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Assigning Probability

It has been shown above that sensitivity analysis provides more than one estimate of the future return of a project. It is, therefore, superior to single figure forecast as it gives a more precise idea regarding the variability of the returns. But it has a limitation in that it does not disclose the chances of occurrence of these variations. To remedy this shortcoming of sensitivity analysis as to provide a more accurate forecast, the probability of the occurring variations should also be given. Probability assignment to expected cash flows, therefore, would provide a more precise measure of the variability of cash-flows. The concept of probability is helpful as it indicates the percentage chance of occurrence of each possible cash flow. For instance, if some expected cash flow has 0.6 probability of occurrence, it means that the given cash flow is likely to be obtained in 6 out of 10 times (i.e. 60 per cent) likewise, if a cash flow has a probability of 1, it is certain to occur (as in the case of purchase lease capital budgeting decision that is, the chances of its occurrence are 100 per cent). With zero probability, the cash flow estimate will never materialize. Thus, probability of obtaining particular cash flow estimates would be between zero and one.

The quantification of variability of returns involves two steps. First, depending on the chance of occurrence of a particular cash flow estimate, probabilities are assigned. The assignment of probabilities can be objective or subjective. Objective probability refers to the assignment of a probability which is based on a large number of observations, under independent and identical situations, on the basis of the experience of happening or not happening of the event. However, objective probability is not of much use in capital budgeting situations because they do not satisfy the requirement of independent observations repeated over time. They are rather based on single event. Probability assignments which are not based on objective evidence of a large number of trials of identical events are called subjective or personal probability assignments. The assignment of probabilities to cash flow estimates is subjective.

The second step is to estimate the expected return on the project. The returns are expressed in terms of expected monetary values. The expected value of a project is a weighted average return, where the weights are the probabilities assigned to the various expected events, that is, the expected monetary values of the estimated cash flows multiplied by the probabilities.

The procedure for assigning probabilities and determining the expected value is illustrated in Table.

TABLE

Calculation of Expected Values

The mechanism for calculating the expected monetary value and the NPV of these estimates is further illustrated.