Risk can be defined as the chance that the actual outcome will differ from the expected outcome. Uncertainty relates to the situation where a range of differing outcomes is possible, but it is not possible to assign probabilities to this range of outcomes. The two terms are generally used interchangeably in finance literature. In investment appraisal, managers are concerned with evaluating the riskiness of a project’s future cash flows. Here, they evaluate the chance that the cash flows will differ from expected cash flows, NPV will be negative or the IRR will be less than the cost of capital. In the context of risk assessment, the decision-maker does not know exactly what the outcome will be but it is possible to assign probability weightage to the various potential outcomes. The most common measures of risk are the standard deviation and coefficient of variations. There are three different types of project risk to be considered:

**1. Stand-alone risk:** This is the risk of the project itself as measured in isolation from any effect it may have on the firm’s overall corporate risk.

**2. Corporate or within-firm risk:** This is the total or overall risk of the firm when it is viewed as a collection or portfolio of investment projects.

**3. Market or systematic risk:** This defines the view taken from well-diversified shareholders and investors. Market risk is essentially the stock market’s assessment of a firm’s risk, its beta, and this will affect its share price.

Due to practical difficulties in measuring corporate and market risk, the stand-alone risk has been accepted as a suitable substitute for corporate and market risk. There are the following techniques one can use to deal with risk in investment appraisal.

**Statistical Techniques for Risk Analysis:**

(a) Probability Assignment

(b) Expected Net Present Value

(c) Standard Deviation

(d) Coefficient of Variation

(e) Probability Distribution Approach

(f) Normal Probability Distribution

**(a) Probability Assignment:**

The concept of probability is fundamental to the use of risk analysis techniques. It may be defined as the likelihood of occurrence of an event. If an event is certain to occur, the probability of its occurrence is one but if an event is certain not to occur, the probability of its occurrence is zero. Thus, the probability of all events to occur lies between zero and one.

**(b) Expected Net Present Value:**

Once the probability assignments have been made to the future cash flows, the next step is to find out the expected net present value. It can be found out by multiplying the monetary values of the possible events by their probabilities.

**(c) Standard Deviation:**

The assignment of probabilities and the calculation of the expected net present value include risk into the investment decision, but a better insight into the risk analysis of capital budgeting decision is possible by calculating standard deviation and coefficient of variation.

**(e) Probability Distribution Approach:**

The researcher has discussed the concept of probability for incorporating risk in capital budgeting proposals. The probability distribution of cash flows over time provides valuable information about the expected value of return and the dispersion of the probability distribution of possible returns which helps in taking the accept-reject decision of the investment decision.

**(f) Normal Probability Distribution:**

The normal probability distribution can be used to further analyze the risk in investment decisions. It enables the decision-maker to have an idea of the probability of different expected values of NPV, that is, the probability of NPV having the value of zero or less, greater than zero and within the range of two values for example, within the range of ` 2,000 and ` 3,000, etc. If the probability of having NPV is low or zero or less, eg. .01, it means that the risk in the project is negligible. Thus, the normal probability distribution is an important statistical technique in the hands of decision-makers for evaluating the riskiness of a project.

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