Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
Method of Express-Estimation of Innovation Project Risk
Based On Fuzzy- Multiple Approach
Tomasova D.A.
Too many imponderables of present day business environment
caused to actuality of the development of methodologies for
assessing the relevance of the innovative projects risk level taking
into account the different levels of ambiguity of the initial parameters.
This article considers the possibility of applying the fuzzy sets
theory’s tools for internal and external accounting, financial, industrial
and strategic factors of uncertainty of the project, also considered an
example of application of this algorithm.
Field of Research: Finance
Introduction
The innovative project is such investment project, comprising a complex of
research, development, manufacturing and other activities, which provide an effective
solution to a specific scientific and technical tasks (problems) associated with the
development, manufacture and marketing of innovative products. [2]
Goals and objectives variety of the innovative project defines a set of projects
varieties, such as modernization, innovative, advance, pioneering, leading to
evolutionary and breakthrough innovations and corresponding the risk level increase.
Along with the features common to any investment project, such as the symptoms
of high volatility, limited duration in time; the limitations of required resources,
complexity, there are some specific characteristics of the innovative project. Among
these are novel features of the product and its market segments for the company
implementing the project, a high level of innovation tasks along with the uniqueness of
the project and expendability of its execution; feature of the legal framework and
organizational structure, the availability of technological risk and a low level of
technological regulation. Internal ambiguity is also increasing by the dependence of the
results of the project in the first place, the quality of personnel and information
resources, the ability to adjust the tasks and resources of the project, depending on the
interim results, the complexity of attracting financial resources from the increased risk
level.
Innovative project’s risk could be formulated as situational characteristic of its
implementation, comprising from the initial conditions ambiguity, as far as ambiguity of
its results and possibility of the failing adverse effects.
_______________________________________________________________
Saint-Petersburg State University of Technology and Design (SPSUTD), Chair of management, Russia,
Saint-Petersburg, street Bolshaya Morskaya, 18, rameria@rambler.ru
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
The ambiguity associated with the activity of the economic system, referred to as
"the ability to transition from its present status under the influence of factors on her
certainty, risk, fear, and ambiguity factors of incomplete information in a certain state in
the future, quantitative and qualitative characteristics of which are uniquely determined."
[1]
Consequently, a key component of the ambiguity is the lack of knowledge, which
can be characterized by the quality of information on the development of external and
internal environment of the economic entity, including market, operational and financial
information.
Companies or individual business units carrying out the innovative projects,
especially in the field of radical and breakthrough innovation, subject to significant
changes in market conditions and operating environment, diverse and multi-directional
influences, about which there is no systematic and adequate information. In this
situation, experience and professional intuition and tacit knowledge managers and
organizers play a significant role in the successful implementation of innovation.
In this context the innovative project can be considered in the economic and
humanistic system in which reasoning and making decisions based not only on
measurements (which nevertheless remains a significant factor), but also to a large
extent on linguistic or perceptual evaluations. For such systems, fuzzy logic allows to
imagine the decision-making processes and situations’ evaluation by person in
algorithmic form. It uses linguistic variables instead of quantitative ones, fuzzy logic
instead of binary for the formal submission of inaccurate subjective categories. Here it is
possible to take into account the experience and person’s intuition, and introduced
linguistic ambiguity characterizes the inaccurate description of the situation or event,
regardless of the time of their examination.
Approaches and performance evaluations of innovative projects risk.
Record for ambiguity and analysis of the risks in the innovative design requires the
use of special evaluation of performance indicators that take into account, on the one
hand, the implementation of all possible conditions, and on the other - the extent of their
capabilities. The indicators characterizing in general the efficiency of the project under
all possible conditions of its implementation, called the index of expected efficiency. The
criterion of efficiency in the non-deterministic environment should also reflect the
preferences of the subject of economic system.
The integral index could be used by various private performance indicators for
achievement, in particular the expected present value, the index of the expected return
and the investment costs, the internal rate of expected yield, the expected payback
period, the expected need for additional financing, and others. Integrated indicators are
characterized by the same advantages and disadvantages as similar private
performance. [4]
One of the most common indicators of efficiency of the innovative project is the net
present value (NPV). It provides a quantitative estimate of the final excess of revenues
over all project costs, taking into account changes in the value of money over time. The
main disadvantage of NPV criterion when comparing the alternatives of investment
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
projects is its dependence on the value of the discount rate (changing the discount rate
alternatives may be reversed), the dependence of income from the investment costs
and the inability to correctly compare alternative investment options with the exception
of special cases. In some cases the assessment may be biased for the project, which
provides for the gradual expansion of production for the accounting period. At the same
time this indicator describes completely the final income, which is obtained by investors
over the life of the project.
In practice, as a generalized indicator at risk conditions is usually applied the
expected value of NPV. The positive value of the index of the integral effect is
interpreted in other way than in the deterministic model, where it clearly shows the
effectiveness of the project. In this case it does not ensure against loss and the project
is considered effective not in the case of guaranteed winning, but if participation in this
project is preferable to be waived. Therefore, under conditions of ambiguity project
performance indicators should be supplemented by specific indicators of the range of
possible values of the effect as well as the instability of the results and costs. They are
called as sustainability indicators in conjunction with allow the different parties to
characterize the overall sustainability of the project. Sustainability of the project means
its efficacy in certain changes in the conditions of its implementation. Depending on the
expected results of the project at the alternative scenarios one may talk can of its
absolute stability, sufficient stability or instability.
Quantitative models of risk estimations differ as to results accuracy, complication
and complexity of assay performance. In the basis of any quantitative model of risk
estimation there is built-in the way to formalize the ambiguity. This method of
expression of initial information about the factors of ambiguities and its admissibility.
Statistic methods of risk evaluation base on the concept of probability, connected
with the possibility of undesired event. In this case for the risk estimation foremost it is
necessary to choose the appropriate possibility models to describe the ambiguity of
each parameter and its’ hesitation, also as possibility models of the project
implementation processes. In this case, it is usually displayed the law of distribution of
possible losses as a random variable.
In practice, when analyze of investment projects it appears that many parameters
fill a slot or several disjoint intervals on the real axis, with all the values in these intervals
are considered to be possible, but outside them - impossible. In this case, we can speak
about the interval uncertainty of the project; this means that the expected effect is
known only to a certain set of values, but not a probability distribution on the set.
When the project data there is a combination of different types of ambiguities, we
can talk about the appearance of interval-probabilistic ambiguity. So an economic entity,
based on the available information, may suggest to which of unknown distribution law
set it belongs to. The extent of the effects of possible values expressed in this case, not
by the number but class of admissible probability distributions.
The two extreme cases as the presence of a strict statistical system, and the case
of complete uncertainty are seldom; much more in real economic practice, one can
observe a situation that explains the concept of quasi statistic. So, the observer has at
its disposal a certain number of relatively homogeneous objects, insufficient for the
formation of the classical sample, but allows, however, suggesting the approximate
spread of key parameters. On the basis of such sample it is possible to justify the law of
subjective observations on particular degree of subjective certainty. It does not have the
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
accuracy of probability law, and its parameters vary according to specific rules in order
to achieve a certain level of confidence.[3] For operating with data of quasi statistic it is
applied the device of fuzzy sets theory, reflecting the subjectively axiological nature.
Therefore, the advantage of multi-fuzzy method is that it makes it possible to simulate a
non-uniform and limited in terms of monitoring economic processes. In addition, it
enables to analyze all possible scenarios (often forming a continuous spectrum), and
not only their boundary values. Convenience method consists in the fact that the work
comes not from the selected point values, and specify a calculated corridor projected
parameters of the project.
The main difficulty in choosing of method of risk assessment is that the application
of a mathematical apparatus directs the analyst to work with one specific type of
ambiguity, while in the real project there are encountered several of its species:
statistical, linguistic, interval uncertainty. Thus, the model adequately reflects only
certain types of data, and other types of information may be lost. To solve this problem
partly allows us the introduction of membership element to the set offered in terms of
the theory of fuzzy sets: it allows you to convert to a single form, and together consider
the different types of uncertainty.
Fuzzy- multiple approach allows you to incorporate into consideration not only the
uncertainty of the initial parameters, but also the uncertainty of production and financial
constraints, fuzzy goals and performance requirements of the project. Existing
algorithms in this approach allow us to find a common measure of risk based on fuzzy
performance indicator, which is a fuzzy set with its distribution. It also makes it possible
to introduce the fuzzy boundary on the size of the budget and to consider increasing
effect with a slight violation of restrictions and to assess its justification. Such
accounting is of great importance, since innovative solutions are strategic in nature and
are aimed at the long term, and thus involve uncertainty with respect to all components
of the project. The investor cannot be sure, not only with respect to the results, but also
with respect to future expenses and reasonable for him in the future, the level of
efficiency, depending on market conditions. Therefore, this approach is the basis for the
proposed methodology rapid risk assessment of the innovative project.
Principles of innovative project risk estimator
General algorithm for estimating the risk level of the innovative project involves the
formulation of the main objectives of the evaluation, development of a system of
classification of projects on the level of risk, the choice of common risk criteria for all
types of projects, carrying out an integrated assessment and linguistic recognition of the
quantified results.
Among four groups of existing project estimation methods (checklists, score
models, models of added values, model on the basis of cash flows) the fourth method
with the money cash discounting providing the most complete and qualitative account of
existing qualitative information and change of money cost in time, is applied.
Hesitation and ambiguity of the predicted value of money flows are reflected with
the help of tools of the fuzzy sets theory.
The fuzzy sets theory involves the formalization of fuzzy sets baselines and
targets for the efficiency of the innovation project (in this case the integral NPV index)
as a vector of interval values (fuzzy interval); entering values in each interval of the
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
vector is characterized by a certain degree of affiliation. That is, all or some of the
parameters of the project are considered to be fuzzy variables and their values
belonging to the set of possible values is defined by a number from zero to one.
In this case the expected efficiency of the project in this case is not an indication of
a point; It is a field interval values with their expectation distribution characterized by a
membership function corresponding to the fuzzy numbers. To assess the degree of
investment risk calculates the cumulative measure of expectations of negative results of
the investment process, based on the evaluated totality of expectations.
The change inherent in any innovation project is seen as a purposeful diversion of
existing in a desired state. The level of the requirements of investors and organizers of
the parameters of the state is determined by the variable G.
All the totality of alternative projects in innovative-investment projecting could be
divide on obligatory (necessary for implementation of rules and provisions, for the
assets and contract), non-obligatory (i.e. desirable development projects), urgent
(unapproachable in future or lose relish if delay), laid aside (i.e. correlated with the
investments, attractibility of which could be changed slightly when laid aside). Project
type largely determines the level of the requirements of investors and organizers: the
less urgent, and the more-delayed project is, the higher value of G. Thus, the features
of this type of project and its strategic goals and objectives are reflected in the level of
variability index G.
As mentioned above, there are several basic units of information related to the
project. Financial information, including a list of required for the start of the project
investment costs, a list of expenditure as direct operating costs and overheads, defines
the structure of financing of the project and its uncertainty.
Market information regarding the competitive advantage of innovative products,
market segmentation and evaluation of its volume, consumer preferences, and
competitor analysis, largely determines the expected volumes and dynamics of sales
and direct impact on the projected value of the cash flows of the project.
Production information, including a description of production needs and
possibilities of the company, the list of necessary raw materials, production facilities and
labor, defines the expected cash outflows for the project, as well as the probability of
technical success. In accordance with it there is laid a certain level of technical risk,
which is reflected in the adjustment of the discount rate used cash flows in accordance
with the applicable procedure. [4]
At the same time the ambiguity of the investors’ requirements and organizers of
the project is determined by the growth of the technical risks and the specifics of the
current innovation environment. It is characterized by the increase in capacity of
technical solutions, the scope of the transformation of nature, the increasing complexity
of technical solutions; reduction of terms of obsolescence of technologies and timing for
their development; the transition from the development of closed systems to open,
operates in conjunction with other objects and the environment and the lowering of the
hierarchical level of modification of material objects, as well as a decrease in the
accuracy of the control of negative effects. This leads to high volatility index G.
These values could be summarized in the risk function of the project, indicating the
degree of risk on the sustainability of the business plan. It allows you to allocate
conditionally acceptable thresholds and risk identification and risk levels of border
projects in the project allows to make timely adjustments related to the increase in
revenues or decrease costs. In the next section we consider the example of the risk
assessment of the innovative project.
5
Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
The calculation of the risk level of the innovative project of the textile
enterprise
Let’s consider the modernized type of innovation project risk factors implemented
by thread combine for the implementation of the release of a new type of thread and
penetrate a new market segment. The project made the purchase of equipment for the
winding department and held technical tests that determine the physical and mechanical
properties and the quality of the product intended for release.
As the interest level and the claims of investors in this project is unstable, there
are considered three options for financing that reflects the uncertainty of the internal
environment of the enterprise. In the present situation the most realistic is the
implementation of the project is completely due to the long-term bank loans, which
should cover the entire amount of the costs of innovation on the zero step. The
calculation in the traditional setting of the company is considered as an option on the
80% self-financing of the project at the expense of own and attracted sources, the
remaining 20% in this case financed by long-term bank loan. The repayment terms of
the loan are the same as in the first case.
The third option also suggests a mixed funding, 40% got from the own sources of
enterprises and 60% - in the long-term loan. In times of crisis to increase the overall
efficiency of the project the company proposed to raise part of the funds through the
sale of illiquid assets and on the balance of the estate and to cover 40% of the
investment costs of the project. Credit for the remaining 60% of the investments
provided under the same conditions as in the previous embodiments.
When calculating the efficiency of the project were examined three scenarios,
reflecting the different state of the market situation (the pessimistic, most likely and
optimistic) with the following results shown in Table 1.
The G level indicator is leveraged funds raised now, as well as the fact that the
project is strategically important for the timely hit on a favorable market segment.
Table 1. The main indicators of innovative project at different variants of financing
Variant of project
Net Present Value (NPV)
In prognostic
prices
(taking into
consideratio
In constant n level of Financial
prices
inflation)
consistency
Present
Value
Index
(PVI)
Most probable scenario
Borrowed financing
Hybrid financing (20% loan
capital, 80% own capital)
Hybrid financing (60% loan
capital, 40% own capital)
33561,160
29563,251
valid
2,1935
34586,025
30691,972
valid
2,237
34093,198
30146,624
valid
2,2159
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
Borrowed financing
Hybrid financing (20% loan
capital, 80% own capital)
Hybrid financing (60% loan
capital, 40% own capital)
Borrowed financing
Hybrid financing (20% loan
capital, 80% own capital)
Hybrid financing (60% loan
capital, 40% own capital)
Pessimistic scenario
-7709,923
-10742,889
-5737,339
-8693,702
-6711,443
-9706,532
Optimistic scenario
48949,543
44610,994
not valid
0,6627
valid
0,7479
not valid
0,7057
valid
2,6389
49672,654
45446,926
valid
2,673
49333,238
45050,459
valid
2,6566
Based on the data given let’s assess the level of risk of the investment project.
When using the fuzzy sets theory the risk is defined as the possibility that the
results of the process of innovation and investment value of NPV is below of the preset
level of efficiency boundary G. That is, in general assessment of investment risk is an
estimate of possible events NPV <G, i.e., the project would be ineffective, with the
proviso that NPV and G represent fuzzy intervals.
Let NPV = [NPV1, NPV2] - the efficiency of investment, G = [G1, G2] - boundary
condition of effectiveness.
In the phase space (NPV, G) stands out a rectangle bounded by the left and right
points of the NPV and G. This box represents a field of equally possible events,
describing the result of the investment process. The mutual correlation between the
parameters and G1,2 and NPV1,2 give the following calculation for the area of the zone
of inefficient investment:
G2  NPV1
0,

2
 G2  NPV1  ,
G1  NPV1  G2  NPV2

2

 G1  NPV1   G2  NPV1   G2  G1 ,
NPV1  G1  G2  NPV2

2
Sa  
 G2  NPV2   G2  NPV1    NPV  NPV ,
G1  NPV1  NPV2  G2
2
1

2

2
G  G  NPV  NPV    NPV2  G1  ,
NPV1  G1  NPV2  G2
1
2
1
 2
2
G  G  NPV  NPV ,
NPV2  G1
1
2
1
 2
Since all implementations (NPV, G) for a given level α accessories are equally, it is
possible to determine the degree of risk of inefficiency of the project as a chance to hit a
geometric point (NPV, G) in the inefficient investments shaded area:
S

NPV2  NPV1  G2  G1 
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
When considering the general case of fuzzy NPV and G is given by the segmental
mean.
NPV = NPV = [NPV1, NPV2]
G = G = [G1, G2]
The ratio of values NPV1, NPV2, G1, G2 depends on the level of α, so the
expression for the area will be as follows:
S
   
NPV2  NPV1   G2  G1 
For the total numbered triangular form the function φ (α) takes the form:
G 2  NPV1 ;
0,

G 2  NPV1 2
 
,
G1  NPV1  G 2  NPV2 ;
 1 2G 2  G1 NPV2  NPV1 

G1  NPV1   G 2  NPV1 

,
NPV1  G1  G 2  NPV2 ;
 2 
2NPV2  NPV1 

    
  G 2  NPV2   G 2  NPV1  , G  NPV  NPV  G ;
1
1
2
2
 3
2G 2  G1 

NPV2  G1 2



1

, NPV1  G1  NPV2  G 2 ;
 4
2G 2  G1  NPV2  NPV1 

NPV2  G1 .
 5  1,
The risk level is calculated by the formula below as the exact terms of the integral
and approximate as the final amount.
The calculation of an integral:
1
Risk    ( ) d
0
Calculation by the final sum:
Risk    ( i )  Δα [3]
(i)
In accordance with the results of carried out calculations G and NPV are triangular
numbers of the general form: G = (Gmin, Gav, Gmax) and NPV = (Gmin, Gav, Gmax); their
values are given in Table 2.
Table 2. Amount of triangular numbers NPV and G
Hybrid
Hybrid
Borrowed
financing
financing
Indicator
financing
(20/80)
(60/40)
NPVmin
-10742,889
-8693,702
-9706,532
NPVav
29563,251
30691,972
30146,624
NPVmax
Gmin
Gav
44610,994
-2500
0
45446,926
-1500
0
45050,459
-2000
0
Gmax
10000
11000
11000
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
Let’s draw the calculation of risk segment method. I.e., based on the formula:
Risk    ( i )  Δα
(i)
The mutual arrangement of NPV1, NPV2, G1 G2 will be determined, based on its’ values
calculated for each level of α.
NPV1   NPVav  NPVmin   NPVmin
NPV2  NPVmax   NPVmax  NPVav 
G 2  G max   G max  G av 
G1   G av  G min   G min
Let us find the values of NPV1, NPV2, G1 G2 and the risk of inefficiency of the
project for each level α for various financing options in Tables 3, 4 and 5.
Table 3. Calculation of risk level for borrowed financing
Alpha NPV1
NPV2
G1
G2
Fi
0
-10742,889 44610,994
-2500
10000
0,2618
0,1
-6712,275
43106,220
-2250
9000
0,2025
0,2
-2681,661
41601,445
-2000
8000
0,1283
0,3
1348,953
40096,671
-1750
7000
0,0471
0,4
5379,567
38591,897
-1500
6000
0,0008
0,5
9410,181
37087,123
-1250
5000
0
0,6
13440,795 35582,348
-1000
4000
0
0,7
17471,409 34077,574
-750
3000
0
0,8
21502,023 32572,800
-500
2000
0
0,9
25532,637 31068,025
-250
1000
0
1
29563,251 29563,251
0
0
0
Risk = ∑φ(αi) * α = 0,2618*0,1 + 0,2025*0,1 + 0,1283*0,1 + 0,0471*0,1 +
0,0008*0,1 = 0,0641
Table 4. Calculation of risk level for hybrid financing (20/80)
Alpha NPV1
NPV2
G1
G2
Fi
0
-8693,702 45446,926
-1500
11000
0,2483
0,1
-4755,135 43971,431
-1350
9900
0,1853
0,2
-816,567
42495,935
-1200
8800
0,1068
0,3
3122,000
41020,44
-1050
7700
0,0316
0,4
7060,568
39544,944
-900
6600
0
0,5
10999,135 38069,449
-750
5500
0
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
0,6
0,7
0,8
0,9
1
14937,702
18876,27
22814,837
26753,405
30691,972
36593,954
35118,458
33642,963
32167,467
30691,972
-600
-450
-300
-150
0
4400
3300
2200
1100
0
0
0
0
0
0
Risk = ∑φ(αi) * α = 0,2483*0,1 + 0,1853*0,1 + 0,1068*0,1 + 0,0316*0,1 = 0,0572
Risk = ∑φ(αi) * α = 0,2594*0,1 + 0,1983*0,1 + 0,1218*0,1 + 0,0426*0,1 +
0,0003*0,1 = 0,0622
The risk in all three cases could be regarded as acceptable, it does not reach
10%. The greatest risk (0.0641) was observed in the case of project financing based
entirely on borrowing basic.
To increase the accuracy of risk assessment is possible, if the investor is required
to determine the effectiveness of it abroad, it is a G gain the point estimate.
Table 5. Calculation of risk level for hybrid financing (60/40)
Alpha NPV1
NPV2
G1
G2
Fi
0
-9706,532 45050,459
-2000
11000
0,2594
0,1
-5721,216 43560,076
-1800
9900
0,1983
0,2
-1735,901 42069,692
-1600
8800
0,1218
0,3
2249,415
40579,309
-1400
7700
0,0426
0,4
6234,730
39088,925
-1200
6600
0,0003
0,5
10220,046 37598,542
-1000
5500
0
0,6
14205,362 36108,158
-800
4400
0
0,7
18190,677 34617,775
-600
3300
0
0,8
22175,993 33127,391
-400
2200
0
0,9
26161,308 31637,008
-200
1100
0
1
30146,624 30146,624
0
0
0
If one of the fuzzy numbers degenerates into an ordinary real number calculation
form is greatly simplifies. If the value of G is quite clearly defined, the previous equation
in the limit G1 → G2 gives the following result:
0,

 G  NPV1
*
    
,
 NPV2  NPV1
1,
G  NPV1
NPV1  G  NPV2
NPV2  G
In the most general form of the risk function for NPV triangular form and numbers
of G in the form of point is calculated by the formula:
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
0, G  NPVmin


1 - α1
R  (1 
 ln(1 - α 1 )), NPVmin  G  NPVav

α1

Risk (G )  
1 - α1
1 - (1 - R)  (1 
 ln(1 - α 1 )), NPVav  G  NPVmax
α1


1, G  NPVmax

Parameter R is taken as a project “instability index”, how much the desired value is
shifted toward the maximum value. The factor of stability of the project can take a
parameter P = 1 - R.
Draw the calculation of risk based on the fact that G receives its average value of
zero.
Let us find the values of the parameters R, α and the total risk value for the three
financing options and reflect the results of the calculation in Table 6.
As the table shows, the risk of the project is acceptable, with a considerable
margin, and ranges from 1.92% to 2.85%. The greatest risk inherent in the project,
based on loan financing. This option also involves the least financial stability coefficient
(0.8059). However, in general it can be assumed that the project has considerable
resistance to changes in the parameters, and this resistance varies slightly when
passing from one to another financing option.
Table 6. Estimaton of project risk level on basis of triangular number NPV and
zero efficacy border
Indicator
Hybrid
Hybrid
Borrowed
financing
financing
financing
(20/80)
(60/40)
NPVmin
-10742,889
-8693,702
-9706,532
NPVav
29563,251
30691,972
30146,624
NPVmax
G
R
α1
Risk (G)
P
44610,994
0
0,1941
0,2665
0,0285
0,8059
45446,926
0
0,1606
0,2207
0,0192
0,8394
45050,459
0
0,1773
0,2436
0,0236
0,8227
The risk level and the acceptability of the project largely depend on external
requirements for its effectiveness, that is, on the value of G. This dependence is the
basis for the construction of a special curve - the risk function of the project. The shape
of the hazard function can be determined by the rate of increase of the risk of the
project to the tightening of the criterion of efficiency, as well as to allocate the threshold
and alertness levels for this criterion.
Let’s consider how the project risk indicators change when requirements of the
investor change and subsequent calculations to determine the admissibility and
relevance of the draft value of G.
In this project for all financing options the apex of the triangular NPV strongly
shifted to the right, i.e., its most probable value is much closer to the maximum than the
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
minimum. In this case, the investor can expect a higher boundary condition G at an
acceptable level of risk.
If an investor wishes to receive not less than the average for the investment
profitability project of about 50%, then the boundary condition G will cost 8000 rubles.
We calculate the risk in this case in the following tables 7, 8, 9.
Table 7. Estimaton of project risk level on basis of triangular number NPV and
efficacy border at the rate of 8 million roubles
Indicator
Hybrid
Hybrid
Borrowed
financing
financing
financing
(20/80)
(60/40)
NPVmin
-10742,889
-8693,702
-9706,532
NPVav
29563,251
30691,972
30146,624
NPVmax
44610,994
45446,926
45050,459
G
8000
8000
8000
R
0,3386
0,3083
0,3234
α1
0,4650
0,4239
0,4443
Risk (G)
0,0949
0,0772
0,0857
P
0,6614
0,6917
0,6766
If available for the enterprise a few profitable areas of to invest in alternative
projects, competition between them is getting tougher, and in the conditions of such a
choice requirements to the lower limit of effectiveness are increased. If we consider this
project as one of the applicants for the funds required for several areas of development,
it is necessary to increase the level of G to 15,000 thousand rubles, it means to lay out
at least 1 ruble of surplus income for each ruble of the initial investment.
Table 8. Estimaton of project risk level on basis of triangular number NPV and
efficacy border at the rate of 15 million roubles
Indicator
Hybrid
Hybrid
Borrowed
financing
financing
financing
(20/80)
(60/40)
NPVmin
-10742,889
-8693,702
-9706,532
NPVav
29563,251
30691,972
30146,624
NPVmax
G
R
α1
Risk (G)
P
44610,994
15000
0,4651
0,6387
0,1972
0,5349
45446,926
15000
0,4376
0,6016
0,1709
0,5624
45050,459
15000
0,4512
0,6199
0,1836
0,5488
As the table shows, the level of risk is growing rapidly when the requirements of
the investor to the project increases. When G is 8000 rubles, i.e. when about 50% of
profitability, the risk remains acceptable, not reaching a value of 10%. Achieving a
higher profitability (with G, equal to 15%) leads to a transition to the zone boundary
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
project risk. Evaluation of the project at inflated claims to the value of G, and to evaluate
its ability to compete with alternative methods of profitable investment.
Consider also the case when the company intends to make full use of the
opportunities and potential, and the threshold level of efficiency equal to the most
probable value of NPV. The results of calculations are presented in the table.
Table 9. Estimaton of project risk level on basis of triangular number NPV and
efficacy border at the rate of NPVav
Hybrid
Hybrid
Borrowed
financing
financing
Indicator
financing
(20/80)
(60/40)
NPVmin
-10742,889
-8693,702
-9706,532
NPVav
29563,251
30691,972
30146,624
NPVmax
G
R
α1
Risk (G)
P
44610,994
29000
0,7180
0,9860
0,6745
0,2820
45446,926
30000
0,7147
0,9824
0,6630
0,2853
45050,459
30000
0,7251
0,9963
0,7101
0,2749
If the company aims to obtain the net present value is not lower than the normal,
the most likely development of the project, it is exposed to a significant risk of about
70%. This risk is considered unacceptable, and the project becomes unstable
(coefficient of resistance is reduced to 28%).
With requirements of the investor to the parameter G increasing, the investment
risk is increasing, but the rate of growth and the shape of the curve of risk depends on
the specific project data. Construction of the risk function in graphical form will
determine the acceptable zone and border risk alertness threshold and threshold of
acceptable risk for the project. We construct three risk functions for the three financing
options for the project on the basis of calculations carried out in Exel accountings of risk
levels for various G with step G to one million rubles.
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
Graph 1. Risk function at borrowed financing
Risk
Risk, %
100
0
20000
40000
100
75
75
50
50
25
25
0
0
20000
40000
0
G, тыс. р.
The figures above allow you to compare the ratio of risk and the required efficiency
in the use of different sources of funds for the project. It is evident that the differences in
financing options for the project is not much impact on the location of the curve, and the
dependence of the level of risk from the investor's requirements is almost identical. In all
three cases the risk function has an asymmetrical appearance, and the inflection point
of the function is significantly shifted to the right on the horizontal axis. A feature of this
function is a long plateau and a gradual transition to the stage of saturation.
The analysis showed that the considered as an example project provides an
acceptable level of risk, if the requirements of the investor does not exceed about 66%
profitability on invested capital. If there is strong competition with other projects and
enhancing the efficiency of the border to 100% of profitability, it goes in the border zone
of risk. In general it may be recommended for implementation when required profitability
of about 55% in this case there is an additional safety margin of the project.
14
Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
Graph 2. Risk function at hybrid financing (20% / 80%)
Risk,%
100
0
20000
40000
Risk
100
80
80
60
60
40
40
20
20
0
0
20000
G, тыс. р.
40000
0
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
Graph 3. Risk function at hybrid financing (60% / 40%)
Risk, %
100
0
20000
40000
Risk
100
80
80
60
60
40
40
20
20
0
0
20000
40000
0
G, тыс. р.
Conclusion
The article describes the method of rapid assessment of the risk level of the
innovative project that takes into account both market factors ambiguity and conjuncture
factors ambiguity, as far as strategic guidelines of the enterprise, as well as the
available financing schemes. The efficiency of the instruments of the theory of fuzzy
sets for quantitative solution of the problem in terms of ambiguity of the majority of initial
parameters of the project.
References
1)
V.A. Algin. Financial diagnosis of the enterprise development strategy:
capital hoarding, investments. Liquidity. Monograph. – Rostov: publishing center DSTU,
2008. – 168 p.
2)
S.Ya. Babaskin, Innovative projects: selection method and tools of risks
analysis: teaching guide. – M.: Publishing house «DELO» АНХ, 2009. – 240 p. – (series
«Educative innovations»).
3)
A.O. Nedosekin, Fuzzy- multivariate analysis of fund investments risks/ А.
О. Nedosekin. - Saint-Petersburg, 2002. - 181 p. (http://sedok.narod.ru/fuzzy.html)
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Proceedings of Annual Switzerland Business Research Conference
12 - 13 October 2015, Novotel Geneva Centre, Geneva, Switzerland
ISBN: 978-1-922069-86-3
4)
P.L. Vilenski, V.N. Livshits, S.A. Smolyak. Investment projects efficiency
estimation/ P.L. Vilenski, V.N. Livshits. –-M.: Publishing house “Delo”, 2002. - 888 p.
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