The Influence of Foreign Investors on the Development of Polish Enterprises: A Case Study of Bank Polska Kasa Opieki Spółka Akcyjna

*Waldemar Milewicz*

## **Abstract**

Pursuant to the definition proposed by Eurostat, foreign direct investment takes place when a resident entity in one economy seeks to obtain a lasting interest in an enterprise resident in another economy. A lasting interest implies the existence of a long-term relationship between the direct investor and the enterprise, and an investor's significant influence on the management of the enterprise. Foreign investors do not only exert impact on a given company's board of directors but, importantly, provide production capital in privatized companies. Additionally, they equip them with both know-how on the performed economic activity and technical know-how. They send their specialists, who introduce international standards in daughter companies smoothly. In this paper, the author deals with the impact of a foreign investor on the development of Bank Pekao. A literature review is applied for this aim. It covers a detailed analysis of transaction documentation and post-audit statements of the Supreme Audit Office and delegations of the Ministry of State Treasury. Thanks to research, it can be assessed how UniCredito Italiano has positively influenced the operation of Polish bank after the acquisition of shares. Thereby, the results of this study contest popular opinion about exploitation of domestic employees by foreign companies.

**Keywords:** foreign direct investment, know-how, performance

## **1. Introduction**

From the methodological point of view, there are many definitions of foreign direct investment. The subject of this article leads to a special emphasis on definitions which refer to the creation of a long-term relationship between an investor and the company in which the shares are acquired [1]. According to the IMF definition, direct investment reflects the aim of obtaining a lasting interest by a resident entity of one economy (direct investor) in an enterprise that is resident in another economy (the direct investment enterprise). The "lasting interest" implies the existence of a longterm relationship between the direct investor and the direct investment enterprise

and a significant degree of influence on the management [2] of the latter. Direct investment involves both the initial transaction establishing the relationship between the investor and the enterprise and all subsequent capital transactions between them and among affiliated enterprises, both incorporated and unincorporated [3]. The similar dimension gives the definition proposed by the Organization for Economic Cooperation and Development (OECD). Due to its interpretation, foreign direct investment means investment that aims at causing long-lasting relationships. In turn, the latter reflects an interest of an economic entity of one country in an economic entity of a country other than the country of permanent residency of the direct investor [4].

In Polish conditions, private economic entities did not have sufficient savings to acquire shares in state enterprises at appropriate prices. The state does not have the possibility to maximize profit with only domestic investors [5]. For this reason, it seems advantageous from the financial point of view to expand the investment circle to include foreign investors (or privatization with the help of foreign investors only) [6]. Moreover, the rapid incorporation of foreign, especially international, enterprises into the national economy compensates for the lack of competitiveness of national entities [7, 8]. The reason for this is a lack of know-how, outdated technology and inadequate product quality. Companies with foreign shareholding usually have a high share of equity, use modern technology [9] and pay above-average salaries [10].

On the basis of the investment data of foreign companies, it can be concluded that they carry out restructuring faster and more intensively than comparable companies with a purely domestic shareholding [11]. This can lead to higher unemployment in the short term [12]. In the long term [13], however, the development of the acquired company will be more evenly matched by subsequent investments [14]. The role of foreign investors in privatized companies refers to providing not only production capital but, above all, business know-how and technical know-how. Both types of knowledge can be passed on by foreign specialists, who should eliminate the previously insufficient level of efficiency [15] and parallelly smoothly introduce international standards in new subsidiaries [16]. Due to a specific "dissemination" of imported know-how, the effect of improved efficiency also influences domestic companies that have not yet been privatized [17].

At this point, it is worth showing how the issue of the impact of foreign investors on domestic firms is presented by other scholars (**Table 1**).

The above-mentioned positive aspects of foreign investors' activity in Poland were accompanied by relevant changes in the law. The Act on Companies with Foreign Participation played an important role here. It came into force on June 4, 1991. The following legal regulations were enshrined in the law:


*The Influence of Foreign Investors on the Development of Polish Enterprises: A Case Study… DOI: http://dx.doi.org/10.5772/intechopen.101453*


#### **Table 1.**

*The impact of foreign investors on domestic enterprises—A review of exemplary research articles.*


This liberalization of the conditions for foreign entities in terms of acquiring Polish companies resulted in rapid capital inflow to Poland. In this paper, the author presents the positive side of privatization in his home country. He deals with the impact of a foreign investor on the development of Bank Pekao S.A. A literature review is applied for this aim. It covers detailed analysis of transaction documentation and post-audit statements of both the Supreme Audit Office and delegations of the Ministry of State Treasury. Thanks to research, it can be assessed how UniCredito Italiano has positively influenced the operation of Pekao S.A. after the acquisition of shares. The objective of this analysis is to show, on the basis of these documents, what changes have taken place in the bank following the entry of a strategic investor. Furthermore, the author shows, on the basis of precise figures, what financial support there was from the new shareholder. It is also important in this context that it is not only about showing the material impact but also about presenting the contributed know-how, e.g. in the form of trainings. Thereby, the results of this study contest popular opinion about exploitation of domestic employees by foreign companies. Furthermore, novelty of my research lies in detailed description of ownership changes in banking with regard to its impact on certain companies and, thereby, the development of capital market in Poland.

## **2. Agreement between the state Treasury of the Republic of Poland and UniCredito Italiano S.p.a. and Allianz AG.: Sale of shares of Pekao S.A.**

Privatization of Bank Pekao S.A. took place in the form of public offering – State Treasury sold 52.1% of shares in Bank Polska Kasa Opieki Spółka Akcyjna. The buyer was a consortium of entities: Credit Suisse First Boston, UniCredito Italiano S.p.A. and Allianz AG. It prepared an investment plan. It undertook to guarantee a capital increase of PLN 1000 million over a two-year period. Investors, in turn, assumed that Pekao would invest PLN 2000 million over five years. In the final offer for the purchase of shares, the consortium indicated that it fully appreciated the importance of Pekao for the Polish economy. For this reason, it intended to develop Pekao into a modern financial institution. According to purchase agreement, it was supposed to:


The partners of the consortium considered the privatization of Pekao as a unique opportunity to create a leader in Poland. He was to be able to face the challenges of Poland's membership in the European Union. In addition, his task was to create a strong base for development in the broader regional context of Central Europe [25].

*The Influence of Foreign Investors on the Development of Polish Enterprises: A Case Study… DOI: http://dx.doi.org/10.5772/intechopen.101453*

## **3. New distribution network in the bank**

In the area of retail banking, the investor's goal was to transform Pekao into the largest provider of financial services for the population in Poland. This was achieved by maintaining and further penetrating the existing customer base. Penetration, in turn, took place by "bringing" the bank closer to customers and expanding the customer base (through selective expansion of the bank's geographical coverage). In accordance with that, Pekao has rapidly developed the branch network in Silesia, Poznań, Gdańsk (the bank had a limited presence there) and strengthened its presence in Warsaw. This process was accompanied by events that also affected the qualitative development of the bank and, thus, the capital market in Poland:


In the field of business services, specifically in the field of business financing, Pekao had a leading market share at the time. The consortium successfully strengthened this position. This was due to the support of Pekao's financing of infrastructure projects, e.g. in the energy sector, telecommunications and construction of toll motorways. The consortium, in addition, strengthened the position of Bank Pekao as a market leader by:


As a result, the improvement of the distribution network closely linked to the regrouping of employees in the company significantly strengthened Pekao's position in the banking market. Thanks to that, Pekao bank developed in terms of quality, which in turn contributed to the qualitative development of capital market in Poland.

## **4. Product support in the bank**

In the field of services for small and medium enterprises, their development was very important from the point of view of maintaining strong economic growth in

Poland. Bearing this in mind, the strategic investor sought to strengthen Pekao's position in the small and medium-sized enterprise market. In this way, it influenced the qualitative development of the capital market in Poland. This was done by:


The qualitative impact on the Polish bank and on the Polish capital market on the part of the Uni Credit consortium was also reflected in another fact. According to the Italian bank's declaration, it passed its knowledge about developing and managing banking products in the following areas, among others:


Knowledge in the field of credit, asset management, cash management, electronic banking and project financing has enriched Bank Pekao with new know-how and, thus, has made a significant qualitative contribution to its development and the capital market in Poland.

In addition, in terms of asset management and bancassurance, a consortium of investors has contributed to the professional implementation of the bancassurance concept at Pekao. This created additional revenue for Pekao. The consortium's activities in this area strengthened the position of Bank Pekao towards customers. This was also done by introducing the offer of a full range of financial services (so-called one-stop shopping, financial supermarket approach). The above activities of the strategic investor made a significant qualitative contribution to the development of Bank Pekao, the banking system in Poland, and thus the Polish capital market.

The consortium's intentions in the area of bancassurance were also made more concrete in the fact that branches and mobile teams of advisers-sales representatives of Bank Pekao were used to sell insurance products and banking products (e.g. mortgage loans, car loans). Bank Pekao has also used Allianz's operations in Poland.

### *The Influence of Foreign Investors on the Development of Polish Enterprises: A Case Study… DOI: http://dx.doi.org/10.5772/intechopen.101453*

It used the existing products of the German insurer to create its own insurance business from scratch. It happened without the need to involve capital and human resources. To sum up, the consortium of investors, by developing bancassurance activities at Bank Pekao, significantly supported the qualitative development of Bank Pekao, the banking market, and thus the capital market in Poland.

In addition, the UniCredit consortium provided Pekao with a range of Polish and international investment funds for use in its distribution network. It is worth noting that at the level of people's wealth then in the country, it was not expected that this would be a significant strengthening of the bank's revenues. Despite this, owning such products has strengthened Pekao's image as a universal financial institution. It also meant readiness to take advantage of the growing popularity of these products. Thanks to the strategic investor's involvement in investment funds, the bank's brokerage activities were further strengthened. Obviously, this translated into the qualitative development of Pekao bank, the banking system, and, thus, the capital market in Poland.

The consortium introduced portfolio management techniques at Pekao bank with a fixed risk/return relationship. It based its activity on the position of the leader of the Central Brokerage House Pekao in brokerage activities. As a result, it increased the quality of services offered at Pekao Bank and reduced their cost. An important element of the qualitative impact on Bank Pekao was also the fact that the consortium had unique qualifications that were needed to implement these activities. It resulted from experience in creating and introducing products and sales methods. The above activities of the Uni Credit consortium improved the position of Bank Pekao on the banking market and made a significant qualitative contribution to the development of the Polish capital market.

The qualitative impact of the UniCredit-Allianz consortium in the field of bancassurance on Bank Pekao was conditioned by the fact that the entities UniCredit and Allianz were partners in the field of bancassurance in Italy. UniCredit sold life and property policies. It did this through a network of over 2000 branches. Unicredit also had an important position in asset management (it managed over EUR 60 million). It was one of the leading brokerage houses in Italy. In turn, Allianz was the world leader in insurance – it concluded a bancassurance agreement with partners in 12 countries. The above facts meant that UniCredit brought significant know-how to Bank Pekao, supported its qualitative development, and, thus, contributed to the development of the capital market in Poland.

The guarantee of a positive qualitative impact on the part of UniCredit on the Polish capital market was additionally the fact that it is one of the leading banks in Italy. In fact, it transferred know-how from its home market to the Polish market. As a result, Bank Pekao received knowledge from the Italian investor in the field of business services. In addition, thanks to Italian financial institution, 500 account managers started servicing companies. The strategic investor also used modern systems to manage contacts with Pekao clients. Not without significance in this context was the fact that UniCredit's credit processes (guarantee methods and so-called early warning systems) corresponded to the latest developments in this field on a global scale. They were considered exemplary in the Italian banking system. Thanks to this, the impact of know-how on the part of UniCredit on Bank Pekao and the Polish banking system and, thus, the capital market in terms of quality was significantly positive.

## **5. New management methods in the bank**

UniCredit declared that it could support Pekao in introducing new IT systems. The Italian bank had experience in transferring systems to other banks. Evidence of this was, for example, the completion by the subsidiary UniCredit (dealing in IT) of the integration of Banca CRT, Banca Cariveron and Cassamarca in 2000. It did so by adding 1000 branches to a common IT platform. Similarly, the implementation of the new IT system – one of the most important processes at Bank Pekao – has been successfully completed. It happened, thanks to the knowledge and experience of specialists from UniCredito Italiano delegated to Polish bank. In addition, UniCredito Italiano has taken actions in the area of credit, market and operational risk management at Bank Pekao. They were oriented towards improving the degree of integration of Pekao's policy with the overall operations of the UniCredito Italiano group. They were also successful. Therefore, it is justified to state that UniCredito Italiano, through its activities in the Pekao bank in the area of IT system and risk, has strengthened its qualitative position. In this way, it made a qualitative contribution to the development of the capital market in Poland.

UniCredit also provided support for Pekao in other areas:


*The Influence of Foreign Investors on the Development of Polish Enterprises: A Case Study… DOI: http://dx.doi.org/10.5772/intechopen.101453*

The impact of the above factors on the quality position of Bank Pekao was considerable. It remained in connection with the qualitative development of the Polish capital market.

## **6. New programs in the company aimed at development of employees**

Regarding the social program, the consortium introduced a number of activities at Bank Pekao. They were aimed at improving the education and motivation of employees. It was about incentive pay, management exchange program and training. UniCredit, while caring for the intellectual development of Pekao bank employees, also made a significant qualitative contribution to its development. Thus, it contributed to the qualitative development of a capital market in Poland.

The needs of the Pekao employees on the part of the UniCredit consortium were also secured, thanks to:


The above elements, brought in by a strategic investor, also had a significant impact on the qualitative development of Pekao bank, and thus the capital market in Poland.

In accordance with the Pekao program for local communities, UniCredit supported higher education in Poland. This was due to the fact that the strategic investor has close links with the Universita Commerciale Luigi Boccioni (the most prestigious and recognized economic university in Italy). In addition, UniCredit also supported the commercial activities of the Pekao bank (with the use of database constructed on the basis of the customer portfolio). The activity of a strategic investor in the educational and operational field at Bank Pekao has made a qualitative contribution to the development of Bank Pekao, and thus – the capital market in Poland.

## **7. Consortium's investment obligations**

The UniCredit consortium has fulfilled its commitment that Pekao's capitalization should be sufficient to implement its development plans. At the same time, it helped maintain the capital adequacy ratio of Pekao at a certain level. It was recognized by international financial markets as safe for a bank from the Central Europe region. The UniCredit consortium, by helping to implement Pekao's plans and maintaining the required level of solvency ratio, has contributed to the qualitative development of Pekao, and thus the capital market in Poland.

The Guaranteed Investment Program should also be mentioned as an important element of the qualitative impact on the development of the Polish capital market in the aspect of UniCredit offer. Under this program, the UniCredit consortium was to

invest at least PLN 1 billion in Pekao over a three-year period. In addition, the consortium prepared an investment plan. It assumed that the bank would invest PLN 2 billion over a five-year period.

As for the implementation of individual strategic investor's obligations, it was presented in the "Information on the implementation of non-price obligations" [26]. It shows that:


The UniCredit investor also undertook that within a period of five years from the signing of the contract, it will support the development of Pekao. This process was to be in line with the provisions of the Bank's Development Program and take place by:

*The Influence of Foreign Investors on the Development of Polish Enterprises: A Case Study… DOI: http://dx.doi.org/10.5772/intechopen.101453*


According to the report of Ernst and Young Audit Sp. z o.o. of June 30, 2003, it was found that the above obligations were met and there were no grounds for charging contractual penalties. The document confirming their implementation was also the investor's annual report for 2000 and additional speeches by the Ministry of Treasury (Application); UniCredit made a qualitative contribution to the development of the capital market in Poland. By investing in development programs and improving access to information technologies, know-how and organizational methods at Pekao Bank, it strengthened its quality position and contributed to its development.

The investor also undertook to fully support Pekao's strategy. It consisted of developing and consolidating his position. It was to be the leading universal bank in Poland and a leading financial institution in Central and Eastern Europe. Other important commitments were that UniCredit:


All the above liabilities, according to the report of Ernst and Young Audit Sp. z o.o. of June 30, 2003, were carried out in a timely manner. In this way, the strategic investor strengthened the quality position of Pekao Bank and thus contributed to the qualitative development of the capital market in Poland.

At that time, the main goal of the bank and the UniCredito Italiano group was to increase the value for the shareholders of Bank Pekao. The strategic investor did this by maintaining and strengthening the leading position of Bank Pekao in selected areas of activity:


• support for microenterprises.

This goal was achieved, thanks to the implemented improvements from the UniCredit group. It introduced in the Pekao bank such elements as product innovation, modern distribution channels and a comprehensive customer service model (a combination of VIP customer service and small and medium-sized enterprises). UniCredit has dynamically developed more advanced distribution channels, such as online banking, telephone banking and direct sales. All the elements listed above, implemented in the Pekao bank by a strategic investor, strengthened its quality position. In this way, UniCredit has contributed to the qualitative development of the capital market in Poland.

In accordance with art. 3 par 12 paragraph 2 sales contracts, the strategic investor undertook to provide technical, technological and organizational solutions to Pekao. Therefore, UniCredit initiated a comprehensive restructuring process of the Pekao bank. It began after the investor purchased the majority stake.

In art. 4 par 2 of the sales contract, the investor assumed that Pekao bank, thanks to the support of UniCredit, will make investments in the amount of PLN 1000 million (Guaranteed Investments). This was in accordance with Annex 11 of the contract. The auditor found that the commitment had been carried out. The UniCredito Italiano consortium stated that in the period up to August 2002, its capital expenditure at Pekao bank amounted to PLN 1010.8 million. In addition, by the end of 2002, he allocated PLN 140 million for investments at Pekao Bank.

Capital expenditures were also subordinated to Pekao's development strategy. They were related to the development of Pekao's business. This was done through its subsidiaries and affiliates. During the Guaranteed Investments period, the bank developed its activities as planned (to the extent provided in Annex 9 to the contract). Thanks to the aforementioned significant capital and investment outlays, UniCredito Italiano has strengthened the quality position of Pekao. Thus, it contributed to the qualitative development of the capital market in Poland.

In art. 4 par 2 of sales contracts, the UniCredito consortium undertook to acquire shares in Bank Pekao for a total amount of PLN 1 billion. This was specified in the contract as a guaranteed capital increase. As a result of the guaranteed capital increase, the capital of Bank Pekao increased by PLN 1000.1 million. Thanks to the increase in capital by UniCredito Italiano, Bank Pekao strengthened its quality position. The increase in the amount of capital gave the bank extensive investment opportunities. Thus, UniCredito Italiano has contributed to the qualitative development of the capital market in Poland [27].

## **8. Conclusions**

In fact, UniCredit (according to source documents) provided Pekao with considerable knowledge and experience at the strategic and operational levels. The innovative activities of the strategic investor were also particularly important here1 . This manifested itself, for example, in the fact that permanent distribution channels were supplemented with automated channels (i.e. ATMs, telephone service). Moreover, the

<sup>1</sup> At this point, it should be mentioned that those who study innovative activities in banking should, in future, pay more attention to all digitization processes, which are currently progressing at a dizzying pace in the banking sector.

## *The Influence of Foreign Investors on the Development of Polish Enterprises: A Case Study… DOI: http://dx.doi.org/10.5772/intechopen.101453*

Italian investor introduced products with the features of the best products on the market and combined new products with mortgage development, credit cards, asset management and insurance. Similarly, the implementation of the new IT system, which stood for innovative support of Pekao's operational activity, has been successfully completed. It happened, thanks to the knowledge and experience of specialists from UniCredito Italiano delegated to Polish financial institution. In this way, Italian bank made a significant contribution to the qualitative development of Bank Pekao, and thus the Polish capital market. Thus, according to Gustav Dieckheuer's theory (see: Introduction), it compensated for the lack of outdated technology and inadequate product quality. By sharing knowledge and experience in these areas, the strategic investor strengthened the quality position of the bank. Evidence of the possibilities for a positive impact of the Italian bank was its growth and profitability. It also had experience in integrating different banks into the group. As a result of the partnership with the Pekao consortium, it strengthened its leadership position in Polish banking. Thanks to this, the quality of the bank's products and services has also improved, and its international prestige has increased. This was reflected in the qualitative development of the bank and, thus, of the capital market in Poland. At the same time, the strategic investor maintained Pekao's identity so outside – through its brand and image – and internally in Poland.

The investor consortium reviewed Pekao's activities and trends on the Polish market. It did so by having a clear and properly implemented Pekao development plan. In this way, the consortium of investors assisted Pekao's management board in facing the competition. At the same time, it reversed the erosion of market share and strengthened the bank's operational efficiency. The following areas have been strengthened:


The above actions of the strategic investor have made a significant qualitative contribution to the development of the bank and, thus, to the development of the capital market in Poland. By strengthening individual areas at Bank Pekao, the Uni Credit consortium has significantly improved the bank's quality position on the market.

## **Classifications**

JEL Classifications: F21, L33

## **Author details**

Waldemar Milewicz German Economy Research Unit, World Economy Institute, Warsaw School of Economics Building A, Rakowiecka, Warsaw

\*Address all correspondence to: wmilew@sgh.waw.pl

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*The Influence of Foreign Investors on the Development of Polish Enterprises: A Case Study… DOI: http://dx.doi.org/10.5772/intechopen.101453*

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## **Chapter 4**

## Innovation and Entrepreneurial Ecosystems

*Alina Ianioglo*

## **Abstract**

Nowadays special attention is paid to ecosystem conditions that encourage innovation and entrepreneurship. This chapter provides a critical review and expands the understanding of the concepts of the innovation ecosystem and entrepreneurial ecosystem. The entrepreneurial ecosystem represents a collection of actors that interact within a geographically bound entrepreneurial environment and factors, which contribute to the development of productive entrepreneurship. Innovation ecosystems represent communities of interacting actors that support innovation processes and create technologies and innovations. The focus of the innovation ecosystem is on value creation through the creation of innovations, while the focus of the entrepreneurship ecosystem is on the development of entrepreneurship. There are differences between the two concepts, but also the relationships and interactions, which are revealed in the chapter. Also, there are highlighted the framework, components and features of both entrepreneurial and innovation ecosystems.

**Keywords:** system, entrepreneurship, entrepreneurial ecosystem, innovation, innovation ecosystem, networks, knowledge

## **1. Introduction**

In current conditions of tough competition, technological advances, digitalization and exponential growth of knowledge, special attention is devoted to entrepreneurship and innovation. Entrepreneurship and innovation are considered the drivers of competitiveness, social and economic development.

Entrepreneurship is essential in amplifying innovation, creating jobs, satisfying customer demands and other economic impacts. It is well known that an important trait of entrepreneurs is their ability to innovate. Globally, people are searching innovative ways to capitalise on an idea, start a new venture and develop the business. At the same time, innovation is recognised as an important factor in fostering growth. In the attempt to improve the efficiency of operation with scarce resources, enterprises do not function in isolation but undertake entrepreneurial activity within a community of interdependent actors. The process of commercialising an idea encompasses numerous parties, and the creation of entrepreneurial and innovation ecosystems has been considered to be an effective way to nurture and support this process [1].

Innovation and entrepreneurial ecosystems are recent phenomenon phenomena that have attracted the increasing attention of policymakers, business practitioners and academics. Today, the ecosystem conditions that encourage entrepreneurial innovations and high-potential entrepreneurship became of great importance [2].

Nevertheless, according to J. Schumpeter, entrepreneurship and innovation have been strongly related [3], the innovation ecosystem and entrepreneurial ecosystem literature mainly evolve in parallel [4]. Nevertheless, there are a number of studies that discuss the main types of ecosystems, the literature suffers from a lack of development. There is little research that has considered the interactions between innovation and entrepreneurial ecosystems.

This chapter provides a critical review and expands the understanding of the concepts of the innovation ecosystem and entrepreneurial ecosystem, their commonalities and differences.

## **2. Introducing the concept of ecosystem**

The term ecosystem (ecological system) has been adapted from biology, where it is seen as a community of living organisms interacting with various components of their environment [5]. Thus, the 'eco' is related to the environment and the 'system' implies a set of interrelated parts that operate as a unit.

J. Moore [6] translated the ecosystem metaphor into the management field. He drew a parallel between a biological system and business, stating that like organisms in nature, companies interact with each other and exist in a given business environment. Since then, the ecosystem literature has obtained increased popularity in academia, business, management and policy. In the last decades, different research streams have been developed: business ecosystem [6], followed by the innovation ecosystem, the entrepreneurial ecosystem, the knowledge ecosystem and others. These ecosystems mainly differ depending on the types of actors involved and the nature of the value proposition.

In business and management, the concept of an 'ecosystem' describes "collectives of heterogeneous, yet complementary organisations" who jointly generate an ecosystem-level output, thus extending beyond the outputs and activities of any individual participant of the ecosystem [7].

There are four commonalities that distinguish ecosystems from other organisational collectives: the system-level outcome, participant heterogeneity, nature of interdependence among ecosystem participants and coordination mechanisms [8]. The presence of one of them does not distinguish an ecosystem, but the combination of all four characteristics is unique to ecosystems. The system approach does not explain the relationship between stakeholders. Comparing to the concept of system, which is perceived as static, the ecosystem concept should not be perceived from a linear point of view, it has a dynamic perspective. Entrepreneurship is a complex process and every ecosystem comprises a unique set of actors and interactions, which determine its evolution and shape the present and future state of the ecosystem.

## **3. Entrepreneurial ecosystem**

The entrepreneurial ecosystem concept consists of two aspects: ecosystem described earlier, and entrepreneurial. Entrepreneurial refers to the process of

### *Innovation and Entrepreneurial Ecosystems DOI: http://dx.doi.org/10.5772/intechopen.102344*

entrepreneurship. The latter is defined as "the process of creating value by bringing together a unique combination of resources to exploit an opportunity" [9].

Entrepreneurial ecosystems have evolved as a result of the changing debates about entrepreneurship. In exploring entrepreneurship, the studies shifted the focus from the personality approach to the broader social and economic environment, where enterprises are located. Entrepreneurial ecosystems offer a more realistic representation of entrepreneurial activity.

E.J. Malecki states that entrepreneurial ecosystem emerged in the early 1990s, identifying contributions from Moore's 'business ecosystem', Van de Ven's 'infrastructure for entrepreneurship' and Spilling's concept of a local 'entrepreneurial system' [10].

Some of the most influential studies, which have driven the popularity of the concept of the entrepreneurial ecosystem are publications of D. Isenberg [11], B. Feld [12], C. Mason and R. Brown [13], E. Stam [14], B. Spigel [15] and others, highlighting that the community and culture in a specific place can have a significant impact on entrepreneurship process. The components of the ecosystem and local context can influence the choices, entrepreneurs make and decisions they take.

The ecological aspect of the entrepreneurial ecosystem has links to 'economic gardening', an entrepreneurial approach to local economic development [13]. Entrepreneurial ecosystems should create supportive environments that foster both new business start-ups and high-growth firms. Thus, there should be created a environment that promotes the creation of new ventures, including innovative start-ups, as well as the development of enterprises. Some practitioners view predominantly start-ups within entrepreneurial ecosystems, but ecosystems are not just about startups, the role of larger enterprises should not be diminished.

The entrepreneurial ecosystem is a recent notion with various definitions suggested, but there is not a widely shared definition yet. B. Spigel [15] sees the concept as a conceptual umbrella that comprises different perspectives on the geography of entrepreneurship rather than a coherent theory.

A list of main definitions of entrepreneurial ecosystem provided in the literature is presented in **Table 1**. Some definitions consider the role of the components (e.g. [13, 14]), while others emphasise the interaction among the elements (e.g. [4]).

The analysis of the main definitions allowed identifying main *characteristics of entrepreneurial ecosystem*:


The entrepreneurial ecosystem implies a shift from traditional economic thinking focused mainly on companies and markets towards new thinking about people and networks. In all presented and other definitions, entrepreneurship does not occur in


**Table 1.**

*Some of the main definitions of the entrepreneurial ecosystem.*

isolation, at the centre of the entrepreneurial ecosystem are the actors with all their interactions and relationships. These relationships among actors support entrepreneurial activities.

### *Innovation and Entrepreneurial Ecosystems DOI: http://dx.doi.org/10.5772/intechopen.102344*

Within the concept of the entrepreneurial ecosystem, many authors mainly consider the creation and activity of high-growth start-ups and scale-ups. E. Stam [14] introduced the concept of productive entrepreneurship, which is interpreted as an entrepreneurial activity that "creates aggregate welfare increases", it is seen as an "outcome of successful ambitious entrepreneurship". Ambitious entrepreneurs are those entrepreneurs who seek to get a higher performance of their ventures and to quickly scale-up [21]. Generally, the modern literature emphasis growth-oriented entrepreneurship. The ecosystem supports venture development and contributes to the determination of opportunities for collaboration and competition. A rich entrepreneurial ecosystem fosters entrepreneurship and therefore value creation, contributing to social and economic development.

A sustainable ecosystem cannot be instantly implemented, it takes decades of effort to achieve this. It should be noted that many studies have been focused on a static picture of entrepreneurial ecosystems. The dynamic perspective started to be considered recently in the literature. Entrepreneurial ecosystems are evolving through the interactions between actors. Also, the dynamics depend on factors of national and international order, as well as cultural specificities in a given locality. Thus, the entrepreneurial ecosystem represents a complex system, which evolves over time.

Entrepreneurial ecosystems have a spatial dimension. Generally, they are geographically bounded, but there is no limitation regarding their geographic scale. The ecosystem emerges through successful interaction between the actors at different levels: university campuses, cities, regional and national levels [22]. Also, there might be links between different ecosystems [23].

Generally, we can conclude that an *entrepreneurial ecosystem* represents a collection of actors that interact within a geographically bound entrepreneurial environment and factors, which contribute to the development of productive entrepreneurship.

The entrepreneurial ecosystem is a complex system that focuses on entrepreneurship and facilitates venture development, leading to value creation in the community.

There is no universal model of an entrepreneurial ecosystem. The structure of entrepreneurial ecosystems is unique, it may vary in different geographic communities, but what is important is their ability to ensure systems-based support for entrepreneurial activity, enabling access to markets, finance, human and intellectual capital.

The dynamic and systemic nature of the entrepreneurial ecosystem involves various actors, institutions and processes.

There are specific components of the entrepreneurial ecosystem, which are necessary to sustain entrepreneurship in a given territory. Several models of the entrepreneurial ecosystem were suggested, for example, the model by D. Isenberg [11]; G. Foster et al. [24], P. Vogel [25]; E. Stam [26], T. Mazzarol [27], B. Spigel [15].

D. Isenberg identified six domains within the entrepreneurial system: a conducive culture, enabling policies and leadership, availability of appropriate finance, quality human capital, venture-friendly markets for products, and a range of institutional supports [28]. This model contains a totally 12 core components.

In comparison, the model suggested by J. Leendertsea, M. Schrijvers and E. Stam [29] emphasises causal relations and includes institutional arrangements (formal institutions, culture and networks of entrepreneurs), resource endowment elements (psychical infrastructure, demand, support services/ intermediaries, talent, knowledge, leadership and finance), outputs (productive entrepreneurship – an "entrepreneurial activity that creates aggregate welfare" [14]) and outcomes (value creation and economic growth). Besides the fact that the model reflects the importance of

different actors and their interactions within the entrepreneurial ecosystem, it also reveals how these conditions support the entrepreneurial activities and value creation, which over time feedback into the system conditions.

Presented models reflect the components of a successful entrepreneurial ecosystem. At the same time, it is important to understand how these ecosystems evolve over time. An example of evolutionary dynamics of entrepreneurial ecosystems was developed by E. Mack and H. Mayer [16], which contain phases of birth, growth, sustainment and decline (self-renewal).

Therefore, there are different approaches to identify components of the entrepreneurial ecosystem, main approaches are presented in **Table 2**.

We can conclude that there are essential components that overlap or are similar, specifically: culture, markets, infrastructure, government, etc. The entrepreneurial ecosystem components are mutually interdependent and co-evolved.

Further, we will consider the main components that are crucial for a successful entrepreneurial ecosystem. We elaborate on the model suggested by E. Stam [14] and complement it with two more relevant components: education and training, innovation (**Figure 1**).

Even though there are more *components* to consider, we will focus on the main ones:

*Infrastructure*. Entrepreneurs are dependent on physical infrastructure, transportation, energy, telecommunications and others.

*Markets/demand*. Accessible markets (local, global) are essential to any enterprise. Customers with their needs create opportunities for entrepreneurship.

*Human capital*. It is an important component in the entrepreneurial ecosystem. Accessible skilled labour is a driver of success in the modern knowledge economy. Workers should have skills, abilities and expertise that meet the specific demand of enterprises.

*Education and training*. It is mainly provided by higher educational institutions. Universities disseminate and commercialise the knowledge; they represent the main resource for talent and are significant in an ecosystem.

*Finance*. Along with human capital, of great importance is the access to finance. Both are necessary and traditional and alternative sources of finance: microloans, bank loans, business angels, seed investors, venture capital, fintech, etc.

*Networks.* The networks of entrepreneurs provide an information flow, enabling an effective distribution of knowledge, labour and capital [30].

*Policy and governance*. Entrepreneurship depends on a context that is shaped by governments. The policies may encourage or hinder entrepreneurs. Efficient policies facilitate the development of the ecosystem. Additionally, there should be paid attention to the political context.

*Support services.* It includes a range of different organisations, intermediaries that provide support to businesses, for example, professional services (legal, accounting, insurance, consulting, technical experts), associations, mentors, clusters, business incubators, etc.

*Culture:* It represents the attitudes towards entrepreneurship. The culture and the presence of success stories can motivate or discourage entrepreneurial activities.

*Knowledge.* It refers to theoretical foundations, tacit, specialised, formal/informal knowledge that are used and generated.

*Innovation*. This is one of the main forces in entrepreneurial activity and allows exploiting opportunities.

## *Innovation and Entrepreneurial Ecosystems DOI: http://dx.doi.org/10.5772/intechopen.102344*


**Table 2.**

*Synthesis of the main approaches to identify components of entrepreneurial ecosystem.*

#### **Figure 1.**

*Key elements, outputs and outcomes of the entrepreneurial ecosystem. Source: adapted from ref. [29].*

Main *actors* in an entrepreneurial ecosystem are entrepreneurs, public sector, service providers (marketing, legal, etc.), financial institutions, academia, investors, non-government organisations, media, etc.

At the same time, it should be kept in mind, that there is no one key factor of success. There are multiple components, which vary in the different entrepreneurial ecosystem, each ecosystem will have its unique structure.

## **4. Innovation ecosystem**

Literature on the innovation ecosystem, similar to the other concepts of the ecosystem in management, experienced significant growth in recent years. Predecessors of the innovation ecosystem are considered the innovation system and the business ecosystem.

Before defining the innovation ecosystem, we will take a look at the innovation aspect of the concept. According to Tidd et al., innovation is "a process of turning opportunity into new ideas and of putting these into widely used practice" [31]. Another definition states that innovation represents "the implementation of a new or significantly improved product (good or service), or process, a new marketing method, or a new organisational method in business practices, workplace organisation or external relations" [32]. At the same time, the concept 'new' could mean new to the world, new to a nation, new to a firm, etc.

The concept of innovation ecosystem became more widely used after the publication of a Harvard Business Review article by R. Adner. He defined an innovation ecosystem as "the collaborative arrangements through which firms combine their individual offerings into a coherent, customer-facing solution" [33]. Some definitions of the innovation ecosystem are presented in **Table 3**.

A more recent and quite comprehensive definition was provided by O. Granstrand, and M. Holgersson: an innovation ecosystem is "the evolving set of actors, activities, and artifacts, and the institutions and relations, including complementary and substitute relations, that are important for the innovative performance of an actor or a population of actors" [37].

This definition highlights five components: actors, activities, relations (collaborative, competitive), artefacts (products and services, tangible and intangible resources, technological and non-technological resources, and other types of system inputs and outputs, including innovations) and evolution.

*Innovation and Entrepreneurial Ecosystems DOI: http://dx.doi.org/10.5772/intechopen.102344*


#### **Table 3.**

*Some of the main definitions of innovation ecosystem.*

Innovation has evolved beyond the boundaries of single companies towards a more network-based approach [38]. This is because innovations are implemented through a system with complex networks, where organisations interact with each other to foster innovation.

While innovation systems can be governed by public policies, being static concepts, innovation ecosystems are perceived as self-organised, dynamic structures, which evolve along with changing market conditions. Similar to an entrepreneurial ecosystem, a successful innovation ecosystem is the result of a long process of evolution and may have different stages of maturity.

Due to the involvement in the network, each ecosystem participant is symbiotic to and co-evolves with other participants [39]. Fast changes in the business environment and increasing uncertainty determine organisations both to compete and to cooperate in order to achieve success. All actors in an innovation ecosystem contribute to the cocreation of the value of a whole ecosystem, which would be hardly possible to produce by a single firm.

Differing from innovation systems, innovation ecosystems involve collaborative activities in the innovation process. In an ecosystem, information, knowledge and tangible resources move around the network. Technology is the main resource of innovation, at the same time, not every technology leads to innovation. In order an idea to become an innovation, it should be implemented. In a successful innovation ecosystem, innovation outputs are commercialised. Therefore, the innovation ecosystem encompasses both R&D and commercial areas.

Ecosystems represent networks of organisations that combine efforts to produce and implement innovations. Ecosystems "'do' something to create value for someone" [36]. In contrast to business ecosystems, which focus on value capture, innovation ecosystems focus on value creation [40].

Some important *features of innovation ecosystem* are:


The innovation ecosystem model is related to various spatial levels, ranging from company, city, regional, to national and even global levels. Ecosystems have also been considered at non-spatial levels of analysis, meaning that the focal firm and its complementors and suppliers are not necessarily located in the same region, as long as they belong to the same sector [7].

Innovation ecosystem consists of interacting actors, relationships, resources and conditions that either enable or impede innovation (**Figure 2**).

Main *actors* in the innovation ecosystem are: entrepreneurs, government, academia (both educational and R&D institutions), industry (various associations), supporting institutions (institutions that provide specialised, professional assistance), financial system (e.g. financial institutions, investors, business angels, venture capitalists) and civil society (non-government organisations, media, etc.) [41]. Innovation ecosystem includes the following main *elements*: human capital,

**Figure 2.** *Innovation ecosystem. Source: own elaboration.*

### *Innovation and Entrepreneurial Ecosystems DOI: http://dx.doi.org/10.5772/intechopen.102344*

knowledge, infrastructure, regulations, ideas, finance, research and development, the interface between actors, culture.

Therefore, innovation ecosystems represent communities of interacting actors that support innovation processes and create technologies and innovations. By using the infrastructure and resources, better ways of doing things are developed and implemented.

## **5. Similarities and differences between innovation ecosystem and entrepreneurial ecosystem**

The concept of ecosystem became widely used in the field of innovation and entrepreneurship by academics, policymakers and practitioners. The entrepreneurial and innovation ecosystems evolved to understand why some places grow, while others stagnate and therefore to explain successful socio-economic development in a particular geographical area. They share closely related issues and have many similarities, being at the same time different in various aspects.

Ensuring growth depends on the social and economic environment for innovation and entrepreneurship. Entrepreneurial and innovation ecosystems represent complex systems with the following common features: self-organisation, complex components, interdependent relationships between different actors, non-linearity, i.e. dynamic nature, adaptability. Both concepts have their roots in the ecosystemic foundation, thus are characterised by non-linearity and include a multitude of actors and factors, interacting at many levels. In an ecosystem, a key feature is that firms do not just compete with each other using their own resources, but cooperate, interact and use shared resources, knowledge, networks, infrastructure and support to cocreate value. Both ecosystems encompass collaboration between new, small ventures and large organisations. Also, innovation is considered to be central to innovation ecosystems as well as entrepreneurial ecosystems. Innovation represents one of the main motive forces of entrepreneurial ecosystems [42].

However, there are a number of differences between the analysed concept, particularly in the units of analysis used, context mechanisms, roles of individual agents in regional economic development [43].

Although there is some relation between the concepts of entrepreneurship and innovation, it should be mentioned that not all entrepreneurs innovate, as well as not all innovations are about entrepreneurial opportunities [44].

In general, both analysed ecosystems involve similar actors, the difference is in the role they play in the respective ecosystem. In terms of the components, there are some components that are essential for both ecosystems, for example, human resources, finance, infrastructure, governance, etc. At the same time each ecosystem includes a number of components that are mainly characteristic to them, for example, ideas, research and development to the innovation ecosystem, and visibility, innovation, markets to entrepreneurial ecosystems (**Figure 3**).

Innovation ecosystem represents a network of legally independent economic agents of different line-ups who can be direct competitors, but collaborate to create a comprehensive value proposition for customers. On the other hand, in an entrepreneurial ecosystem, there is no value offering targeted at a defined audience. Instead, it implies a network of interrelated economic agents from a specific area and results in the creation of new ventures and stimulation of regional development [45]. The proximity of all actors is essential in an entrepreneurial ecosystem, which is place-based,

#### **Figure 3.**

*Entrepreneurial ecosystem vs. innovation ecosystem. Source: own elaboration.*

but it is more flexible in an innovation ecosystem, which is non-location specific with a possible virtual presence.

Another difference between innovation ecosystem and entrepreneurial ecosystem refers to various emphases: it is on innovation and entrepreneurs correspondingly. Innovation ecosystems focus on value creation through innovation creation, while entrepreneurial ecosystems focus on entrepreneurship development. Entrepreneurial activity, as an output of the entrepreneurial ecosystem, creates opportunities for innovation. While innovation, in turn, contributes to new value creation, which is the outcome of an entrepreneurial ecosystem [21]. The output of collaboration in the innovation ecosystem may be in form of various innovations, innovative technologies, products, services, it supports processes of innovation. The output of the entrepreneurial ecosystem is the entrepreneurial activity and entrepreneurship development, where the interactions between actors and the infrastructure create conditions for new ventures creation.

## **6. Conclusions**

The chapter expanded the understanding of the concepts of the entrepreneurial ecosystem and innovation ecosystem. Different approaches to defining entrepreneurial and innovation ecosystems, as well as determining their structures were considered.

Innovation and entrepreneurial ecosystems are a recent phenomenon that evolved in an attempt to determine what leads to the success of socio-economic development.

An entrepreneurial ecosystem represents a collection of actors that interact within a geographically bound entrepreneurial environment and factors, which contribute to the development of productive entrepreneurship.

On the other hand, innovation ecosystems represent communities of interacting actors that support innovation processes and create technologies and innovations.

It was identified that entrepreneurial and innovation ecosystems are complex systems with the following common features: self-organisation; encompass complex components; interdependent relationships between different actors; non-linearity,

## *Innovation and Entrepreneurial Ecosystems DOI: http://dx.doi.org/10.5772/intechopen.102344*

i.e. dynamic nature; adaptability. Innovation is considered to be central to both innovation and entrepreneurial ecosystems, innovation ecosystems representing an important context for entrepreneurship. However, there are a number of differences between the entrepreneurial and innovation ecosystems, particularly in location, the main focus, context mechanisms, roles of individual actors, the output of the ecosystem. Both analysed ecosystems involve mainly similar actors, the difference is in the role they play in the respective ecosystem. It was stated that innovation ecosystems focus on value creation through the development of innovations, while entrepreneurial ecosystems on entrepreneurship development.

Nevertheless, further research is needed to identify the direction of strengthening entrepreneurial and innovation ecosystems, which will contribute to economic growth and social development.

## **Author details**

Alina Ianioglo National Institute for Economic Research, Chisinau, Republic of Moldova

\*Address all correspondence to: alina.ianioglo@gmail.com

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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## **Chapter 5**

## Valuation and Capital Return as Inverse Problems

*Petri P. Kärenlampi*

## **Abstract**

The capital return rate is the relative time change rate of value. Correspondingly, the current value can be produced in terms of value change rate divided by capital return rate. There is a variety of ways to approximate the expected capital return rate. These are briefly discussed. The approximation of the value change rate is still more variant, depending on the type of businesses discussed. A variety of businesses may appear within a firm, in which case the value change rates must be integrated. An example is provided of a real estate firm benefiting from the growth of multiannual plants of varying age. It is found that the application of a duration-dependent reference capital return rate increases the value increment rate of juvenile stands and decreases that of mature stands, however increasing the valuation result of both.

**Keywords:** capitalization, capital return rate, value increment rate, expected value

## **1. Introduction**

The capital return rate is the relative time change rate of value. We choose to write

$$r(t) = \frac{d\kappa}{K(t)dt} \tag{1}$$

where *κ* in the numerator considers value growth, operative expenses, interests and amortizations, but neglects investments and withdrawals. In other words, it is the change of capitalization on an economic profit/loss basis. *K* in the denominator gives capitalization on a balance sheet basis, being directly affected by any investment or withdrawal.

A significant finding in Eq. (1) is that the capital return rate *r* depends not only on the value change rate *<sup>d</sup><sup>κ</sup> dt*, but also on the current valuation *K t*ð Þ. Apparently, there is an intimate relationship between the capital return rate and the valuation. A fundamental question then is whether the valuation can be approached by inverting Eq. (1) as

$$K(t) = \frac{d\kappa}{r(t)dt} \tag{2}$$

Obviously, Eq. (2) is mathematically correct. However, in comparison with Eq. (1), it may appear less intuitive. While Eq. (1) provides the definition of capital return rate as a function of observable valuation, does Eq. (2) provide the definition of valuation as a function of observable capital return rate? Or does it possibly provide the definition of valuation as a function of the required capital return rate? Any of these interpretations is possible.

The quantities appearing on the right-hand side of Eq. (1) are observable in a variety of ways, including profit-loss—statement, balance sheet, and market valuation. As the right-hand side has been determined, the left-hand side is naturally known. However, this results in a circular definition in Eq. (2). Alternatively, the capital return rate appearing on the right-hand side of Eq. (2) can be determined from comparable reference investments.

The momentary definitions appearing in Eqs. (1) and (2) provide a highly simplified description of valuation and capital return rate. In reality, there is variability due to a number of factors. Enterprises often contain businesses distributed to a variety of production lines, geographic areas, and markets. In addition, quantities appearing in Eqs. (1) and (2) are not necessarily completely known but may contain probabilistic scatter. Correspondingly, the expected values of capital return rate and valuation can be written as

$$
\langle r(t)\rangle = \frac{\int p\_{\frac{d\kappa}{dt}} d\frac{d\kappa}{dt}}{\int p\_K K(t) dK} = \frac{\int p\_{\frac{d\kappa}{dt}} r(t)K(t) d\frac{d\kappa}{dt}}{\int p\_K K(t) dK} \tag{3}
$$

and

$$
\langle K(t) \rangle = \int p\_K K(t) dK = \int p\_K \frac{d\kappa/\_{\rm dt}}{r(t)} dK \tag{4}
$$

where *pi* corresponds to the probability density of quantity *i*. It is found that while the capital return rate and the capitalization are simply invertible in the absence of any variation (Eqs. (1) and (2)), the same is not the case in the presence of variation, either deterministic or probabilistic (Eqs. (3) and (4)). Here, it is worth noting that the capital return rate in the denominator of Eq. (4) obviously tends to a "reference" capital return rate, rather than a directly observed one.

In the remaining part of this chapter, we will first discuss the practical implementation of the determination of capital return rate and firm value using Eqs. (3) and (4) in the case of a real estate firm benefiting from the growth of multiannual plant stands of varying age. Then, we will discuss the determination of the values of the quantities appearing in Eqs. (3) and (4), as well as factors contributing to them. Finally, a few applications are discussed, as well as interpolation techniques.

## **2. Application to stands of multiannual plants**

In this section, the determination of capital return rate and enterprise value is discussed in the case of a real estate firm benefiting from the growth of multiannual plant stands of varying ages. Conducting a change of variables in Eqs. (3) and (4) results as

$$
\langle r(t)\rangle = \frac{\int p\_a(t)\frac{d\kappa}{dt}(a,t)da}{\int p\_a(t)K(a,t)da} = \frac{\int p\_a(t)r(a,t)K(a,t)da}{\int p\_a(t)K(a,t)da} \tag{5}
$$

*Valuation and Capital Return as Inverse Problems DOI: http://dx.doi.org/10.5772/intechopen.101943*

and

$$
\langle K(t) \rangle = \int p\_a(t) K(a, t) da = \int p\_a(t) \frac{\frac{d\kappa}{dt}(a, t)}{r(a, t)} da \tag{6}
$$

where *a* refers to stand age. Again, the capital return rate in the denominator of Eq. (6) rather refers to a reference rate than a directly observed one.

It is found from Eqs. (5) and (6) that the probability density of stand age is a function of time, and correspondingly, the capital return rate, as well as the estate value, evolves in time. A significant simplification would appear if the probability densities appearing on the right-hand side of Eqs. (5) and (6) would not change along with time. Within forestry, such a situation would be denoted "normal forest principle." corresponding to evenly distributed stand age determining relevant stand properties [1].

$$
\langle r(t)\rangle = \frac{\int \frac{d\kappa}{dt}(a)da}{\int K(a)da} = \frac{\int r(a)K(a)da}{\int K(a)da} \tag{7}
$$

and

$$
\langle K(t) \rangle = p\_a \int K(a, t) da = p\_a \int \frac{\frac{d\kappa}{dt}(a, t)}{r(a, t)} da \tag{8}
$$

The "normal forest principle" is rather useful when considering silvicultural practices, but seldom applies to the valuation of real-life real estate firms, with generally non-uniform stand age distribution. However, it has recently been shown [2] that the principle is not necessary for the simplification of Eqs. (5) and (6) into (7) and (8). This happens by focusing on a single stand, instead of an entire estate or enterprise, and considering that time proceeds linearly. Then, the probability density function p (a) is constant within an interval [0, τ]. Correspondingly, it has vanished from Eq. (7) and appeared outside of the integral in Eq. (8).

The topic of this chapter, however, is firm valuation. As the relatively simple Eqs. (7) and (8) are useful in the design of silvicultural practices, firm valuation typically happens at a specific instant of time, and the probability density *p(a)* generally is non-uniform. Correspondingly, Eqs. (5) and (6) must be applied. Fortunately, *p (a)* usually is known for any property where recent inventory results are available. It is further fortunate that Eqs. (4), (6), and (8) contain simple summations, unlike Eqs. (3), (5), and (7).

## **3. Determination of stand capitalization**

There is a variety of methods to determine the value *K* appearing in Eqs. (3)–(6). In the case of an incorporated company or a firm with equivalent reporting, the value can be found from the balance sheet. Such an outcome does depend on applied accounting practices. On the other hand, the value can be determined as a market value. The latter is straightforward in the case of publicly listed companies, or other companies with the established share trading records. A third alternative for firm value determination is the computation of an "intrinsic value," considering the prognosticated future development of the firm [3–5].

In the case of a real estate firm benefiting from the growth of multiannual plants of varying age, the value *K* within any stand may be approached as the sum of the value of the plants on the stand, the value of bare land, and the value of non-amortized investments. Such computation is problematic if non-mature plants do not have any immediate sale value. In such a case, it is not uncommon to determine stand value by discounting expected future revenues [6–9]. The discount rate is sometimes taken arbitrarily, but often it can be determined as an internal rate of return [10].

We here provide a few examples of the determination of the value of forest stands by interpolation. It is not uncommon that planted seedlings may require several years to mature to young trees of commercial value. However, during those years, expected revenues become closer in time. Correspondingly, it would be unrealistic to assume the growth of saplings would not add value. The capitalization, including such an additional expected value, could be approximated by some kind of a smoothing function. One possibility could be

$$k(a) = \frac{1}{\tau - a} \int\_{a}^{\tau} K(t) \exp\left[r(t) \* (a - t)\right] dt\tag{9}$$

where r(t) is the capital return rate at stand age t. A simpler version would be

$$\lambda(a) = \frac{1}{\pi - a} \int\_a^\tau K(t) \exp\left[ \langle r \rangle \* (a - t) \right] dt \tag{10}$$

Both of the above equations converge to terminal capitalization *k*ð Þ¼ *τ K*ð Þ*τ* , regardless of the capital return rate *r(t)* or h i*r* . However, there is no guarantee of any definite convergence in a newly established stand. Such convergence *k initial* ð Þ¼ *K initial* ð Þ could be approached by fitting an internal rate of return *i*, which provides convergence. That would correspond to assuming that the bare land value includes any additional expectation value for a newly established stand, resulting as

$$k(a) = \frac{1}{\pi - a} \int\_a^\pi K(t) \exp\left[i\*(a-t)\right] dt\tag{11}$$

It might be possible to determine capitalization indirectly by discounting revenue. This would result as

$$k(a) = BL + \int\_{a}^{\tau} R(t) \exp\left[j\*(a-t)\right] dt\tag{12}$$

where *BL* denotes bare land value, and *R(t)* net revenue at time *t*. Again, the discount rate j shall be fitted for convergence *k initial* ð Þ¼ *K initial* ð Þ.

The functionality of Eqs. (11) and (12) are investigated in **Figure 1**, in the case of a spruce stand established with 1800 saplings/ha, and a wooded stand observed at the age of 35 years. The former initial condition is based on the early application of a growth model on saplings stands [11, 12], the latter on the observations of the wooded stand [12, 13]. The former shows a positive additional expectation value of trees for

*Valuation and Capital Return as Inverse Problems DOI: http://dx.doi.org/10.5772/intechopen.101943*

#### **Figure 1.**

*Capitalization, as appearing in Eq. (1), as well as smoothed capitalization according to Eqs. (11) and (12), in the case of the two example stands. (a) (above) shows a spruce stand established with 1800 saplings/hectare. (b) (below) shows a spruce stand first observed at the age of 35 years.*

young stands and after thinnings. If such additional values would be considered, microeconomically optimal rotation ages would be affected. However, Eq. (11) results as the additional value being negative before the first thinning. It is not known how the negative additional expectation value should be considered in management. Within the wooded stand observed at 35 years of age, the additional expectation value of trees of young stands according to Eq. (11) would be negative, being slightly

positive only after thinning. Eq. (12) would indicate zero additional value before thinning and somewhat negative after thinning. An explanation for the latter is that regeneration expenses are carried in the balance sheet until the end of the rotation. This results in the capitalization at mature age being greater than the sum of discounted terminal revenue and bare land value.

**Figure 1a** indicates that in the case of the early application of the growth model, internal rate of return-based interpolation could be useful in the determination of young stand capitalization. In the absence of such adjustment, there would be a negligible value increment for a period of two decades. Eq. (12) can be straightforwardly applied by substituting k(a) from in place of K(a) in Eqs. (5), (6), (7), or (8). However, interpolation is possible only after an initial treatment schedule has been designed using Eqs. (5) or (7). Correspondingly, Eq. (12) must be used iteratively with the other equations.

On the other hand, in the case of **Figure 1b**, interpolation of capitalization appears irrelevant. A natural reason is that the stand has been first observed at the age of 35 years. The capitalization from the stand establishment to the time of observation already has been approximated by exponential interpolation. Correspondingly, results based on the observations of wooded stands do not appear to be in the need of any further interpolation.

## **4. Determination of a reference capital return rate**

In money market theory, increased duration of commitments tends to increase the risk experienced by the borrower [14–16]. However, in **Figure 1**, the discount rates do not depend on the delay time of revenues. This could be corrected by introducing a delay-dependent discount rate. One possibility is a spot discount rate

$$j = \ln\left(u + \frac{d}{s}\right) \tag{13}$$

where *d* is time to maturity, and *u* and *s* are constants. Now, the constants *u* and *s* can be adjusted to gain the correspondence *k initial* ð Þ¼ *K initial* ð Þ in Eq. (12). On the other hand, it is only the constant *u* that determines the discount rate at maturity and that can be determined through matching terminal discount rate to terminal capital return rate, determined as the ratio of terminal value increment rate to terminal capitalization. The outcome, in terms of stand capitalization, is shown in **Figure 2**. At intermediate stand ages, the capitalization becomes higher when Eq. (13) is applied. This is because the revenue is less severely discounted close to maturity. Greater discount rate close to the stand establishment then ensures the correspondence *k initial* ð Þ¼ *K initial* ð Þ.

## **5. Determination of stand value increment rate**

There is a variety of methods to determine the value increment rate *<sup>d</sup><sup>κ</sup>=dt* appearing in Eqs. (1)–(8). In the case of an incorporated company, or a firm with equivalent reporting, the value increment rate can be found from a(n annual, quarterly, or prognosticated) profit/loss—statement. The outcome does depend on applied accounting practices.

*Valuation and Capital Return as Inverse Problems DOI: http://dx.doi.org/10.5772/intechopen.101943*

#### **Figure 2.**

*Capitalization, as appearing in Eq. (1), as well as smoothed capitalization according to Eq. (12) with constant discount rate and (12) together with (13), in the case of the two example stands. (a) (above) shows a spruce stand established with 1800 saplings/hectare. (b) (below) shows a spruce stand first observed at the age of 35 years.*

In the case of a real estate firm benefiting from the growth of multiannual plants of varying age, the value increment rate within any stand may be approached by the value increment rate of the plants on the stand, possibly complemented with the increment rate of bare land value. The value increment rate generally is constituted on volumetric increment on the one hand and increment of volumetrically specific value on the other hand [17]. Again, such computation is problematic if non-mature plants do not have any immediate sales value.

#### **Figure 3.**

*Annual monetary value increment rate, as appearing in Eq. (1), as well as Eq. (12) with constant discount rate and (12) together with (13), in the case of the two example stands. Fig. 3a (above) shows a spruce stand established with 1800 saplings/hectare. Fig. 3b (below) shows a spruce stand first observed at the age of 35 years.*

**Figure 3** shows the annual value increment rate per hectare, determined using three different methods. Firstly, the annual value increment is determined directly using the growth model, as often applied in Eq. (1). With the initial condition based on the early application of a growth model on saplings stands (**Figure 3a**), the initial value increment rate is small, increasing rapidly later. Value increment rate based on discounting of revenue with the constant discount rate (Eq. (12)) is smoother, even if not monotonic. Incorporating the delay-dependent discount rate (Eq. (13)) increases

## *Valuation and Capital Return as Inverse Problems DOI: http://dx.doi.org/10.5772/intechopen.101943*

the value increment rate at a young age and reduces it at a mature age (**Figure 3**). Similar trends are observable in the case of the example stand first observed at the age of 35 years, except for early stand development according to Eq. (1) is similar to the discounting result with the constant discount rate (Eq. (12) (**Figure 3b**).

The relative annual value increment rate can be readily found by normalizing the monetary increment rate of **Figure 3** with the capitalization appearing in **Figure 2**. The outcome is in **Figure 4**. With the initial condition based on the early application

#### **Figure 4.**

*Annual relative value increment rate, as appearing in Eq. (1), as well as Eq. (12) with constant discount rate and (12) together with (13), in the case of the two example stands. (a) (above) shows a spruce stand established with 1800 saplings/hectare. (b) (below) shows a spruce stand first observed at the age of 35 years.*

of a growth model on saplings stands (**Figure 4a**), direct application of the growth model induces a volatile relative value increment rate. On the contrary, capitalization determined by discounting revenue yields stationary value increment rates, except for increases after thinnings. Again, delay-dependent discount rate (Eq. (13)) induces larger value increments at a young age and lower at a mature age. The latter effect is more pronounced in the case of the example stand observed at the wooded state (**Figure 4b**).

## **6. Further valuation attempts**

It is of interest whether Eqs. (4) and (13) can be combined for the valuation of an individual stand. A possibility is

$$K(a) = \frac{\int\_{a}^{\tau} d\kappa \langle\_{dt} \exp\left[j(t-a)\*(a-t)\right]dt}{(\tau-a)\*r(a)}\tag{14}$$

where reference capital return rate r(a) comprises a numerical solution of Eqs. (12) and (13), appearing in **Figure 4**. The result is shown in **Figure 5**. The reference capital return rate according to Eq. (13) increasing with increasing time to maturity, it is found that mature stands show greater value than the reference curves, whereas juvenile stands show lower value. Eq. (14), however, has an obvious deficiency: The value estimate does match the known terminal value but not the initial value.

The obvious deficiency in Eq. (14) can be simply corrected. The reference capital return rate *r(a)* can be modified, however possibly retaining the simple form of Eq. (13). Eq. (14) can possibly be further simplified by using the same reference rate in the discounting of the value increments. The outcome would be

$$K(a) = \frac{\int\_{-\pi}^{\pi} d\kappa \sqrt{\_{dt} \exp\left[l(t-a)\*(a-t)\right]} dt}{(\pi-a)\*l(a)}\tag{15}$$

However, there is another deficiency in Eq. (14) and in **Figure 5**. The approximated stand value before the first thinning appears lower than the immediate sales value of the trees. This deficiency does not become corrected by Eq. (15). Correspondingly, Eqs. (14) and (15) cannot be considered appropriate.

## **7. Discussion**

The capital return rate and firm valuation have been discussed as inverse problems. The invertibility is obvious in the absence of probabilistic or deterministic scatter. In the presence of scatter, the invertibility is less straightforward. However, the firm valuation corresponds to a simple sum of units or compartments according to Eqs. (4), (6), and (8).

A real estate firm benefiting from the growth of multiannual plant stands of varying age was discussed as a practical example. Again, the total value is a simple sum of the values of compartments, which transfers the focus to the valuation of

*Valuation and Capital Return as Inverse Problems DOI: http://dx.doi.org/10.5772/intechopen.101943*

#### **Figure 5.**

*Capitalization, as appearing in Eq. (1), as well as Eq. (12) with constant discount rate and (12) together with (13), in the case of the two example stands.*

individual stands. Young stands with small immediate sales value, or other stands expected to increase in value rapidly in the future, appear to be a problem in stand valuation. Attempts in discounting future capitalization appear to be unsuccessful but attempts in discounting revenue successful. Such discounting appears necessary if the value of the plants is determined through high-resolution observation or computation. Observation of more mature stands, along with interpolation to more juvenile stands, takes care of such interpolation in value (**Figures 1, 2**, and **5**).

Discounting of revenue with constant discount rate, however, appears to be unsatisfactory since it produces stand values slightly lower than the immediate sales value (**Figures 1, 2,** and **5**). This can be corrected by introducing a discount rate that considers the duration effect (or time-to-maturity), according to Eq. (13). Such discount rate slightly increases stand value estimates (**Figure 2**). It increases value increment rate at a young age and reduces it at a mature age (**Figures 3** and **4**).

This chapter, after introducing generic expressions for valuation and capital return as inverse problems, has discussed the valuation of two example cases in a restricted manner. In other words, the initial value and the terminal value are taken as known quantities, and value evolution between these extremes has been interpolated. Such a restricted treatment has some definite benefits: Internal consistency of the results can be relatively easily verified. An important tool in the verification is the noninterpolated sum of value components generally used in Eq. (1). In the case of a forestry firm, that might become

*K a*ð Þ¼ *bare land value* <sup>þ</sup> *value of trees* <sup>þ</sup> *value of non*‐*amortized investments* (16)

The last term in Eq. (16) depends on investment intensity, as well as the amortization schedule. For the purposes of an internal consistency criterion, we define a *reduced current capitalization* as

$$K'(a) = bare\ land\ value + value\ of\ trees\tag{17}$$

Approximations of capitalization established in Eqs. (9) to (12) are designed to include expectations of forthcoming value increment. Consequently, one can take for granted

$$k(a) \ge K'(a) \tag{18}$$

The brief examination above revealed that Eqs. (9), (10), (11), and (14) generally do not satisfy this internal consistency criterion and must thus be rejected. Eq. (12), applied with or without Eq. (13), often does satisfy the consistency criterion. However, this does not happen in all circumstances. Particularly, Eq. (12) with a constant discount rate fails to comply with Eq. (18) with large rotation ages, where the value increment rate becomes essentially non-exponential.

Other kinds of problems relate to Eq. (13). First, there are circumstances where the parameter *s* turns negative. In particular, this happens in the case of young, productive stands with growth only slightly differing from exponential. Consequently, increased duration of commitments tends to decrease the discount rate or, in other words, invert the yield curve.

Another issue related to Eq. (13) is that it is sensitive to short-range disturbances close to maturity. In particular, recent thinning typically increases the relative value increment rate. Consequently, parameter *u* in Eq. (13) increases. The estimated capitalization then decreases, and the expected value of capital return rate according to Eqs. (3), (5), or (7) increases. This suggests terminal clear-cutting soon after thinning —a result which obviously is a computational artifact. Instead, Eq. (12) with a constant discount rate appears to remain a valid estimate, provided the internal consistency criterion of Eq. (18) is satisfied.

As mentioned, this chapter has discussed the valuation of two example cases in a restricted manner. A less restricted treatment might open further avenues. A

*Valuation and Capital Return as Inverse Problems DOI: http://dx.doi.org/10.5772/intechopen.101943*

particular possibility might be the introduction of a variety of reference capital return rates in the denominator of Eqs. (2), (4), (6), and (8). Linking the reference rate to alternative investments like interest instruments or shares of listed companies would significantly change valuations—not only intermediate valuations but also the initial and terminal values. The initial value would likely be more affected since the proportion of the bare land value is greater than in the terminal value, the latter including the terminal sales value of mature timber.

## **Acknowledgements**

This work was partially supported by Niemi Foundation. Prof. Dr. Lauri Mehtätalo is gratefully acknowledged for fruitful discussions.

## **Author details**

Petri P. Kärenlampi Lehtoi Research, Finland

\*Address all correspondence to: petri.karenlampi@professori.fi

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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## **Chapter 6**
