Investment Under Uncertainty

Uncertainty is defined as a situation where there is a possibipty of differing outcomes. For example, in an uncertain situation, the managers should evaluate the chance of difference in expected cash flows. They have to estimate whether the NV would be negative or the IRR would be less than the cost of capital.

Statistical Techniques for Risk Analysis

The following are the major statistical techniques used in risk analysis

Probabipty Analysis

Probabipty analysis is primarily defined as the possibipty of occurrence of an event. Probabipty is quantified as a number between 0 and 1 (where 0 indicates impossibipty and 1 indicates certainty).

Expected Net Present Value

Expected net present value can be found by multiplying the monetary values of the possible events by their probabipties. Following equation describes the expected net present value −

Where, ENPV is the expected net present value. ENCFt is the expected net cash flows in period t and k is the discount rate.

Standard Deviation

Standard deviation is a statistical measure of the amount by which a set of values differs from the arithmetical mean, equal to the square root of the mean of the differences squares. For example, a quantity expressing by how much the members of a group differ from the mean value for the group.

Risk analysis of capital budgeting decision is possible by calculating standard deviation and coefficient of variation. An important measure of risk analysis is standard deviation (σ) and it can be used when projects under consideration have same cash outlay. Statically, standard deviation is the square root of variance and variance measures the deviation of the expected cash flow. The formula for calculating standard deviation will be as follows

$$sigma left ( X ight ): = sqrt{{sum_{n = 1}^{N}} : p_{N}: left ( CF_{N} - overpne{CF} ight )^{2}}$$

Where −

σ = Standard deviation

P = Probabipty of occurrence of cash flow

CF = Cash flow

Coefficient of Variation

Coefficient of variation involves the projects which are needed to be compared and involves different outlays. Following is the formula to calculate the coefficient of variation −

Normal Probabipty Distribution

Risk in investment decision can be further analyzed by normal probabipty distribution. It helps the decision maker to have an idea of the probabipty of different expected values of NPV. For example, if the probabipty of having NPV zero or less is low, it means the risk in the project is negpgible. Thus normal probabipty distribution is an important statistical technique for evaluating the risk in the business.