Risk and uncertainty are an excludable part of the financial analysis of projects, therefore it is necessary to know the tools and instruments that are developed to facilitate decision-making
The situations that the financial manager faces daily in terms of decision-making with respect to project evaluation is very complex, but most of these decisions are made with certainty, in future cash flows with probability one.
However, there is almost always the uncertainty factor in the final result of an investment which is very difficult to quantify mathematically, because in new projects there is almost always no a priori information base and in projects that have already been applied, there is no You can argue that the experience of other projects is a true reflection of what will happen with the project, since in economic matters many social, technical, technological, tax, etc. conditions can change.
Multiple scenarios
When analyzing a project, all its foundations must be evaluated within the real, critical and prosperity economic framework
Probability distribution
Any decision to invest involves forecasting the future and this forecast can be made optimistically called the best estimate, realistically called the most likely estimate or pessimistically called the worst estimate, these can occur when the economy is in prosperity, normal and in repression.
In the probability distribution, each possible outcome is assigned a probability, and the sum of all the probabilities equals 1.
When a project is going to be evaluated under risky conditions, it is because the probability allocation has been done objectively, that is, using statistical methods, but when the probability allocation is done subjectively by an expert in this type of project, but in almost all projects the probability assignment is done subjectively.
Expected value
An expected value is understood to be the probabilistic arithmetic mean, which can be calculated with the following formula:
Where:
XE = Expected value.
X K = Value of the result K.
P K = Probability of the result K.
n = Total number of results.
Standard deviation
When there are several possible results and they are widely dispersed, it is clearly seen that there is insecurity in the final result of a project, the more concentrated the results are, the more confidence there will be in the final result and the more dispersed the results, the more mistrust there will be in the result. final.
The standard deviation is the most appropriate measure for this class of dispersions and according to the statistics it can be calculated with the following formula:
Where:
s = Expected value.
X K = Value of the result K.
XE = Probability of the result K.
P K = Total number of results.
In almost all financial projects the probability allocation is done subjectively
Coefficient of variation
When it comes to comparing two to more projects in which their values are different, the coefficient of variation is used to perform the analysis of financial projects. This is given by dividing the standard deviation by the expected value, that is:
To choose the best project, take the one with the lowest coefficient of variation, since this is the one with the lowest risk.
Uncertainty vs. Project evaluation
To measure the uncertainty presented in the evaluation of projects, there are different methodologies, the most important are:
- The expected net present value method The probability of acceptance loss method The increased risk rate method
Expected Net Present Value (NPV) Method
The expected net present value method is the most used because it allows risk to be incorporated directly into uncertainty and is based on the following principle:
Where:
NPVP = Expected net present value.
XE K = Expected value in period K.
i = effective rate for the period.
n = Total number of periods.
Probability of loss in acceptance method
The acceptance probability of loss method consists of finding the probability that the NPV is less than zero and therefore that there is a loss.
In this method, it is necessary to calculate the standard deviation of the entire project and to normalize the results in order to apply the normal curve and thus find the area that corresponds to an abscissa less than zero.
The standard deviation in this method depends on the deviations of the cash flows of each period and can be calculated by the following formula:
sP = Standard deviation of the entire project.
s K = Standard deviation of cash flow for period K.
n = Number of periods.
i = interest rate.
Risk increased rate method
The risk-increased rate method, also called the risk-adjusted rate method, consists of evaluating the project with a rate that must be equal to the risk-free rate plus the risk's own rate.
The risk-free rate can be the rate that would be used in the project when there is certainty and the risk rate itself is the surcharge that must be made for the very existence of the risk, then we have:
Where:
i = Risk-adjusted rate.
i 1 = Risk-free rate.
i 2 = Risk rate.
In this case we are talking about risk and not uncertainty, because the i2 rate can be calculated objectively by statistical methods.
It is obvious that by increasing the rate it is more difficult for the project to be approved, therefore the i2 rate should be a few additional percentage points in order to have a safety margin that compensates for possible errors of judgment but leads to fixed and independent criteria of changes in the financial market.
For the calculation of the i2 rate and making the assumption that the economic conditions of the country are stable, an estimate is made based on historical data, this means that the rate that was presented in similar risks must be found to apply it to the new project.
