Standalone Risk: Overview, Measurement and Formulas
The measure of standalone risk is the coefficient of variation of the project’s returns. Standalone risk views the risk of a project in isolation without regard to portfolio effects. The starting point for analyzing a project’s standalone risk involves determining the uncertainty in the cash flows.
There are four techniques in assessing the project’s standalone risk.
1. Sensitivity Analysis
Sensitivity analysis is a technique which indicates exactly how much the NPV will change in response to a change in an input variable, other things held constant.
It begins with a base situation where values of the inputs like price, variable costs, sales are given. Then each variable is changed by a specific percentage above and below the expected value, holding other variables constant. The NPVs are calculated and finally the derived NPVs are plotted against the variable that was changed. The slope of the lines reflect how sensitive NPV is to changes in each of the inputs; the steeper the slope, the more sensitive is NPV to changes in the variable.
2. Scenario Analysis
Sensitivity analysis is widely used but does have serious limitations. In general, a project’s stand alone risk depends on both the sensitivity of NPV to key variables and the range of likely values of these variables as reflected in their probability distributions.
The sensitivity analysis considers only the first factor and so, it is incomplete. Scenario analysis considers both of these factors.
In scenario analysis, the NPVs under bad and good scenarios are compared to the average case NPV. The result of the scenario analysis is used to determine the expected NPV, standard deviation of NPV and coefficient of variation of NPV.
The standard deviation of NPV can be calculated in different ways:
a. If the cash flows are normal and are not correlated (independent), then
n
σ NPV = ( ∑ σ2t / (1+k)2t )) ½
t=0
b. If cash flows across time are normally distributed and are completely dependent on one another ( or perfectly correlated) where r=+1, then
n
σNPV = ( ∑ σt / (1+k) t )
t=0
If cash flows of a project are correlated over time, the standard deviation of the probability distribution of possible NPVs or IRRs is larger than under independence. The greater is the correlation, the greater is the dispersion of the probability distribution.
So, projects that provide independent cash flows have lower risk than those with correlated cash flows. As degree of correlation between cash flows increases, the riskiness of the project increases.
3. Monte Carlo Simulation
This method, so named because it is derived from the mathematics of casino gambling ties together sensitivities and input variable probability distributions.
- The first step in a computer simulation is to specify the probability distribution of each uncertain cash flow variable.
- The computer chooses at random, a value for each uncertain value, based on its specified probability distribution.
- The value for each uncertain variable, along with values for certain variables such as tax rates, depreciation charges are used to determine the net cash flows for each year which in turn are used to determine NPV for this particular run.
- Steps above are repeated many times, e.g.1000, resulting in 1ooo NPVs which make up a probability distribution. Then the probability of NPV being above or below a value is estimated. A project’s stand alone risk is estimated from the coefficient of variation of its NPV distribution.
4. Decision Tree Analysis
Sometimes project expenditures are not made at one point in time but are made over a period of years which gives the managers the opportunity to reevaluate the decisions and either invest additional funds or cancel the project.
A decision tree is used to analyze multistage, sequential decisions. Abandonment of a project can effect a project’s risk as well as NPV. Managers can reduce risk if they can structure the decision process to include several decision points rather than one. Including abandonment alternative as a branch in the decision tree causes NPV to improve and lowers the standard deviation of NPV, thus its risk.