## Sunday 6 February 2022

Why do I need a sensitivity analysis of the project?

One of the most common methods of risk assessment is a sensitivity analysis of the project.

The fact is that investment analysis and business planning are forecasting methods. They, unlike accounting data, which reflect retrospective, are built for the future.

When drawing up an investment project, all initial data are predicted. That is, forecast values are determined: sales volumes, fixed and variable costs, etc. The initial result of the project's effectiveness (discounted and non-discounted indicators) depends on how accurately these values are determined.

In this regard, even before the start of investment activities, it is necessary to understand as accurately as possible what will happen to the project if for some reason the level of variable costs changes, for example.

Thus, sensitivity analysis consists in assessing the impact of changing the initial parameters of the project on its final characteristics, which are usually used as an internal rate of return or NPV.

Risk is a situation of uncertainty in the consequences of decision-making, which can lead to various alternative outcomes, the probability of which can be determined quantitatively or qualitatively.

Project Sensitivity Formula

The sensitivity of the project can be assessed by the following formula.

For example, if with a 20% increase in price, the net discounted income increases by 250%, then the sensitivity of the project is 12.5. This means that if the price changes by 1%, the NPV will increase by 12.5%.

### Algorithm for analysis

To perform the analysis, you must perform the following steps:

• identification of the most significant potential risk situations from the perspective of a particular project.
• formation of a complete list of factors for analysis. At this stage, the final selection of factors for analysis takes place. For example, the factors can be price, volume, costs, amount of investment, etc. However, it must be understood that the factors can be more detailed. For example, you can analyze not just the impact of changes in average variable costs on the NPV of the project, but analyze the impact of only a part of them – workers' wages, etc.
• sensitivity analysis;
• for factors that have the maximum impact on the effectiveness of the project, conducting a detailed sensitivity analysis;

development of a set of measures aimed at reducing the likelihood of an unfavorable situation;
at the production stage of the investment project, an analysis of the effectiveness of the proposed set of measures should be carried out. As part of the analysis, the effectiveness of the proposed set of measures should be determined.

### Example of project sensitivity analysis

Assess the sensitivity of the project to changes in: (a) the price level; b) the level of average variable costs; c) changes in the level of total fixed costs. If the one-time initial investment in the project amounted to 800,000 rubles, the calculation horizon is 3 years. The expected performance indicators of the travel agency do not change by year and are: the volume of sales of the travel agency - 145 vouchers with an average check of 25,000 rubles; variable costs per unit of production – 14 200 rubles; total fixed costs for the year - 1 024 000 thousand rubles Discount rate 15%.

1. To begin with, it is necessary to determine the value of NPV without taking into account the influence of factors:

NPV= \frac{542000}{(1+0,15)^1} +\frac{542000}{(1+0,15)^2}+ \frac{542000}{(1+0,15)^3}  - 800000 = 437508rub.

2. Next, it is necessary to determine what the net discounted income will be if, for example, the price increases by 20%. All other factors do not change.

Price (+20%) = rub. 25000 * 1,2 = 30000

NPV= \frac{1267000}{(1+0,15)^1} +\frac{1267000}{(1+0,15)^2}+ \frac{1267000}{(1+0,15)^3}  - 800000 = 2092846rub.

3. Similarly, NPV values are calculated for other factor deviations. For example, if the price changes by -20%, -10%, +10%, +20%.

4. Further, the influence of other factors on NPV is similarly determined.

(a) sensitivity to changes in the price level

From the table it can be seen that with an increase in price by only 20%, the net discounted income of the project increases by 378%. Similarly, a 20% drop in price causes NPV to fall by 378%. Thus, the project is very sensitive to price changes. And the investor needs to pay great attention to this problem.

b) sensitivity to changes in the level of average variable costs

c) sensitivity to changes in the level of total fixed costs

Conclusion: Based on the calculations, it can be seen that the project is most sensitive to changes in the price level (average check), and the least sensitive to changes in total fixed costs.

### Project sensitivity graph

Based on the data of the previous example, we will conduct a graphical analysis of the sensitivity of the NPV project to changing factors.

Graph of NPV sensitivity to deviations of influencing factors
Graph of NPV sensitivity to deviations of influencing factors
From the chart it can be seen that the project is most sensitive to price changes. With a price reduction of only 5%, the project goes into the negative area, that is, the NPV < 0.

The next most sensitive factor in this example is the average variable costs. With their increase by 10%, the investment project becomes unprofitable.

### Conclusion

Thus, the sensitivity analysis of the project allows you to assess how changes in the factors of the external and internal environment of the project affect its effectiveness. This allows you to proactively manage your project to mitigate its risks.

In addition to sensitivity analysis, a project risk assessment can be carried out, for example, by determining the break-even point and the financial strength of the project.