
Sensitivity Analysis:
Sensitivity analysis is a simulation technique in which key variables are changed and the resulting change in the rate of return or [the NPV] is observed. Some of the key variables are cost, prices, project life, market share, etc.
The most practical way to do this is to select those variables whose estimated values may contain some significant errors or an element of uncertainty, and then to calculate the effect of errors of different sizes on the present value of the project.
The common operating mechanism would be to vary each strategic variable by certain fixed percentages in both positive as well as negative directions in turn, say plus or minus 10% or plus or minus 5% etc., and study the effect of change on the rate of return [or on NPV].
It is an effective tool to handle risk in project appraisal. However, there are certain limitations in using this tool.
They are:
(a) Unless the combined effect of change in a set of Intercorrelated variables is examined, single variable sensitivity testing could be worse than useless. It may lead to wrong conclusions. Hence, it is a very difficult task.
(b) The second limitation lies in the fact that the values of the variables [components] are generally changed in an arbitrary manner by say 5% or 10% to examine the effect on the returns. Unless it is done in a meaningful manner, it might mislead the investor.
(c) The third one is that it ignores the chances associated with the different possible values of the components.

Probability Analysis:
Probability may be defined as a measure of some one’s opinion about the likelihood that an event [cash flow] will occur. The likelihood of occurrence normally ranges from 1 to 0 i.e., 100 per cent certainty to 100 per cent uncertainty.
In this analysis, in the place of one single estimate a range of estimates and their associated probabilities are calculated. A probability distribution in its simplest form could be with a few estimates such as “optimistic”, “pessimistic”, and “most likely”.
The real problem, however, is how this probability distribution can be obtained. Two types of probabilities – objective and subjective – are normally used for decisionmaking under uncertainty.
The objective probability is the probability estimate, which is based on a very large number of observations, say, for example, on the objective evidence of 100 trials conducted repeatedly under independent identical situations.
Subjective probabilities are those probability measures, which are based on the state of belief of a person rather than the objective evidence of a large number of trials.
As the capital expenditure decisions are mostly nonrepetitive and not made under identical situations, only subjective probabilities are useful.

Expected Values [EV]:
EV is the sum of products of estimated outcomes and their respective probabilities. For example, if three possible yields for an investment are 8%, 12%, and 16% and the probabilities that any one of these will be achieved is 0.25, 0.50, and 0.25 respectively, the EV of the yield is as follows:
In advance, while uncertainty refers to a situation where such probability distribution cannot be objectively known, but only guessed. However, in the case of investment decisions, such a theoretical distinction is hypothetical and may not serve much useful purpose in practice.
Even the best estimates of the project manager regarding the probability of the expected cash flows materializing, and their magnitude are only subjective guesses. Hence, both risk and uncertainty are used interchangeably to mean the same thing.
Some of the factors, which add to the degree of risk or uncertainty of an investment, are the possibilities of:
(a) The process or product becoming obsolete,
(b) Declining demand for the product,
(c) Change in government policy on business,
(d) Price fluctuations,
(e) Foreign exchange restrictions, and
(f) Inflationary tendencies, etc.
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