The risk of an investment project can be viewed as the variability of its cash flows from those that are expected.
The possible outcomes for an investment project can be expressed in the form of probability distributions of possible cash flows. Given a cash-flow probability distribution, we can express risk quantitatively as the standard deviation of the distribution.
A measure of the relative risk of a distribution is the coefficient of variation (CV). Mathematically, it is defined as the ratio of the standard deviation of a distribution to the expected value of the distribution.
One approach to the evaluation of risky investments is the direct analysis of the probability distribution of possible net present values of a project calculated at the risk-free rate. A probability tree or simulation method may be used to estimate the expected value and standard deviation of the distribution. Management can then use this information to determine the probability that the actual net present value will be lower than some amount, such as zero.
The probability that a projectâ€™s internal rate of return will be less than the risk-free rate is equal to the probability that the projectâ€™s net present value will be less than zero where the risk-free rate is used in discounting. If we view an opportunity loss as any return less than the risk-free return, then the likelihood of an NPV less than zero can be interpreted as the chance of incurring as the chance of incurring an opportunity loss if the project is accepted.
Investment projects can also be judged with respect to their contribution to total firm risk which implies a firm-portfolio to risk assessment.
By diversifying into projects not having high degrees of correlation with existing assets, a firm is able to reduce the standard deviation of its probability distribution of possible net present values relative to the expected value of the distribution. The correlations between pairs of projects prove to be the key ingredients in analyzing risk in a firm-portfolio context.
Often managerial options are important considerations in capital budgeting. The term simply means the flexibility that management has to alter a previously made decision.
An investment projectâ€™s worth can be viewed as its traditionally calculated net present value together with the value of any managerial option(s). The greater the uncertainty surrounding the use of an option the greater is its value.
Managerial options include the options to expand (contract), the option to abandon, and the option to postpone. Consideration of these various options can sometimes turn a reject decision otherwise made in evaluating a capital budgeting project into an accept decision and an accept decision into a decision to postpone.