2009 International Conference on Computer Engineering and Applications
IPCSIT vol.2 (2011) © (2011) IACSIT Press, Singapore
Entropy Evaluation of Uncertainty in M&A Transaction System
Changbing Tong, Qiusheng Zhang, Jinchuan Ke
School of Economics & Management, Beijing Jiaotong University, Beijing 100044
Email：tongcb01@163.com, qszhang@bjtu.edu.cn, jchke99@126.com
Abstract: Because of the indeterminations in Merger and Acquisition (M&A) trading, the participants are
not always able to achieve the objective. This paper conducts a study on the comprehensive evaluation of
M&A uncertainty from the angle of complexity science. In the process of study, beginning with the
discussion of uncertainties in M&A transaction and trading environment, a structure diagram of the system
uncertainty is created, and then the system is evaluated based on the entropy information theory. It is
concluded that a low information entropy would be helpful to reduce the system uncertainty and facilitate the
development of M&A transaction towards an orderly, steady and efficient direction.
Keyword: Complexity; M&A; Entropy; Evaluate; Uncertainty.
1. Introduction
There exists the mutual penetration and interaction between the M&A transaction and the environment,
from which the exchange of material, energy and information speeds up the development of M&A
transactions. As the impact of environment on M&A transactions increases, the environmental subsystems
might be converted into M&A transaction’s subsystems. For example, with the involvement of potential
third-party competitor for M&A transaction, the intervention of arbitrageurs, and the public voices in the
market have a direct impact on the M&A transactions. It is known that the border of the open M&A
transaction system is vague and is equipped with access way which can be in and out. To some extent, the
key to the M&A transaction success depends on whether the involvers can adapt to a changing environment
or not. The M&A system consists of the enterprise entities, intermediary organizations, and environments. A
simple M&A transactions is constructed as shown in Table 1.
Table 1: The complex M&A transaction system framework indicated
M & A E n te r p r is e s /
T a rg e t E n te rp ris e
I n te r m e d ia r y o r g a n iz a tio n s
board of
shareholders
Board of Directors
Executives
label union
Investment Bank
public accounting
firm
law issue office
other
microenvironment
M & A e n v iro n m e n t
the overall
environment
o th e rs
…
545
The personnel actually
involved in the M&A
transaction
M&A
Team
Accountants
Lawyers
…
legal agent
public relation staffs
analysts
public opinion
local government
economic environment
social environment
market environment
political setting
entironment
Although the rules of M&A transaction system are exactly the same for all participants, it is difficult to
make two M&A transactions identical. The M&A market provides a trade-off for all parties involved in the
transactions, however, because of the existence of uncertainty, the participants are not always able to achieve
the desired goals. During the M&A transaction process, the involvers will face with a lot of uncertainty such
as the uncertainty of negotiations, the uncertainty of payment, the uncertainty of decision-making, the
uncertainty of social environment and so on.
Uncertainty can be measured by assessing the probability of all possible occurrence, the associated risks,
as well as gains (or "effect"), that is, link the uncertainty with the probability of event, using the variance of
random variable to describe the size of its uncertainty. The decision making is often based on the assessment
of the risk and return which are associated with the probability. For instance, in the famous Arrow - Debreu
model, uncertainty is assumed to be: (i) Each of the uncertainty factors is identifiable in advance; (ii) Each of
the uncertainty factors is tradable, and the transaction is in balance, which means each of the consequence of
uncertainties is specific, or can be offset through the transaction. In the presence of uncertainty, the rational
knowledge could be expressed as the capacity to judge and analyze the likely outcome of various behaviors,
including the possible results and the possibility of results. The uncertainty problem is expected to be an
outcome with deterministic probability distribution. As a consequence, it can be translated into a calculation
problem. In this paper, the theory of information entropy is introduced to evaluate the uncertainty of M&A
system.
2. Information power and entropy measure
As a measure of information content, entropy can be used to study the changes and uncertainties of the
system’s internal and external environment. The concept of entropy which comes from the thermodynamics
was brought forward by Germany Clausius in 1865, it reflects the degree of confusion in the micro system.
From then on, the models of entropy has been well developed and widely used.
For a set A = (x1, x2 ,...} and a set B={y1，y2，...}，where X and Y are random variables, A and B have
intersection with some constraints between the two sets. The information contained in the set A and B can be
measured through the probability distribution function P (X) and P (Y), and the conditional probability
distribution function can be expressed as P (Y | X). The entropy for X is:
H ( X ) = − P ( xi ) log P ( xi )
(1)
∑
i
The conditional entropy of the average amount of information about X provided by Y can be expressed
as:
H ( X ; Y ) = −∑∑ P ( xi , y j ) log
P ( xi | y j )
(2)
P ( xi )
For any k, if an estimated value Q has QK(X|Yk) ＝ P(X|zk), then it indicates that the prediction is in
line with truth. When all QK (xi | yk) ∈ (0,1) , it indicates that this prediction is a determined case.
Generalized information measure can be measured and expressed as:
j
I ( xi ; y k ) = log
i
Q ( xi | y k )
Q ( xi )
(3)
When Q(X) is determined, the predictive value of Q(X|yk) is more closer to the truth, and the greater the
amount of information would be. After averaging I(X；yk), we can obtain mutual probability prediction
information:
Q ( xi | y k )
(4)
I ( X ; Y ) = ∑∑ P( xi , y k ) log
Q ( xi )
k
i
Generally, P(xi) and P(xi| yj) are unknown. What we can do is to judge if Q(xi) and Q(xi| yj) are truth
based on the experience and semantics. Therefore, we have to use the probability logic in lieu of the
probability. If and only if the truth of xi occurs, expression (4) can be extended:
Q( x i | y j _ is_true)
Q( xi | A j )
Q( A j | xi )
(5)
I ( xi ; y j ) = log
= log
= log
Q( xi )
Q( xi )
Q( A j )
Expression (5) shows that: The smaller the transcendental logic probability Q (Aj) and the greater
the posterior logic probability Q (Aj | xi), the greater the amount of information. In the contrary, the
amount of information is smaller, or even negative, and the statement is more vague.
546
3. The entropy evaluation of the M&A transaction system’s uncertainty
System uncertainty can be evaluated from the following aspects: (i) the uncertainty of time. To predict
the future event, the historical records should not be ignored. (ii) the uncertainty of the semantics itself. The
understanding of the concept and rules might result in different uncertainty. (ii) The uncertainty resulted by
the nonlinear interaction between the elements both in inner system and the environment.
From the analysis of M&A market, there are a lot of uncertainties in M&A transactions system. For a
simple case study, some factors are selected and formed a tree like diagram as shown in the Figure 1 and
Table 2. In order to facilitate the calculation, we have directly given the probability which uncertainty
variable may happen (information content) listed in Table 3:
M & A transactions
uncertain system
The main bodies of M &
A transactions
Trading environment
M & A market
Market Order
Market Structure
Supervision environment
Social environment
Financing
Negotiation
Decision-making
Figure 1: The schematic diagram of M&A transaction uncertain system
Table 2: The factors hierarchy of M & A transaction uncertainty
The mai n
bodi es of
t r ansact i on
( X)
The M&A
t r ansact i on
syst em’ s
Tr adi ng
uncer t ai nt y envi r onment
( Y)
M& A
mar ket ( Z)
P1,P2,P3,P4
Deci si onmaki ng( Xx)
Board of Directors,Shareholders,Trade
unions, Individual
Negot i at i on( Xy)
The structure style, Price, Ownership, P5,P6,P7,P8
Location
Fi nanci ng t o
pay( Xz)
Cash, Debt financing, Securities,
Other ways
Soci al
envi r onment ( Yx)
Local governments, Institutions,
Public opinion
Super vi si on
envi r onment ( Yy)
Antitrust, Trade regulation, Judicial
decision
Mar ket
St r uct ur e( Zx)
Intermediaries, Investment banks,
Consultants, Competitors
Mar ket Or der ( Zy)
Purpose, Disclosure of information,
Synergies
P9,P10,P11,P12
P13,P14,P15
547
P16,P17,P18
P19,P20,P21,P22
P23,P24,P25
Table 3: The uncertainty probability of M & A transaction system
P1
P2
P3
P4
P5
25%
20%
10%
5%
30%
P6
P7
P8
P9
P10
50%
40%
10%
20%
10%
P11
P12
P13
P14
P15
20%
15%
20%
25%
25%
P16
P17
P18
P19
P20
10%
20%
30%
30%
5%
P21
P22
P23
P24
P25
15%
30%
5%
30%
30%
4. The comprehensive evaluation of M & A system’s uncertainty
Suppose management activities: T1, T2,…, Ti,…, Tn. Subsystems or departments constitute a concerted
activity set: [S1,S2,…, Si,…, Sm], so the department coordination matrix as follows:
⎡ A11
⎢A
Aij = Ti , S j = ⎢ 21
⎢M
⎢
⎣ An1
[ ] [
A12 L L A1m ⎤
A22 L L A2 m ⎥⎥
M
M M
M ⎥
⎥
An 2 L L Anm ⎦
]
(6)
After evaluate information entropy of the various events, in order to assess the uncertainty of the whole
system and further assess the ordering of various subsystems, we introduce the evaluation value of the
orderliness unification.
Assuming entropy function H has a vector with variable X, Y and Z. Elements of E are defined as the
complexity three-dimensional vector: ei=(xi, yi, zi), or two-dimensional vector: ei=(xi, yi), or one-dimensional
vector: ei=(xi).
If ‖ei‖: E→H is expressed as information entropy of the complexity of vector ei, then ‖ei-ei+1‖is
called the E value, and the distance is[3]::
d (ei , ei +1 ) = ( xi − xi +1 ) 2 + ( y i − y i +1 ) 2 + ( z i − z i +1 ) 2
(7)
Corresponding to the M&A system tree structure, Bi+1 produces the amount of entropy information after a
structure Bi. The interaction of the various synergies exists in the organizational system. The definition of
entropy vector can be obtained from the synergistic information force field and its components:
w
m
X
= ∑ Z xi
i =1
e xi
2
− z xi
(8)
2
Table 4, Table 5 and Table 6 list the evaluation of the M&A subsystem transactions’ uncertainty, as well
as the calculations of each component’s information entropy.
Tabl e 4: The t he uncer t ai nt y scal e cal cul at i on of t he M & A t r ansact i ons' mai n bodi es
Decision-making
Negotiation
Financing to pay e(Xxi) e(Yxi) e(Zxi)
(Xx)
(Xy)
Structure
Board of Directors 0.25
The mai n
style
bodi es of
0.20 Price
t r ansact i on Shareholders
Subt ot al
(Xz)
0.30 Cash
0.50
Debt
financing
H(Xx) H(Yx) H(Zx)
e(x)
W(x)
0.20 0.1584 0.147 0.1575 0.2674 0.03403
0.10
0.159 0.1596 0.12506 0.2577 0.02818
Trade unions
0.10 Ownership
0.40 Securities 0.20 0.1297 0.1575 0.1575 0.2577 0.03213
Individual
0.05 Location
0.10 Others
0.15 0.0899 0.0857 0.14696 0.1924 0.01825
0.60
1.30
0.65 0.5371 0.5498 0.58703 0.9753 0.1126
548
Tabl e 4: The t he uncer t ai nt y scal e cal cul at i on of t he M & A envi r onment
Supervision
Social environment
e(Xyi)
e(Yyi) e(Zyi)
environment
(Yx)
Local government
Tr adi ng
envi r onment
Institution
Public opinion
Subt ot al
0.20
(Yy)
Antitrust
0.10
H(Xy)
H(Yy) H(Zy)
0.15544801 0.1297
e(y)
W(y)
0.2024 0.02016
0.25
Trade
regulation
0.20
0.1596993
0.159
0.2254 0.0254
0.25
Judicial
decision
0.30
0.1596993 0.1505
0.2195 0.02404
0.60
0.47484661 0.4392
0 0.6473 0.0696
0.70
Tabl e 5: The t he uncer t ai nt y scal e cal cul at i on of t he M & A mar ket
Market Structure(
Market Order
e(Xzi)
e(Yzi) e(Zzi)
(Zx)
(Zy)
H(Xz)
H(Yz) H(Zz) e(z)
W(z)
Intermediaries
0.30 Purpose
0.05 0.15973827 0.0857
0.1813 0.01369
M& A
mar ket
Investment banks
0.05
Consultants
Competitors
0.15
0.30
0.80
Subt ot al
Disclosure of
information
0.30
Synergies
0.30
0.65
0.0752575
0.155
0.1723 0.01166
0.13631226 0.155
0.15973827
0.53104631 0.3956
0.2064 0.02113
0.1597
0
0 0.7197 0.04648
5. Conclusion
The nonlinear interaction between the system and the elements as well as interaction between the
element subsystems and environments are keeping change. On the one hand, participants constantly sum up
experience in order to reduce or even eliminate uncertainty in the process of M&A transactions; On the other
hand, with the creation of new rules, the system would result new uncertainties. It is this kind of interaction
between the orderliness and uncertainties that makes the M&A transactions complex and diverse. From the
viewpoint of the entropy information theory, the contribution of information entropy reduction to the system
would give rise to a decrease of the uncertainty, the greater the value of information entropy is, the more
undetermined the system would be. Therefore, it is important to reduce the uncertainty for the M&A
transaction system to develop towards an orderly, steady and efficient direction.
6. References
[1]. Song Hualing, Evaluation for the Complexity of Enterprise System Management, Economic and Management
Press, 2004
[2]. Li Hongquan, Ma Chaoqun, Complexity and Risk Management of Financial Markets, Economic Science Press,
2006
[3]. Hong Hanpo, Decision-Making theory of Entropy and Applied Research of Strategic M&A of Chinese Enterprises,
Intellectual Property Press, 2004
[4]. Wang ZhaoHong, application study in the investment decision of the securities of entropy theory, meteorological
institute of Nanjing Press, 2003.
[5]. Patrick. A. Gaughan, Mergers, Acquisitions and Corporate restructuring, translated by Zhu Bao-xian, et al, China
Machine Press, 2004, p. 109.
[6]. John. Holland, the emergence - from chaos to order, translated by Chen Yu, et al, Shanghai Science and
Technology Press, 2001, p. 265.
549
550
AUTHOR INDEX
A. Brabazon
A. Jaapar
A. Rauf Baig
A.S. Ali
Abbas Vafaei
Abdul Razak Hamdan
Abdullah Mohd Zin
Abdullah S. Al-Mudimigh
Ahmad Adel Abu Shareha
Ahmad Faraahi
Ailing QIAO
Alaa M. Wadi
Albert Y.C. Fong
Ali Munir
Amir Khademhoseini
AmirMasoud Rahmani
Amr Ahmed
Anas F. Bayan
Ankit Charls
Ankit Charls
Anurag Dixit
Anwar M. Mirza
Ardeshir Bahreininejad
Arfan Jaffar
Arshad Ali Shahid
Ashfaq H. Farooqi
Aws Alaa Zaidan
Ayad Ahmed Yass
Ayyappan Palanissamy
Ayyaz Hussain
Azizah A. Manaf
Azuraliza Abu Bakar
467,
285,
316, 430,
355,
316,
504
540
290
540
66
476
487
424
140
321
311
174
163
290
66
419
461
326
152
158
61
435
321
435
400
290
360
360
260
430
370
467
B. PARATHASARATHY
Bhabani Sankar Prasad Mishra
Biju Issac
Bilal Bahaa Zaidan
Bi-wu Xiao
338
221, 536
147
360
211
C.P. Chen
Camelia Elena Ciolac
Camelia Ratiu-Suciu
Catherine Weddum
Cha Narisu
Changbing Tong
Changchun Li
Changi Nam
134, 163
497
497
275
231
545
179
301
Dai Hao
Darryl K Forsyth
Deepak P C
Denis Mušić
Devi Prasad Bhukya
Dhanesh Ramachandram
Duraiswamy K
16
140
408
E.M.A. Zawawi
Edwin Y.S. Sim
Emilyn B. Escabarte
540
163
206
F.Y.C. Albert
Fahriana Abdul Karim
Fang Zhu
Faranak Mohsenzadeh
Farrukh Saleem
Fasee Ullah
Fernando Almeida
Florica Luban
134
113
1
444
424
244
280
497
Gabriel F. Villorente
Gu Liu
Guang Xu
Guanzhong Li
206
27
27
509
H.Mirsalari
Habibollah Haron
Hamidah Jantan
Hao Yan
Hassan Abolhassni
Haytham Mohtasseb
Hejab M. Al Fawareh
Hiren H D Sarma
Homayoun Motameni
Hong An
Hongming Li
Hongpeng Wang
Hossein Rajabalipour Cheshmehgaz
Huan Wang
Huei-Tse Hou
Jarrod Trevathan
Jasmin Azemović
Jen-Teng Tsai
Jia-Nan Yen
Jiannong Cao
Jin Deqiang
Jinchuan Ke
Jisoo Nam
Jonas Talon
Jose Cruz
Jose Oliveira
Juggapong Natwichai
39
106
482
83
K Rajani Kanth
551
195
118
476
179
321
461
520, 526
414
419
27
44
44
118
123
456
6, 254
83
96
96
44
21
545
301
275
280
280
514
190
K Venkatramaiah
K. Arulanandam
Kalpana Sharma
Kenji Imou
Khairulmizam Samsudin
Khalil El-Khatib
Kim Dong Yoon
Kuo-En Chang
Laiha Mat Kiah
Legesse Zerubabel
Lei Guo
Leqiu Qian
Li Bin
Li Xianghong
Liana Khamis Qabajeh
Lingling Zi
Liqiang He
Lloyd R Jenkins
Luisito Tabada
M. Arfan Jaffar
M. Halaiyqah
M. O'Neill
M. Yasir Khan
M.Mrunalini
M.Sulleman Memon
Ma Mingkai
Maheyzah Md Siraj
Manadava Rajeswari
Manjur S. Kolhar
Manzoor Hashmani
Mark Oliver L. Ouano
Mary Grace C. Dy Jongco
Masoud Goli
Maya Ingle
Mazdak Zamani
Mazura Mat Din
Md. Asri Ngadi
Megat Norulazmi Megat Mohamed
Noor
Mehdi Dehghan
Mehdi Rahmati
Mehdi Vojdani
Mikiyas Teshome
Ming Li
Mo Siquan
Mohamad Shanudin Zakaria
Mohammad Moustafa Qabajeh
Mohammad Ramzan
Mohammad Reza Meybodi
Mohd Aizaini Maarof
Mosleh AbuAlhaj
Mouhcine Guennoun
M-Tahar Kechadi
Mu Xu
482
338
414
129
113
265, 270, 275
12
456
50
12
44
123
90
39
50
472
231
106
295
316, 430
226
504
169
190
348
39
395
140
226
348
206
206
321
76
370
385
385
531
365
306
365
12
129
21
487
50
400
118
390, 395
226
265, 270, 275
504
27
552
Muhammad Asif
Muhammad Ibrahim
Muhammad Ishtiaq
Muhammad Tahir Qadri
Myungbae Yeom
332
244
430
169
301
Nan Wang
Navneet Goyal
Nhien An Le Khac
Niaz A. Memon
Niaz Memon
Noppamas Pukkhem
Norazwin Buang
Norhazilan Mohd. Noor
Norizan Mohd Yasin
285, 311
482
504
348
348
71
487
385
355, 360
O. Abouabdalla
Omid Gholami
226
419
P.C. Saxena
P.K. Singh
Pierre Tagle
Ping Yao
Ping-bo Liu
Poonam Goyal
Preeti Paranjape
Punam Mishra
Puttamadappa C
61
152, 158
295
27
211
482
450
536
414
Qiusheng Zhang
545
R. Sureswaran
R.A.Khan
R.Madhav Prashanth
Rabiah B. Ahmad
Rafia Khalid
Rahmat Budiarto
Rashidah Kadir
Rodel Balingit
Rostam Mozafari
226, 326
216
184
370
169
380
390
6, 254
444
S Ramachandram
S. Jagannatha
S. R. Biradar
S.Akbarpoor
S.Amjadi
S.K.Tiong
S.K.Tiong
S.M.Hosseini
S.P. Koh
S.Senbaga Devi
S.Y.S. Edwin
Sai Peck Lee
Sajid Anwar
Sammer Markos
Samreen Amir
16
190
414
195
195
134
163
195
134, 163
343
134
174
400
504
332
Samsudin Wahab
Sanoop P S
Sasmita Behera
Seongcheol Kim
Seyed-Amin Hosseini-Seno
Shahab Bayati
Shahrel A. Suandi
Shaidah Jusoh
Shilpa Bhalerao
Shinya Yokoyama
Shirou Tani
Shuichi Enokida
Shui-Shun Lin
Siti Zaiton Mohd Hashim
Songyot Nakariyakul
Subhra Swetanisha
Subir Kumar Sarkar
Sudeepta Mishra
Sun Park
Suraiya Parveen
Syahrul N. Kamaruzzaman
Syed Shafi-Uddin Qadri
Valliappan Raman
Vijayaragavan S
Visanu Changniam
250
482
375
301
380
321
32
520, 526, 531
76
129
129
32
96
395
492
221
414
375
101
216
540
169
T V Suresh Kumar
T.R.Ganesh Babu
Tahir Mehmood
Tat-Chee Wan
Tayyaba Azim
Tiange Zhang
Toshiaki Ejima
Tushar Sharma
190
343
244
326, 380
435
123
32
152, 158
Umesh Deshpande
450
V.janani
V.Prasanna Venkatesh
V.Ranjana
Vahid Tabataba Vakili
184
184
184
306
Wan Azizun Wan Adnan
Wang Rui
Wayne Read
WEI Yu-wei
Weigang Hou
Wenting Han
Wenyi Liu
Wiwat Vatanawood
Wu-yi LU
553
260
408
514
113
39
6, 254
56
44
27
240
71
201
Xiaochun Xiao
Xiaodong Liu
Xiao-hong NIAN
Xingwei Wang
123
179
201
44
Yadong Meng
Yan Zhang
Yang Wenlin
Yao-Ting Sung
Ying-Shen Juang
Yong Jin Lee
Yong-min Liu
179
240
440
456
96
6
201, 211
Zahid Ullah
Zalizah Awang Long
Zeshan Hayder
Zhang Lei
Zhenhe Ma
Zhiyong Tao
Zhou Entao
Zhu Juan
Zine E.A Guennoun
Zulaiha Ali Othman
424
467
316
39
472
472
440
21
265, 270
476