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.
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.
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
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.
C, V = Rs. 6,00,000 / ` 18,00,000 = 0.33
Risk Return Analysis for Multi Projects