance. It may be defined as "a situation where a constraint is placed on the total size of capital investment during a particular period". In such an event the firm has to select combination of investment proposals that provide the highest net present value subject to the budget constraint for the period. Selecting of projects for this purpose will require the taking of the following steps;
(i) Ranking of projects according to profitability index or internal'-rate of return. (ii) Selecting projects in descending order of profitability until the
budget figures are exhausted keeping in view the objective of maximising the value of the firm.
Meaning Of Risk And Uncertainty
Risk and uncertainty are quite inherent in capital budgeting decisions. Future is uncertain and involve risk. Risk involves situations in which the probabilities of an event occurring are known and these probabilities are objectively determinable. Uncertainty is a subjective phenomenon. In such situation, no
observation can be drawn from frequency distribution. The risk associated with a project may be
defined as the variability that is likely to occur in the future returns from the project. A wide range of factors give rise to risk and uncertainty in capital investment, viz. competition, technological development, changes in consumer preferences, economic factors, both general and those peculiar to the investment, political factors etc. Inflation and deflation are bound to affect the investment decision in future period rendering the deeper of uncertainty more severe and enhancing the scope of risk. Technological developments are other factors that enhance the degree of risk and uncertainty by rendering the plants or equipments obsolete and the product out of date. It is worth noting that distinction between risk and uncertainty is of academic interest only. Practically no generally accepted methods could so far be evolved to deal with situation of uncertainty while there are innumerable techniques to deal with risk. In view of this, the terms risk and uncertainty are used exchangeably in the discussion of capital budgeting. The capital budgeting decision is based upon the benefits derived from the project. These benefits are measured in terms of cash flows. These cash flows are estimates. The estimation of future returns is done on the basis of various assumptions. The actual return in terms of cash inflows depends on a variety of factors such as price, sales volume, effectiveness of the advertising campaign, competition, cost of raw materials, etc. The accuracy of the estimates of future returns and therefore the reliability of the investment decision would largely depend upon the precision with which these factors are forecast. In reality, the actual returns will vary from the estimate. This is referred to risk. The term ‘risk’ with reference to investment decisions may be defined as the variability in the actual returns emanating from a project in future over its
dispersion of income; (ii) Measures can be adopted to prevent profit from falling below some minimum level; (iii) Measures can be adopted to increase the firm's ability to withstand unfavourable economic outcomes.
Risk And Investment Proposals
There are two measures of incorporating risk in the decision – making. They are: 1) The expected value and 2) The standard deviation.
1) The Expected Value : In a situation of certainty, any investment gives only one possible cash flow out in a risky situation several cash flows are possible, each with a given probability. By as certaining the average of all such possible outcomes (X) 1 weighed by their respective probabilities (P) we can get a single value for the cash flows. The value is known as expected value E (X), whose generalized expression is
n
E (X) = F 0 5 3F 0 2 0^ Xi^ pi
i=
2) The Standard Deviation : The statistical concept of standard deviation is used as a yard stick that reflects the variations of possible outcomes from its mean value. The standard deviation is calculated as:
n -
F 0 7 3= F 0 5 3F 0 2 0 (Xi – X) Pi
1. Shorter Payback Period. According to this method, projects with shorter payback period are normally preferred to those with longer payback period. It would be more effective when it is combined with “cut off period". Cut off period denotes the risk tolerance level of the firms. For example, a firm has three projects. A , B and C for consideration with different economic lives say 15,16 and 8 years respectively and with payback periods of say 6, 7 and 5 years. Of these three, project C will be preferred, for its payback period is the shortest. Suppose, the cut off period is 4 years, .then all the three projects will be rejected. 2. Risk Adjusted Discount Rate (RADR). Risk Adjusted Discount Rate is based on the same logic as the net present value method. Under this method, discount rate is adjusted in accordance with the degree of risk. That is, a risk discount factor (known as risk-premium rate) is determined and added to the discount factor (risk free rate) otherwise used for calculating net present value. For example, the rate of interest (r) employed in the discounting is 10 per cent and the risk discount factor or degrees of risk (d) are 2, 4 and 5 per cent for mildly risky, moderately risky and high risk (or speculative) projects respectively then the total rate of discount (D) would respectively be 12 per cent, 14 per cent and 15 .per cent.
That is RADR = 1/ (8+r+d). The idea is the greater the risk the higher the discount rate. That is, for the first year the total discount factor, D= 1 / (1+r+d) for the second year RADR = 1 / (1+r+d)2 and so on.
Normally, risk discount factor would vary from project to project depending upon the quantum of
risk. It is estimated on the basis of judgment and intention on the part of management, which in turn are subject to risk attitude of management.
It may be noted that the higher the risk, the higher the risk adjusted discount rate, and the lower the discounted present value. The Risk Adjusted Discount Rate is composite of discount rate which combines .both time and risk factors.
Risk Adjusted Discount Rate can be used with both N.P.V: and LRX In the case of N.P.V. future cash flows should be discounted using Risk Adjusted Discount Rate and then N.P.V. may be ascertained. If the N.P.V. were positive, the project would qualify for acceptance. A negative N.P.V. would signify that the project should be rejected. IfLR.R. method were used, the I.R.R. would be computed and compared "with the modified discount rate. If it exceeds modified discount rate, the proposal would be accepted, otherwise rejected.
Risk Adjusted Discount Rate Method – Merits :
i) This technique is simple and easy to handle in practice.
ii) The discount rates can be adjusted for the varying degrees of risk in different years, simply by increasing or decreasing the risk factor (d) in calculating the risk adjusted discount rate. iv) This method of discounting is such that the higher the risk factor in the remote future is, automatically accounted for. The risk adjusted discount rate is a composite rate which combines both the time and discount factors.
This co-efficient is calculated for cash flows of each year. The value of the co-efficient may vary-between 0 and 1, there is inverse relationship between the degree of risk, and the value of co- efficient computed. These adjusted cash inflows are used for calculating N.P.V. and the I.R.R. The discount rate to be used for calculating present values will be risk- free (i.e., the rate reflecting the time value of money). Using this criterion of the N.P.V. the project would be accepted, if the N.P.V were positive, otherwise it would be rejected. The I.R.R. will be compared with risk free discount rate and if it higher the project will be accepted, otherwise rejected.
The Finite-horizon Method. This method is similar to payback method applied under the condition of certainty. In this method, a terminal data is fixed. In the decision making, only the expected returns or gain prior to the terminal data are considered. The gains or benefit expected beyond the terminal data are ignored me gains are simply treated as non-existent. The logic behind this approach is that the developments during the period under Consideration might render the gains beyond terminal date of no consequence. For example, a hydel project might go out of use, when, say, after 50-years,of its installation, the atomic or solar energy becomes available in abundance and at lower cost.
Sensitivity Analysis
MODERN METHODS
This provides information about case flows under three assumptions: i) pessimistic, ii)
most likely and iii) optimistic outcomes associated with the project. It is superior to one figure forecast as it gives a more precise idea about the variability of the return. This explains how sensitive the cash flows or under
the above mentioned different situations. The larger is the difference between the pessimistic and optimistic cash flows, the more risky is the project.
Decision Tree Analysis
Decision tree analysis is another technique which is helpful in tackling risky capital investment proposals. Decision tree is a graphic display of relationship between a present decision and possible future events, future decisions and their consequence. The sequence of event is mapped out over time in a format resembling branches of a tree. In other words, it is pictorial representation in tree from which indicates the magnitude probability and inter-relationship of all possible outcomes.
Elements Of Decision Theory
Managerial Economics focuses attention on the development of tools for finding out an optimal or best solution for the specified objectives in business. Any decision has the following elements:
- The Decision Maker.
- Objectives or goals sought to be achieved by the decision maker; for example, maximisation of profit or sales revenue may be the objective of the business.
- A set of choice alternatives. For example, in Capital budgeting, the available projects.
- A set of outcomes or pay-offs with each alternatives; that is net benefits from the projects. Outcomes may be certain or uncertain. In case of former, the selection of any alternative leads
- A number of states of the environment whose occurrence determines the possible outcomes. For example, inflation and depression would be two alternative states, hi the absence of risk and uncertainty, the outcome of a project is known. Therefore only one state of the environment is possible. The study of Managerial Economics begins with developing awareness of the environment within which managerial decisions are made.
- Criteria derived from the general objectives which enable the decision taker to rank the various alternatives in terms of how far their pay-offs lead to the achievement of the decision maker's goals. This is known as the decision process.
- Constraints on the alternatives when the decision maker may select. For example, the government policy on monopoly control; top management directions regarding business undertakings, diversification of business or diversifying an existing product line or to refrain from certain types of business, etc.
Risk Analysis in the case of Single Project
Project risk refers to fluctuation in its payback period, ARR, IRR, NPV or so. Higher the fluctuation, higher is the risk and vice versa. Let us take NPV based risk.
If NPV from year to year fluctuate, there is risk. This can be measured through standard deviation of the NPV figures. Suppose the expected NPV of a project is Rs. 18 lakhs, and std.'- deviation of Rs. 6 lakhs. The coefficient of variation C V is given by std. deviation divided by NPV. C, V = Rs. 6,00,000 / Rs. 18,00,000 = 0.
Risk Return Analysis for Multi Projects
When multiple projects are considered together, what is the overall risk of all projects put together? Is it the aggregate average of std. deviation of NPV of all projects? No, it is not. Then What? Now another variable has to be brought to the scene. That is the correlation coefficient between NPVs of pairs of projects. When two projects are considered together, the variation in the combined NPV is influenced by the extent of correlation between NPVs of the projects in question. A high correlation results in high risk and vice versa. So, the risk of all projects put together in the form 'of combined std. deviation is given by the formula: F 0 7 3p = [ F 0 5 3Pij F 0 7 3i F 0 7 3j ] 1/
where,
F 0 7 3p – combined portfolio std. deviation
Pij^ – correlation between NPVs of pairs of projects. F 0 7 3i F 0 7 3j – std. deviation of i th and j th projects, i.e., any pair time.
Summary
Capital rationing refers to a situation where a firm is not in a position to invest in all profitable projects due to the constraints on availability of funds. We know that the resources are always limited and the demand for them far exceeds their availability, It is for this reason that the firm cannot take up ail the projects though profitable, and has to select the combination of proposals that will yield the greatest profitability. Risk and uncertainty are quite inherent in capital budgeting decisions. Future is uncertain and involve risk. Risk involves situations in which the probabilities of an event occurring are known and these probabilities are objectively determinable. Uncertainty is a subjective phenomenon. In such
Risk. Refers to a situation in which there are several possible outcomes, each outcome occurring
with a probability that is known to the decision-maker. Risk-adjusted discount rate (RADR). Sum of risk-free interest rate and a risk premium. The former is often taken as the interest rate on government securities. The risk premium is what the decision-maker subjectively considers as the additional return necessary to compensate for additional risk. Standard deviation. The degree of dispersion of possible outcomes around the expected value. It is the square root of the weighted average of the squared deviations of all possible outcomes from the expected value. Certainty equivalent. A ratio of certain cashflow and the expected value of a risky cashflow between which the decision-maker is indifferent. Coefficient of variation. A measure of risk is used for comparing standard deviations of projects with unequal expected values. Uncertainty. Refers to situations in which there are several possible outcomes of an action whose probabilities are either not known or are not meaningful. Decision Tree. A graphic device that shows a sequence of strategic decisions and expected consequences under each possible situation. Maximax. Maximum profit is found for each act and the strategy in which the maximum profit is largest is chosen. Maximin. When maximum of the minimums are selected. This criterion is used by decision-makers with pessimistic and conservative outlook. Minimax. When minimum of the maximums are selected. This criterion is used
for minimising cost (unlike maximin, where pay-off and profit are maximised). Minimax Regret. Finding maximax regret value for each act, and then choosing the act having minimum of these maximum regret values. Opportunity Loss (or Regret). The difference between actual profit from a
decision and the profit from the best decision for the event.
Simulation Analysis. A method that assigns a probability distribution to each of the key variables
and uses random numbers to simulate a set of possible outcomes to arrive at an expected value and dispersion. Sensitivity Analysis. Defined as the examination of a decision to find the degree of inaccuracv in the underlying assumptions that can be tolerated without causing the decision to be inappropriate.
