Methods of quantitative risk assessment, Project sensitivity...

Methods for quantitative risk assessment

Let's consider some methods of such estimation, often used in practice.

Project sensitivity analysis

The previously considered methods of assessing the effectiveness of IP ( NPV , IRR, PBR, PI ) are based on the use of cash flows, which in themselves are estimated values ​​and represent the forecast of project managers . It is clear that many variables that determine cash flows are not known for certain and are, most likely, random values. If a key variable, for example, production costs, changes, then integral measures of efficiency undergo changes. The sensitivity analysis is a method that accurately shows how the integral performance indicators ( NPV or IRR ) change when one of the input variables changes if all other variables do not change.

The sensitivity analysis begins with the construction of the base version, developed based on the expected values ​​of the input quantities. We will choose as an option the example of the realization of the investment project considered by the company "Orion", discussed in the previous chapter. For this project, the value NPV = + 2068 thousand rubles was calculated. Then, several key input parameters are set, which have a significant impact on the value NPV, for example, revenue, production costs and discount rate. After that repeatedly change each variable, reducing or increasing it in a certain proportion, leaving other factors unchanged. Each time, the values ​​of NPV, are calculated and the graph of the NPV dependence on the variable is plotted on their basis.

Let's analyze the sensitivity of the project of the company "Orion", for which, based on the cash flow tables used in the previous chapter, calculate the values ​​ NPV for different deviations of the three selected variables from the base level and reduce the data to Table. 2.9.

Table 2.9

Project sensitivity analysis

Deviations from the baseline,%

Net present value, thousand rubles, when changing

Revenue volume

variable costs

discount rates






+ 1061









+ 1397

+ 1972




+ 1830

Let's plot the net present value NPV as a function of the changes in the selected variables (Figure 2.4).

In Fig. 2.4, a reflects the impact on the NPV project changes in revenue, in Fig. 2.4, b - changes in variable costs, and in Fig. 2.4, in - changes in discount rates. Since

NPV - is a nonlinear function, then on each of the graphs the really computed values ​​of NPV slightly deviate from straight lines. This allows us to understand the essence of project risks.

As it is obvious from the figure, the investigated project has the greatest sensitivity to changes in revenue, is less sensitive to fluctuations in variable costs, and reacts poorly to changes in the discount rate. In the analysis, a project with steeper sensitivity curves is considered more risky, since even relatively small deviations of the estimated variable from the baseline (for example, revenue) give a big error in the projected NPV of the project.

NPV sensitivity analysis of the project

Fig. 2.4. Sensitivity Analysis NPV Project

Script Analysis

The sensitivity analysis of the project provides an opportunity to imagine how significant the impact of a particular indicator is on the NPV of the project. However, the fact that the project we are considering is the most sensitive to changes in revenue, does not answer another important question: how likely are such changes in revenue? In other words, the risk of the project should be determined by the interaction of two factors: first, the sensitivity of its NPV to changes in key parameters; secondly, the range of probable values ​​of these parameters, which is reflected in the distribution of their probabilities.

The scenario analysis method is based on a comparison of these two factors.

Let's turn again to the project of Orion and consider three options for the development of the situation:

a) pessimistic - revenue will decrease by 5%, costs will increase by 5% and the discount rate will also increase by 5%;

b) the most expected - corresponds to the initial project data;

c) optimistic - revenue will increase by 5%, costs will be reduced by 5% and the discount rate will decrease by 5%.

We estimate the value of the NPV project in each of the three variants, for which we use the tables discussed in the previous chapter. At the same time, we will assume that, but the project managers estimate the probability of a pessimistic option is 30%, the expected one is 50% and the optimistic variant is 20%. Let us summarize the results obtained in Table. 2.10.

Table 2.10

Project risk assessment using scenario analysis


NPV project, thousand rubles.







(4) = (2) • (3)





The most likely



+ 1034





Expected value of NPV

+ 1371




The expected (mean) value NPV is found by the formula

where P t - the probability of each option; N - number of options;

The standard deviation of σNPV is found from the expression

Comparing the values ​​of E ( NPV ) and σ ΝΡV allows you to estimate the risk of the project.

In this example, the expected value of NPV is 1371 thousand rubles, and the standard deviation o NPV is

3492 thousand rubles. This indicates a sufficiently high risk of investing in the project being evaluated. Indeed, we estimate the probability that the NPV of the project will be less than zero - see formula (1.7):

In our case, , and . Since , we get:

Hence, there is about 35% probability that under the selected conditions of the three options for the development of the situation the project will be ineffective.

Scenario analysis extends the scope of project risk assessment capabilities, but this method is limited to considering only a few discrete project outcomes, whereas there are infinitely many options for changing project parameters.

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