=Paper=
{{Paper
|id=Vol-2933/paper6
|storemode=property
|title=Optimization of the Process of Adoption of Innovations in the IT Sector: What is the Right Time to Invest in IT Equipment?
|pdfUrl=https://ceur-ws.org/Vol-2933/paper6.pdf
|volume=Vol-2933
|authors=George Popov,Antoaneta Popova
}}
==Optimization of the Process of Adoption of Innovations in the IT Sector: What is the Right Time to Invest in IT Equipment?==
https://ceur-ws.org/Vol-2933/paper6.pdf
Optimization of the Process of Adoption of Innovations
in the IT Sector: What is the Right Time to Invest in IT
Equipment?
George Popov1 and Antoaneta Popova2
1
Technical University FCST– Sofia, Bulgaria
2
Technical University FM– Sofia, Bulgaria
popovg@tu-sofia.bg
Abstract. The predominant part of the innovations is the implementation of the
achievements of modern information technologies in business organizations. The
main problem for investors is that they cannot determine the exact moment to
do so, because the industry is directly related to the technological revolution in
microelectronics. New IT products are constantly coming to market, and the price
of existing ones is collapsing under Moore’s Law. This article answers the question,
when to invest in new technology, if the price of the investment is reducing about 2
times for a period of a year and a half.
Keywords: Analytical Model, Innovation, Investment, Moore’s Law.
1 Introduction
According to a study by UNCTAD [1], over the last 10 years, the industrial
policies of more than 100 economics, representing more than 90% of world
GDP, have adopted formal industrial development strategies. It is noteworthy
that in recent years the formulation of new industrial policies and strategies has
increased sharply. Over time, they become more diverse and complex, focusing
on newer topics setting a growing number of goals. This development cannot be
described by the classical principles of conventional industrial development but
is a complete reengineering, including:
• development of the knowledge economy;
• building sectors related to sustainable development goals;
• integration and modernization of the global value chain (GVC);
• competitive positioning for the new industrial revolution (NIR).
The dynamics of this change mainly affect foreign direct investment FDI
(FDI), where there are different models of industrial policies. This is a set of in-
dustrial policies, as they reflect a number of factors: development of the country,
Copyright © 2021 for this paper by its authors. Use permitted under
Creative Commons License Attribution 4.0 International (CC BY 4.0).
legislation, and way of investment: purchase of an enterprise or shares from it,
mixed production, mergers, and acquisitions. Investment policies are investments
in management restructuring, NIR technology transfer, innovation, training, and
more. On the other hand, FDI can be horizontal, vertical, and platform [2].
The industrial investment policy is a package of interactive strategies and
measures aimed at building a favorable industrial environment:
• construction of global transport, logistics, production, and financial in-
frastructure;
• development of the domestic and export markets, including reengineering
procedures at company, industrial and sectoral levels.
Nowadays, the innovations are at the top of the business agenda. The main
reason for this rapid development is the technological revolution, especially in in-
formation technology. Moore’s Law [3] refers to Gordon Moore’s 1965 view that
the degree of integration of microchips (the number of transistors in them) dou-
bles every two years, although the cost of the products is halved. In the last 20-30
years, the doubling period has been reduced from 24 to 18 months, ie. the line of
growth became steeper. This growth is not only valid for microprocessors – but
it also applies to memory, hard drives, communication equipment, video cards,
data volume, and more. Due to different interpretations of this increase [4,5] de-
termined by Moore’s formalism, it is specified analytically by the coefficient R:
(1)
where N is the number of years for the given growth period.
On the other hand, the obsolescence (default) D of IT equipment according
to Moore’s Law is:
(2)
where Q is the initial value of the IT equipment. Fig.1 gives a graphical interpre-
tation of (2) for Q = 1 graphical interpretation of (2) for Q = 1 (100%)
Fig. 1. Graphical interpretation of the depreciation of IT equipment over time.
51
This accelerated development leads to the following characteristics of the
modern investment business:
• larger and more frequent investments in innovations in order to maintain
the competitiveness of the enterprise;
• due to the rapid development of technologies and the sharp devaluation
and obsolescence of investments (respectively innovations), it is espe-
cially important to specify the correct investment portfolio, as well as
the moment of investment, which determines the continuous increase of
investment risk;
• The biggest risk in investing is the refusal to invest, which also applies to
investing in innovation.
When making investment decisions, two diametrically opposed errors are
possible (Fig. 2):
• Doing something that does not work (false positive, type 1 error);
• Nothing is done that would work (false negative, type 2 error).
In practice, investors worry more about a type 1 error – accepting a false
result, thinking it is real. The second type of error is also important – to reject a
real result, thinking that it is false [6].
Fig. 2 shows a model based on which an assessment can be made of the cor-
rect perception of the innovation.
Fig. 2. Venn diagram illustrating the correctness of an innovation solution.
From Fig. 2 can be derived analytical dependences, giving a quantitative as-
sessment of the correctness of the decision for the perception of innovation:
− Probability of correct adoption of innovation :
(3)
52
− Probability of wrong rejection of innovation :
(4)
− Probability of wrong adoption of an innovation :
(5)
A very important indicator giving an integral assessment of the correctness
of the adoption of the innovation is the identification coefficient :
(6)
The identification coefficient gives a complete picture of how it is adopted,
taking into account both inverse risks – wrong adoption (optimism) and absti-
nence (skepticism).
2 Existing computable models for investment and innovation
2.1 Analytical models of investment
The introduction of innovations in production (new technologies, organizations,
products) leads to drastic improvements in quality and cost reduction. Companies
invest to get more benefit. In this process, some companies succeed and others
lose. As a result, there is a rapid growth of the industry. Eventually, when everyone
has introduced innovation and it ceases to bring benefit as markets are saturated.
In economics, to illustrate the spread of innovation through its life cycle, the
so-called logistics curve described by the so-called logistics function.
The logistic function used in economics [7] (logistic, sigmoid curve) is an
S-shaped curve given by the equation:
, (7)
where:
• G is the maximum value of the curve, resp. the improvement of innovation;
• k is the speed of logistic growth (steepness);
• m is the mean value of the sigmoid.
It is obvious that this application of an analytical model through a logistic
curve gives satisfactory accuracy only for uniform distribution (ie fashion, me-
dian and mathematical expectation coincide). In most cases [13,14] there is a de-
flected (asymmetric) distribution and the investment life cycle model represented
by a logistic curve becomes inaccurate.
53
Another model that more accurately describes the process of saturation of
innovation was proposed in 1962 by Rodgers [8] in his seminal book The Diffu-
sion of Innovation. This is a theory explaining the spread of new ideas and tech-
nologies. The basic thesis is that diffusion is a process of transmitting innovation
between the participants in a given system. Each new idea is adopted, with 4 main
categories that adopt the innovation (Fig. 3):
• early adopted;
• early majority;
• late majority;
• lagging behind.
According to the author, the diffusion of innovations manifests itself in dif-
ferent ways and is highly dependent on the type of adopters and the decision-
making process. The criterion for categorization of adopters is innovation, de-
fined as the degree to which a person perceives a new idea.
Fig. 3. Diffusion of Innovation DoI (Rogers Everett - Based on Rogers, E. (1962) Diffusion of
innovations. Free Press, London, NY, USA).
Fig. 3 is widely distributed in various literature sources [9]. In the given ex-
ample is shown so-called “skewed distribution”, which in practice is more com-
mon. Of particular note is the error that the cumulative distribution function is
below the probability distribution function of innovation, which is impossible be-
cause the relationship between the two functions is determined by the expression:
, (8)
where f (t) always has a positive value. On the other hand, two dimensions rel-
evant to the described functions could be assigned to the ordinate.
54
Fig. 4 shows the correct type of the two functions obtained by simulations
of MS Excel.
Fig. 4. Correct drawing of DoI curve (instead this from Fig. 3).
Greg Lowe (2012) evaluates cost-benefit considerations regarding the Rodg-
ers product perception curve [9]. Lowe looks at investment and return separately,
and believes that those who slowly adopt innovation are skeptics, bystanders, and
enemies. Lowe believes that in most cases, lagging behind is counterproductive.
He argues that the highest return on investment comes from the early majority
and skeptics (Fig. 6).
Fig. 5. Return on investment according to Lowe (Rogers Everett - Based on Rogers, E. (1962)
Diffusion of innovations. Free Press, London, NY, USA).
2.2 Supposed analytical model
If needs to find a return on investment in the IT industry should be placed on a
chart and the same scale, the functions of the continuous reduction in the price of
a given technology (Fig. 1) and profit from it (Fig. 6).
55
Fig. 6. Return on investment in IT innovation. An example of an investment is given: moment ti,
value of the investment and expected added value.
If you invest at the time ti (Fig.6), the RoI will be:
(9)
The costs of the investment, started from the moment ti, are:
10)
At all other things being equal (variable interest rate, force majeure obsta-
cles, etc.), the profit from the adoption of the new technology is determined:
(11)
Due to the fact that the investment adoption density function is normalized,
the following can be written:
(12)
At distribution close to normal with sufficient accuracy instead f(t) (8) can be
used the logistic function (3):
56
(13)
This transformation allows studying the return on investment function ROI
(11) in the interval [0; ti]:
(14)
The extremum of (14) is sought with aim to determine the best time to invest.
The first derivative of the above is:
(15)
The result of the simulation by [11] of formulas (14) and (15) is given at
Fig.7, where is shown an integral idea of RoI. If the efficiency of the expected
profit in relation to the invested funds is to be obtained, the so-called efficiency
of the investment is obtained:
(16)
Fig. 7. Return on investment ROI in the implementation of IT innovations as a function of the
moment of adoption, calculated by the formula (14). The values of G = Q = k = 1 and m = 5. It
can be seen that late investments can lead to losses.
After the replacement of f (t) with a logistic function (16) obtains the type:
(17)
57
Fig. 8 shows the graphic form of the effectiveness of ROI (EROI), calculated
according to (17).
Fig. 8. EROI depending on the adoption time calculated by formula (17).
The values of G = Q = k = 1 and m = 5.
Fig. 8 and Fig. 9 shows that the ROI and EROI maxima diverge. The logical
explanation is that investment must be made earlier in order to capture the peak
of EROI.
Similar calculations (14) and (17) were made using MS Excel, based on the
data in Figs. 8. ROI and EROI are calculated as the difference and ratio of the
functions f (t) and D (t). The results are shown in Figs. 10 and Fig. 11.
58
Fig. 9. Return on investment ROI in the implementation of IT innovations as a function of the
moment of adoption, calculated using MS Excel. The values of G = Q = k = 1 and m = 5.
Fig. 10. The ROI and EROI as a function of the moment of implementation calculated using MS
Excel. The values of G = Q = k = 1 and m = 5.
It can be seen that the results of the two calculation methods coincide, which
confirms the calculations made. The use of MS Excel is more accurate and pro-
vides opportunities for convenient specification of various functions. For its part,
the analytical approach offers a ready-made formula suitable for direct calcula-
tions.
59
Figures 12 and 13 show examples of investments with different initial data.
The optimal time for adopting the innovation is marked with tin. Fig. 13 shows
that it is possible to incur financial losses if the investment time is not chosen
appropriately.
Fig. 11. ROI as a function of the moment of implementation. The values of G = 4, Q = k = 1 and
m = 5. Maximum profit is obtained if the innovation is implemented after 18 months.
Fig. 12. ROI as a function of the moment of implementation for G=4, Q=3, k=1 and m=5. It can
be seen that if the investment is made very early or significantly late, losses occur.
60
3 Conclusion
Proof of the accuracy of the calculations is obtained in two different ways – they
coincide completely. New analytical material has been added to the theory of
innovation. The proposed mathematical apparatus makes it possible to determine
accurately the optimal time for the perception of innovation in fast-growing
industries such as information technology [12]. The proposed formalism can
be further developed and used for calculations that are more complex such as
modeling of continuous simultaneous innovations in a heterogeneous investment
fund.
An additional contribution is a theory of identifying the correctness for ac-
cepting investments. This makes it possible to quantify the probability of proper
investment.
With a few changes, current models will be able to include additional calcu-
lations for the impact of inflation, key interest rates and market risk. In this way,
based on the assessments, a detailed analytical model can be developed, allowing
a quantitative assessment of the processes in the management of innovation and
investment.
4 Acknowledgment
This research is conducted and funded in relation to the execution of a scientific-
research project № КП-06-Н35/12 „An Innovative Approach in Developing an
Intelligent Information System for Detection and Prevention of Financial and
Customs Fraud“ under the contract with National Science Fund in Bulgaria.
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