A Scenario Analysis is a variation of Sensitivity Analysis . The Scenario Analysis examines different possible scenarios that would change the output of a project. Managers would then estimate what the value of the items on the Income Statement would be if this scenario were to occur, they would determine the Cash Flow and then the NPV.
In a scenario analysis you would make a list of possible scenarios with a list of possible outcomes (returns) that are associated with the scenarios. This list of returns is called the probability distribution. A list of scenarios and the probability distribution are shown in the Spread sheet example below.
The probability distribution will allow us to calculate the risk and the rewards of the Investment . The reward for the investment would be the Expected Return E(r), which is the average return considering the probability of the possible scenarios. The formula for calculating the Expected Return E(r) is as follows:
In the example below you can see that the expected return is 10% however there is risk involved with this investment, so the actual return could be more or less than 10%. In a boom the investment could earn 30% where in a severe recession the investment could lose 38%. How are we able to quantify the uncertainty of this investment? If we were to experience a boom than the investment would have a 20% surprise and if we were to experience a severe recession then we would experience a 48% surprise. The uncertainty associated with this investment is a function of the possible surprises. The way that we can summarize the risk into a single number is to first define the variance. The variance is the sum of all scenario's squared deviations from the expected return multiplied by their probabilities. The formula is shown below:
The reason that we square the deviations is because the negative deviations would offset the positive deviations. Als by squaring the deviations the variance has a dimension of percent squared. To give the measure risk the same dimension of the expected return (%), we use the standard deviation. The standard deviation is simply the square root of the variance.
Below is an excel sheet example of a scenario analysis for a stock Portfolio :
Another example would be a car dealership which specialized in massive trucks. What would happen to the size of the massive trucks market if gas prices rose 100%? Management would have to run a scenario analysis based on this particular scenario.