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.
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 infrastructure; • 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
information 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)
doubles 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]
determined by Moore’s formalism, it is specified analytically by the coefficient R:
where Q is the initial value of the IT equipment. Fig.1 gives a graphical
interpretation of (
On the other hand, the obsolescence (default) D of IT equipment according
to Moore’s Law is:
(
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 especially 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 correct perception of the innovation.
From Fig. 2 can be derived analytical dependences, giving a quantitative
assessment of the correctness of the decision for the perception of innovation:
− Probability of correct adoption of innovation :
(
A very important indicator giving an integral assessment of the correctness of the adoption of the innovation is the identification coefficient :
The identification coefficient gives a complete picture of how it is adopted, taking into account both inverse risks – wrong adoption (optimism) and abstinence (skepticism). 2
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: 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, median and mathematical expectation coincide). In most cases [13,14] there is a deflected (asymmetric) distribution and the investment life cycle model represented by a logistic curve becomes inaccurate. ,
(
Another model that more accurately describes the process of saturation of innovation was proposed in 1962 by Rodgers [8] in his seminal book The Diffusion of Innovation. This is a theory explaining the spread of new ideas and technologies. 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 different ways and is highly dependent on the type of adopters and the decisionmaking process. The criterion for categorization of adopters is innovation, defined as the degree to which a person perceives a new idea.
Fig. 3 is widely distributed in various literature sources [9]. In the given
example is shown so-called “skewed distribution”, which in practice is more
common. Of particular note is the error that the cumulative distribution function is
below the probability distribution function of innovation, which is impossible
because the relationship between the two functions is determined by the expression:
,
(
Fig. 4 shows the correct type of the two functions obtained by simulations of MS Excel.
Greg Lowe (2012) evaluates cost-benefit considerations regarding the Rodgers 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).
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). 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: The costs of the investment, started from the moment ti, are: (9) 10) (11) (12)
At all other things being equal (variable interest rate, force majeure obstacles, etc.), the profit from the adoption of the new technology is determined:
Due to the fact that the investment adoption density function is normalized, the following can be written:
At distribution close to normal with sufficient accuracy instead f(t) (
This transformation allows studying the return on investment function ROI (11) in the interval [0; ti]:
The extremum of (14) is sought with aim to determine the best time to invest. The first derivative of the above is:
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: (14) (15) (13) (16)
After the replacement of f (t) with a logistic function (16) obtains the type: (17)
Fig. 8 shows the graphic form of the effectiveness of ROI (EROI), calculated according to (17).
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. 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.
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 provides opportunities for convenient specification of various functions. For its part, the analytical approach offers a ready-made formula suitable for direct calculations. 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 accepting investments. This makes it possible to quantify the probability of proper investment.
With a few changes, current models will be able to include additional calculations 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
This research is conducted and funded in relation to the execution of a scientificresearch 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. 9. https://en.wikipedia.org/wiki/Diffusion_of_innovations -last accessed 03.02.2021 10. https://www.derivative-calculator.net/ -last accessed 03.02.2021 11. Stefanova-Stoyanova V.,” Study of scientific publications on the nature of Industry 4.0 and Bulgarian case”, 28th national conference with international participation TELECOM 2020 29-30 October, DOI: 10.1109/TELECOM50385.2020.9299548