XI INTERNATIONAL CONFERENCE
“INFORMATION TECHNOLOGY AND IMPLEMENTATION” (IT&I-2024)
Method of assessing investment risks based on fuzzy modeling of the net present value of innovative projects
Yuri Samokhvalov (Ukraine), Bohdan Zhuravel (England)
1. Introduction
The last few decades have clearly demonstrated the scientific and practical significance of innovation-driven development as a crucial factor in the economic growth of national economies and all economic entities. A distinctive feature of innovation project design is the predictive nature of its outcomes.
In investment analysis, the most frequently used predictive model for evaluating the efficiency of innovation projects is the net present value (NPV) of the project. This metric reflects the profit that an investor expects to receive from implementing the project.
2. Efficiency Indicator of Innovation Projects
Net present value is calculated using the following formula:
If NPV>0, then there is full payback on the investment, and the NPV value indicates the investor’s profit. If NPV<0, the investment does not pay off, resulting in a loss for the investor.
3. Fuzzy Linguistic Assessments
A fuzzy linguistic assessment is a numerical evaluation expressed in statements with qualifiers like "approximately/about":
"the cash inflow is approximately equal to c"
or
"the cash inflow is approximately in the interval from c to d".
Triangular numbers (c,α,β) are assessments of the first kind, and trapezoidal numbers (c,d,α,β) are assessments of the second kind.
4. Calculation of Fuzziness Coefficients
c
d
c
b
0.5
1
x
µ
a)
b)
0
Figure: Gaussian membership functions: a) - standard; b) - combined (double)
5. Calculation of Fuzziness Coefficients
6. Calculation of distance between transition points
7. Algorithm for Calculating the Distance Between Transition Points
8. Modelling Random Scenarios and Risk Assessment
9. Practical Realisation
An experiment was conducted to assess the investment risk of a certain three-year innovative project
with an initial investment amount of IC=265 and an interest rate of p=5%.
The table provides estimates of the expected profit for each year.
Based on this data, for the random variable X ≜ "cash flow", the following intervals were obtained for each year using the aforementioned mathematical framework: [77,113], [107,123], [66,139].
Simulation of the net present value within these intervals over 1,000 model runs indicated that the investment risk is 0.065, which is considered moderate.
10. Conclusions
An approach to assessing investment risks based on fuzzy modelling of the efficiency
of innovative projects has been considered. The fuzzy model of efficiency is represented
by the net present value indicator, where the cash flow parameter is defined using fuzzy
linguistic numbers.
A procedure for approximating linguistic evaluations with fuzzy numbers based on the
Gaussian membership function has been proposed. To simulate the NPV indicator, the Neyman
rejection method is applied, with Gaussian functions serving as the probability density functions for
the expected cash flow distribution.
The conducted experiment demonstrated the practical feasibility of the approach,
along with its simplicity and versatility.