Risk and Uncertainty incorporated methods of
Capital Project evaluation - Risk Analysis In Capital Budgeting
Risk with reference to capital (budgeting)
investment decisions may be defined as the variability which is likely to occur
in future between estimated return and actual return. Uncertainty is total lack
of ability to pinpoint expected return.
Risk and
Uncertainty incorporated methods of Capital Project evaluation
Risk with reference to capital (budgeting) investment decisions may be defined
as the variability which is likely to occur in future between estimated return
and actual return. Uncertainty is total lack of ability to pinpoint expected
return.
Situations of pure risk refer to contingencies which have to be protected
against the normal insurance practice of pooling. For this to be so, risk
situations are characterized by a considerable degree of past experience.
Uncertainty on the other hand relates to situations in some sense unique and of
which there is very little certain knowledge of some or all significant
aspects.
The techniques used to handle risk may be classified into the groups as
follows:
(a) Conservative methods: These methods include shorter payback period, risk-adjusted discount rate, and conservative forecasts or certainty equivalents etc., and
(b) Modern methods: They
include sensitivity analysis, probability analysis, decision-tree analysis etc.
(a) Conservative methods
The conservative methods of risk handling are dealt with now.
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 18 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 NPV and LRX. In the case of
NPV future cash flows should be discounted using Risk Adjusted Discount Rate
and then NPV may be ascertained. If the NPV were positive, the project would
qualify for acceptance. A negative NPV would signify that the project should be
rejected. If LRR method were used, the IRR 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:
1. This
technique is simple and easy to handle in practice.
2. 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.
3. 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.
Risk Adjusted Discount Rate Method –
Demerits:
i) The value of discount factor must necessarily remain subjective as
it is primarily based on investor’s attitude towards risk. .
ii) A uniform risk discount factor used for discounting al future returns is
unscientific as it implies the risk level of investment remains same over the
years where as in practice is not so.
Certainty-Equivalent Coefficient Approach
This risk
element in any decision is often characterized by the two Outcomes: the
‘potential gain’ at the one end and the ‘potential loss’ at the other. These
are respectively called the focal gain and focal loss. In this connection,
Shackle proposes the concept of “potential surprise” which is a unit of
measurement indicating the decision-maker’s surprise at the occurrence of an
event other than what he was expecting. He also introduces “another concept -
the “certainty equivalent” of risky investment. For an investment X with a given
degree of risk, investor can always find another risk less investment Xi such
that he is indifferent between X arid Xi. The difference between X and Xi is
implicitly the risk discount.
The risk level of the project under this method is taken into account by
adjusting the expected cash inflows and the discount rate. Thus the expected
cash inflows are reduced to a conservative level by risk-adjustment factor
(also called correction factor). This factor is expressed in terms of Certainty
- Equivalent Co-efficient which is the ratio of risk less cash flows to risky
cash lows. Thus Certainty — Equivalent Co-efficient;
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 the 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
Hyde 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.
(b) Modern Methods
Sensitivity Analysis
This provides
information about cash 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:
1. The
Decision Maker.
2. 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
3. A set of choice alternatives, for example the available projects in Capital budgeting.
4. 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 uniquely to a specific pay-off. In case of later, any one of a number of outcomes may be associated with any specific decision.
5. A number of states of the environment whose occurrence determines the possible outcomes. For example, inflation and depression would be two alternative states, in 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.
6. 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.
7. 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.
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:
0 Comments