An Approach To The Valuation Of

TREEOR Model: An Approach to the Valuation of
Intellectual Capital
María Sarabia and José M. Sarabia
University of Cantabria, Santander, Spain
sarabiam@unican.es
sarabiaj@unican.es

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 www.ejkm.com

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.

www.ejkm.com 120 ©Academic Conferences Ltd


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

www.ejkm.com 121 ISSN 1479-4411


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



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 4.0.1.0. 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



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.



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 4.0.1.0. 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.



In other case, the knowledge which is Groupe D’Estudes Des Strategies
absorbed and it is not processed, causes Technologiques (1986) Grappes
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