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An Approach To The Valuation Of

  1. 1. TREEOR Model: An Approach to the Valuation of Intellectual Capital María Sarabia and José M. Sarabia University of Cantabria, Santander, Spain Abstract: Following the biological behaviour of a tree and its growth system, this paper proposes a model of valuation of the Intellectual Capital of an organization based on a variation of the classical Lotka-Volterra equations system. The proposed model explains the growth of an organization as a consequence of its Intellectual Capital (increment of the surface of the roots), its Knowledge (the consumption of nutritious) and its Learning (fertility of the floor). And based on the proposed model, an example with real data is given. Keywords: Intellectual Capital, Organizational Learning, Knowledge Management, Lotka-Volterra system. 1. Introduction the type of soil or Learning that it has. Finally, we try to value the speed with Nonaka and Takeuchi (1995) define an which the Knowledge reaches every part analogy as being halfway between the of the Tree-organization. imagination and logical thought. The definition of concepts through analogy is The paper proceeds as follows. In section one of the fundamental steps in the 2., we explain the key elements of the tree construction of new theoretical analogy with the organization; section 3., perspectives (Kaplan, 1964; Tsoukas, reflects the contents from the classical 1991; Van de Ven and Poole, 1995). In Lotka-Volterra model and straight off, in this way, we study the analogy that exists section 4., we explain the proposed model: between trees and organizations, starting from a system of differential explaining similarities and differences equations, and using the Runge Kutta between them and proposing a model for method of the Mathematica program, we the valuation of Intellectual Capital based try to recognize the organizational on an analogy already mentioned mechanism of growth in analogy with the previously in the literature: G.E.S.T (1986) growth of a tree. In section 5., we generate with their quot;bonsai treequot; about the idea of the discussion and to finish, in section 6. technology; Edvinsson (1997), who made we study the Bankinter case. use of the metaphor of a tree to define the Intellectual Capital concept; Giget (1988) with their tree of company competitions; 2. Tree-organization: Elements Viedma (2002) which represents the of the analogy OICBS system; or GIDE (2002), which The model of Tree-organization or identifies each managerial quot;occupationquot; as TREEOR model presents the following a type of tree. elements: Intellectual Capital, Organizational Learning and Knowledge. The proposed model tries to measure the length of the roots or Intellectual Capital 2.1 Intellectual Capital (IC) of an organization and incorporates a bifurcation parameter that values the The concept of roots or Intellectual Capital growth according to the capacity that the follows the proposed definition by organization has to increase their IC. In Euroforum (1989), where their key turn, the roots are responsible of the elements are: Human Capital, Structural absorbing nutrients or Knowledge, Capital and Relationship Capital. generating two kinds of Knowledge flows: those with aims of consumption for growth Human Capital is made up of (Explicit-conscious) and those whose competences (knowledge and abilities) dimension is the regulation or and attitudes (such as loyalty, flexibility, maintenance of the Tree-organization etc). The essence of this capital survival, (Implicit-automatic). The Knowledge that is the core competence which absorption depends, to a great extent, on provides, goes through the stimulation, ISSN 1479-4411 119 ©Academic Conferences Ltd Reference this paper as: Sarabia M and Sarabia J (2005) “TREEOR Model: An Approach to the Valuation of Intellectual Capital” The Electronic Journal of Knowledge Management Volume 3 Issue 2, pp 119-128, available online at
  2. 2. Electronic Journal of Knowledge Management Volume 3 Issue 2 2005 (119-128) retention and appropriation of the benefits Strategy: for elaborating the organizational which brings the existence of people with strategy, several factors converge: from managerial talent, technological the environment, giving rise to a deliberate knowledge, etc. According to Milgrom and strategy, that is to say, quot;the circumstances Roberts (1993), the organization should of the moment, the events that arise from centre their attention on reducing the the environment, lead to the abandonment mobility as an incentive to the investment or revision of strategic elections, although, in the specific human capital. Although the firmly wantedquot; (Strategor, 1993); to the real important thing, is to capture the best memory on which learning is based, this of each person so that it doesn't is, quot;in the exchange of ideas, knowledge disappear, and in case of replacement, the and mental models [...] and it’s based on cost is low (Kay, 1994). the previous experience” (Stata, 1989). Senge (1990), maintained that quot;our mental Structural Capital is divided in models not only determine the way of Organizational Capital (Organizational interpreting the world, but also the way of Routines) and Innovation Capital. Inside actingquot;, so that, every organizational the Organizational Capital, the routine behaviour, as a result of a strategic concept is framed as a “complex model of application, goes through a mental models behaviour, unchained by a number of lattice that form distorted perceptions of former incentive, working automatically the reality. and as an unit” (Winter, 1986). These organizational routines are the previous Environment: climatology (in terms of step to the accumulative learning of the fertility of the soil) where a Tree- organization, because the repetition of the organization lives, influences directly in the these is done with the objective of learning behaviour of this one. “An obtaining success (Gavetti and Levinthal, organization that learns is an expert 2000). On the other hand, the Innovation organization in creating, acquiring and Capital is shaped by the formalized and transmitting knowledge, and in modifying protected (patents) knowledge of its behaviour to adapt itself” (Garvin, innovation. That knowledge protection 2003). That necessity of adaptation on tries to keep them safe from competitors continual improvement, of survival, is and this way, provide competitive intimately related with the environment advantages to the organization (Teece, where the organization competes. It is 1990). such, that depending on the stability or dynamism of the environment, the learning Finally, the objective of Relationship is modified. A stable environment can Capital is the creation and maintenance of restrain the development of the the relationships that the organization has organizational learning (Lant and Mezías, with its environment. Starting from the 1992; Fiol and Lyles, 1985), while a affectionate communications between dynamic, unstable and highly competitive company and environment, intangible environment, causes organizations more actives are born outstanding as the capable when developing its learning reputation, or the alliances (essential for capacities, as well as more active for the strategy success). acting of sustainable competitive advantages that allow its survival. 2.2 Organizational learning Culture: it defines how manhood is The soil fertility is its own capacity to identified with the organization, and how supply all and each one of the nutrients he conceives his system of values and that the tree needs at that moment, relates it with his own (de Val, 1994). It is quantity and appropriate form. The an accumulation of answers that the following factors influence on the soil organization has learned in view of raised fertility: type of crop, climatology, cultural problems (Schein, 1988). The question practise and soil texture (quantity of clay). lies in how the culture is detected and the If we make an analogy between soil consequences that it implies for the fertility and organizational learning, and organization development in a unsettled following Fiol and Lyles (1985), we will find environment. The organization survival these similarities: Strategy, Environment, requires its capacity of adaptation or Culture and Structure respectively. transformation that will depend on the organizational learning processes. 120 ©Academic Conferences Ltd
  3. 3. María Sarabia and José M. Sarabia great inconvenience is its inefficacy Structure: According to Strategor (1995), when processing it by its roots, that is quot;structure is a group of functions and to say, the Intellectual Capital is relationships that determine the tasks that unrecognizable, replaceable and each organization unit should complete identifiable with difficulty, due to a formally and the ways of collaborating structure that suffocates the intangible among themquot;. The relationship between ones. strategy and structure, is characterized by c) Mix: it’s the desired structure for the the existence of a complex component in organization, where the channels which variables such as the environment provide the knowledge flow, the take part in it, and the capacity of permeability provides nutrients for its transmission in the management activities survival and the Intellectual Capital (culture). The behaviour of the secures the growth and the flow of the organization, has a permanent movement organizational knowledge increases. of sorting its structure, that is to say, the change dynamics causes a continual 2.3 Knowledge evolution for the sake of its survival: quot;foreseen and systematic process which is Nonaka (1994) clearly summarizes the carried out to change the culture, systems actual importance of knowledge: quot;in an and organizational behaviour, to improve economy where the only certainty is the the effectiveness in solving their problems uncertainty, the best source to obtain and for the objective attainmentquot; (Lippit, lasting competitive advantage is the Langset and Mossop, 1989). knowledge.quot; The knowledge is the source of life of the Tree-organization, but its 2.2.1 Types of organizational floor reception needs of a root lattice (Intellectual Capital) depending on certain Which are the most appropriate soils for conditions of the soil. The fertility of this the growth and root fortifying (Intellectual one will provide a larger bifurcation of the Capital) of the Tree-organization? There roots, that in turn will increase the are three soil classifications to study: (a) knowledge flow and in consequence, the Sandy: characterized by its great survival and the growth of the organization permeability. These are soils that, due to will be larger. their scarce retention, they present a huge poverty in nutrients (knowledge); (b) Nonaka (1994), offers an idea of company Clayey: tendency to be flooded and to innovating, founded on ideas and ideals, suffocate the roots (Intellectual Capital). and whose existence is based on the Their main characteristic is its wealth in creation of knowledge: quot;creating new nutrients (knowledge); (c) Mix: appropriate knowledge means literally to recreate the for most crops, susceptible of company and each one of the people who improvement and with intermediate work in it by means of an uninterrupted characteristics between the sandy and the process of personal and managerial clayey ones. remodelling”. Now then, how can we identify each one Authors such as Huber (1991), Nevis et al. of these types with the current (1995), or Winter (2000) have tried to organizational structures? Let us analyze agree on the process of organizational each one of them: learning, bringing forward key concepts of a) Sandy: it has a great communication the essential stages of this. Within the idea channel, where the whole knowledge of of Knowledge Acquisition, two supply the organization could flow channels coexist: internal and external. satisfactorily, but it moves in a simple The internal development of knowledge, environment, where the processed follows a process of essential information isn’t valued nor understood competitions, heroines in the cases of as a competitive advantage. These are assumption and assimilation of irreversible companies that do not learn and do not decisions in the past, as well as in the negotiate with effectiveness the absence of flexibility in the adaptation to acquired experience. the change (Leonard-Barton, 1992). b) Clayey: the knowledge of the However, while the external acquisition of organizational structures that lives on knowledge, makes use of contractual this type of soil is remarkable. The mechanisms that define the knowledge 121 ISSN 1479-4411
  4. 4. Electronic Journal of Knowledge Management Volume 3 Issue 2 2005 (119-128) and protect it from the effect provide a larger or smaller accessibility to quot;benchmarkingquot;, the knowledge the nutrients (knowledge) and in apprehension from the environment, uses consequence, the sustainability to the soil the relationships between staff, clients and of the roots (intellectual capital) will suppliers. determine the survival of the tree. As we have previously seen, and following 3. A basic model of Lotka- Moráveck and Fiala (2004) in analogy with Volterra the organization, we present an empiric formulation based on a Lotka-Volterra The Lotka-Volterra Model studies the equations system (table 1). interactions between two species, the Table 1: Description of the TREEOR depredator and the prey and it has the model variables. following characteristics: a) preys are the Variable Description only source of feeding for depredators; b) Parameter name it explicitly includes the dependence of the species of preys of population density; c) Intellectual Capital there is no emigration or immigration (IC) measured phenomena. Λ(t) Root length according to the last bifurcation of the The model was independently developed corresponding root. by Lotka (1925) and by Volterra and it is developed by the following differential It values the growth equations system(1926): according to root branching of the tree- • organization, so that H (t ) = r ⋅ H (t ) − A ⋅ H (t ) ⋅ P (t ) the smaller • Bifurcation ramification capacity α(t) P (t ) = B ⋅ H (t ) ⋅ P (t ) − m ⋅ P (t ) parameter (creation of value- IC), the smaller • where and absorption of H (t ) = dH (t ) dt nutrients • (knowledge) and in P (t ) = dP (t ) dt . The interpretation of consequence, a these two equations is explained by the slower growth. following parameters: H(t) = density of prey; r = intrinsic rate of prey population Quantity of increase; B= reproduction of predators per knowledge in 1 prey eaten; P(t) = density of predators; A movement, = predation rate coefficient; and m = differentiating Nutrient between predator mortality rate. Φ(t) flow: consumption aim for knowledge the growth (Explicit- From Lotka-Volterra classical Model, conscious) and Moráveck and Fiala (2004), an applicable whose dimension is version of the biological systems is carried the regulation or out and they include another equation in maintenance the system. This way, the constant (Implicit-automatic). parameters of the classical model become functions of the following type in the Speed in which the proposed model that we will explain in the Tree-organization Knowledge supplies the next section: ς(t) supply knowledge to every A = A(t ) = b ⋅ α(t) speed part of it and it allows its absorption from B = B (t ) = b ⋅ [d − φ(t ) ] ⋅ α ( t ) the roots (Intellectual Capital). a, b, c, d, Dynamical 4. The proposed model: e, f, g parameters TREEOR The formulation (1), shows the behaviour We have formulated a model that supports in the root length with regard to the speed the idea of growth and survival of the of nutrients supply. So, we try to study the Tree-organization according to soil fertility growth of the organization according to the where it’s located (learning), which will 122 ©Academic Conferences Ltd
  5. 5. María Sarabia and José M. Sarabia grade in knowledge absorption on behalf of the Intellectual Capital (IC): (3) Φ (t ) = f ⋅ Λ2 (t ) − g ⋅ Λ3 (t ) • (1) Λ(t) = a ⋅ Λ(t ) − b ⋅ α(t ) ⋅ ς(t ) ⋅ Λ(t) 5. Discussion • ς(t ) = b ⋅ [d − Φ(t )] ⋅ α(t ) ⋅ ς(t ) ⋅ Λ(t ) − c ⋅ ς(t ) The system of equations (1)-(3) has been solved by Runge Kutta’s method of • e Mathematica program, version For (2) α(t ) = Φ(t ) the resolution and interpretation of this model, we will study a simulation of their dynamical parameters, starting from a non The equation (2) tries to value which trivial initial solution: a = 1; b = 1; c = 100; would be the bifurcation parameter of the d = 2.5; e = 1; f = 2; g = 0.1. root balance or Intellectual Capital because, according to the last of the We start from an initial situation (table 2), bifurcations, we will measure the length of where the root length as well as nutrient the roots. So we can extract a polarity: (i) speed supply, diminish intensely. This is, if a longer length of the roots or Intellectual the capacity of the organization to create Capital, a larger growth speed of the Tree- value or IC decreases, then it will have organization; (ii) a larger length of the fewer tools to absorb the knowledge and roots (IC), a slower speed of nutrient or in consequence their global growth will be knowledge supply. slower. Besides, if the speed of knowledge supply diminishes, fewer nutrients enter Starting from Moráveck and Fiala’s (2004) each time, and the IC is held back. empiric definition about nutrient flow, we assume that: Table 2: Graphic behaviour of the variables: Length of roots or IC, Knowledge Supply Speed and Bifurcations Parameter, respectively How do each of the variables behave increase its intangible and in this way before parameter changes? We will begin absorb the knowledge and give it carrying out a small variation on the efficiently to every part of the company. parameters a and b, responsible for the What does the quantity of knowledge variations in the root length or IC and of depend on what takes over the the speed supply. organization and allows it to grow? The fertility of the soil on which the The table 3, presents an important organization is influences in the quantity of situation for the Tree-organization: the nutrients that are absorbed, that is to say, intellectual capital of the company grows the organizational learning allows a larger because it has the necessary capacity to takeover of knowledge. Table 3: Graphic behaviour of the variables: a = 53 and b = 53 What is learning translated into?: Strategy, way in which the four pillars of the learning Environment, Culture and Structure. This combine, gives rise to different soils: group of elements represents the fertility sandy, clayey and mix. In table 3, the for the organization growth. Now then, the organization soil is mix, because it 123 ISSN 1479-4411
  6. 6. Electronic Journal of Knowledge Management Volume 3 Issue 2 2005 (119-128) expedites the knowledge absorption by experiences and more appropriate administrating an appropriate intellectual practices of the other companies capital. (benchmarking), and in transmitting quick and efficiently the knowledge to the whole According to Garvin (2003), the organization. The simulation of table 3 organization that learns is an expert in five reflects a mixed learning on which a activities: systematic resolution of company is settled which knows how to problems, experimentation of new negotiate their human, relationship and focuses, use of their own experience and structural capital, as well as their of the past to learn, learn from knowledge. Table 4: Graphic behaviour of the variables: a = 53, b = 53 and e = 3 Let us suppose now that, about the The soil is infertile because it is a sandy simulation of table 3, we carry out a soil that it does not retain knowledge. We change in parameter e. This is, we vary would be faced with a permeable learning; the length of the roots, the knowledge the organization possesses IC but the soil supply speed and the parameter of on which it is settled does not favour the bifurcations. What happens now to the absorption of knowledge and in learning? In table 4, we have the answer: consequence stops growing. grow and absorbing knowledge is stopped. Table 5: Graphic behaviour of the variables: a = 53, b = 53, e = 3 and c = 200 The companies with a sandy learning live 6. Numerical example: Bankinter a stable environment (Lant and Mezías, case 1992; Fiol and Lyles, 1985) that obstructs the growth of their IC and ignores the In this section we present a numerical importance of the intangible such as the example of the proposed model, using culture. quot;The ability of learning more data from Bankinter, a Spanish Industrial quickly than competence is nowadays the Bank which was founded in June 1965 only sustainable competitive advantage” through a joint venture by Banco de (De Geus, 1988), and it hopelessly goes Santander and Bank of America. Bankinter by the organizational pillars that provides has ranked 107 when it was founded and the culture. And if we carry out a new is currently among the top six Spanish variation on the previous simulation (table banks. 4)? On this occasion (table 5), we vary lightly the knowledge supply speed and we We are interested in the behaviour of observe an interesting behaviour: in spite Intellectual Capital variables of Bankinter of the growth of knowledge speed, the in two periods of time. The first period is organization stops growing. This is a case from 2001 to 2003 and the second one is of clayey learning because the company from 2002 to 2004. We have used data does not negotiate the knowledge. The IC from Bankinter Annual Report and we becomes flooded and it cannot grow, it have identified the variables of our absorbs knowledge but it does not know TREEOR model with Bankinter indicators what to do with it, it does not learn and it of Intellectual Capital (Table 6). also oppresses its intellectual capital. 124 ©Academic Conferences Ltd
  7. 7. María Sarabia and José M. Sarabia Table 6: BANKINTER indicators for the proposed model, an estimation of the numerical example of TREEOR parameters a, b, c, d, e, f and g have been model obtained (table 8). TREEOR BANKINTER indicators Table 8: Parameters of the TREEOR variables model in Bankinter case Λ(t) Percentage of solved economic Parameters Period 2001- Period 2002- incidences in 48 hours (%) 2003 2004 α(t) Contribution to GDP per a 0,0651 0,0633 employee (in thousands of b 0,0000 0,0000 euros) c 12,1417 -8,1646 Φ(t) Internal job rotation (%) d 505,5661 -246,5072 ς(t) Percentage of employees who e 6441,8010 3654,9810 meet or exceed their targets f 1,0000 1,0000 (%) g 0,0123 0,01250 Following the same way for resolution the In the first period (2001-2003) we can simulations of TREEOR model, we have observe how the Intellectual Capital or solved the equations system by Runge length of the roots grows and the Kutta’s method of Mathematica program, Knowledge supply speed diminishes (table version But, in this case we will 9). At the same time, the bifurcation analyse the model through real data from parameter starts to decrease. It means Bankinter case (table 7). that the company has a great Intellectual Table 7: Real data from Bankinter. Capital Structure, which gets knowledge TREEOR 2004 2003 2002 2001 from the soil or Learning Structure. Λ(t) 85,26 82,64 78,38 75,00* Bankinter is an interesting case of learning α(t) 134,65 150,90 121,61 106,81 organizations where its bifurcation Φ(t) 28,80 27,71 17,65 23,61 parameter diminishes when the Intellectual Capital increases. The Bankinter soil is ς(t) 48,71 83,43 29,31 62,27 very close to mix learning because the (* they are not available data of this year, communication channel of knowledge so we have approximated it through exists and the structure of Intellectual known data of previous years) Capital is developed. According to the previous values and solving the equations system of the Table 9: Graphic behaviour of the variables in the period 2001-2003 (Bankinter): Length of Roots or IC, Knowledge Supply Speed and Bifurcations Parameter, respectively The bifurcation parameter does not grow knowledge that is not used in maintenance as the Intellectual Capital due to Bankinter actions (equation 2), and every has not found its equilibrium parameter of organization must know what is the “new knowledge” in this period. That is to quantity of “new knowledge” that it can say, Φ(t) is the resulting part of the whole process. Table 10: Graphic behaviour of the variables in the period 2002-2004 (Bankinter): Length of Roots or IC, Knowledge Supply Speed and Bifurcations Parameter, respectively. 125 ISSN 1479-4411
  8. 8. Electronic Journal of Knowledge Management Volume 3 Issue 2 2005 (119-128) In other case, the knowledge which is Groupe D’Estudes Des Strategies absorbed and it is not processed, causes Technologiques (1986) Grappes reductions in the knowledge supply speed. technologiques. Les nouvelles In the second period (2002-2004) (table stratégies d’entreprise. McGraw-Hill. 10) we can observe how Bankinter gets its Paris. right bifurcation parameter which allows it Grupo de Investigación en Dirección to reach a higher level of knowledge Estratégica (GIDE) (2002) Nuevas supply speed (it increases) and in claves para la dirección estratégica, consequence, the Intellectual Capital Ariel Economía. Barcelona. increases too due to a great management Huber, G (1991) “Organizational Learning: channel about intangible values. Contributing Processes and the Literatures”, Organizational Science, The TREEOR model, tries to value the No.2, pp88-115. responsible elements for the firm growth, Kaplan, A (1994) The conduct of Inquiry. and presents the knowledge as Chandler, New York. indispensable food and the intellectual Kay, J (1994) Fundamentos del éxito capital, as the absorption tool. Mentioning empresarial. Ariel, Barcelona. the classical model of Lotka-Volterra, we Lant, TK & SJ Mezías, (1992) “An would be speaking about the depredator Organizational Learning Model of (IC) and the prey (Knowledge). Now then, Convergence and Reorientation”. the place where the hunt takes place is Organization Science, No.3, pp47-71. vital, because it is not the same to speak Leonard-Barton, D (1992) “Core about sharks and fish than about cats and Capabilities and Core Rigidities: A mice, that is to say, the soil on which the Paradox in Managing New Product absorption of Knowledge is developed Development”. Strategic Management influences greatly on the growth and Journal, Summer Special Issue, organization maintenance. It seems that, No.13, pp111-125. the Learning is responsible for the larger Lotka, A J (1925) Elements of physical or smaller Intellectual Capital creation of biology. Baltimore: Williams & Wilkins the organization. Co. Milgrom, P and J Roberts, (1993) References Economía, organización y gestión de empresas, Ariel Economía, Edvinsson, L (1997) “Developing Barcelona. Intellectual Capital at Skandia”. Longe Moráveck, Z and J Fiala, (2004) “Fractal Range Planning, No.30, pp366-373. Dynamics in the Growth of Root”, Euroforum (1998) Proyecto Intelect. Chaos, Solitions and Fractals, No.19, Medición del Capital Intelectual, pp31-34. Euroforum, Madrid. Nevis, EC, AJ Dibella, and JM Gould, Fiol, CM and MA Liles, (1985) (1995) “Understanding Organizations “Organizational Learning”, Academy as Learning Systems”. Sloan of Management Review, No.10, Management Review, No.36, pp73- pp803-813. 85. Garvin, DA (2003) “Crear una Nonaka, I (1994) Harvard Business Organización que Aprende”. Harvard Review in Knowledge Management. Business Review: Gestión del Harvard Business Scholl Press. Conocimiento. Ediciones Deusto, Boston. pp51-89. Bilbao. Schein, EH (1988) La cultura empresarial Gavetti, G and D Levinthal, (2000) y liderazgo. Plaza y Janés. “Looking forward and Look backward: Barcelona. Cognitive and Experiential Search”, Senge, PM (1990) The Fifth Discipline: Administrative Science Quarterly, The Art and Practice of the Learning No.45, pp113-137. Organization. Doubleday, New York. Geus de, A (1988) “Planning as Learning”, Spender, JC (1996) “Making Knowledge Harvard Business Review, No.66, the Basis of a Dynamic Theory of the pp70-74. Firm”. Strategic Management Journal, Giget, M (1988) La conduite de la réflexion No.17, pp45-62. et de l’action stratégique dans Stata, R (1989) “Organizational Learning: l’entreprise. Euroconsult. the Key to Management Innovation”. 126 ©Academic Conferences Ltd
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  10. 10. Electronic Journal of Knowledge Management Volume 3 Issue 2 2005 (119-128) 128 ©Academic Conferences Ltd