THE BCG MATRIX REVISITED: A COMPUTATIONAL APPROACH

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THE BCG MATRIX REVISITED: A COMPUTATIONAL APPROACH
Although the Boston Consulting Group’s growth share matrix has been the subject of
many critiques, there has been surprisingly little empirical research that directly examines
the effectiveness of the model. The current study uses a computational model based on
Nelson and Winter’s (1982) evolutionary model of economic change to test whether
firms using BCG’s investment rules outperform firms using Nelson and Winter’s
investment rules. We found that the original BCG rules were not capable of
outperforming the Nelson and Winter rules even under the most favorable conditions.
However, we were able to use this data to construct a set of modified BCG rules that
outperformed the Nelson and Winter on almost every occasion. The implications of these
results are discussed.
Key Words: portfolio planning; simulation; agents; evolutionary economics
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The Boston Consulting Group’s (BCG) growth share matrix is one of the best known and
persistent tools in strategic management. At the height of its success between 1972 and
1982, the BCG matrix was used by around 45% of the Fortune 500 (Bettis & Hall, 1981;
Haspeslagh, 1982). The JSTOR database reports that no fewer than six major journal
articles were authored on the BCG matrix in 1982.
However, in the first decade of the 21st century, the BCG matrix is certainly in the decline
phase of its product life cycle; perhaps qualifying for ‘dog’ status in its own terminology.
References to the BCG matrix have disappeared from graduate textbooks and academic
journals, and are slowly being phased out of undergraduate and marketing texts except,
perhaps, as historical footnotes.
There are several sound reasons for this decline, including: the model’s use of only two
dimensions (growth and share) to assess competitive position, the focus on balancing
cash flows rather than other interdependencies, the emphasis on cost leadership rather
than differentiation as a source of competitive advantage, and the poor correlation
between market share and profitability (Morrison & Wensley, 1991).
Despite the numerous theoretical critiques of the BCG model, empirical studies that
directly examine whether the BCG matrix delivers superior profitability as a portfolio
management system are surprisingly scarce (Hambrick, MacMillan, & Day, 1982;
MacMillan, Hambrick, & Day, 1982; Armstrong & Brodie, 1994). In fact, Armstrong and
Brodie (1994) report they could find only one empirical study prior to their own that
directly tested whether firms adopting the BCG matrix outperformed those that did not.
Furthermore, while 66% of students familiar with the BCG matrix thought it would
produce better decisions under certain circumstances, the same students were unable to
describe any such circumstances (Armstrong et al., 1994). The primary purpose of this
paper is to take up this challenge and discover the circumstances under which the BCG
matrix works as a comprehensive resource allocation system.
A computational model is used in the current study to analyze the efficacy of the BCG
matrix under various contingencies. Specifically, we test different formulations of the
matrix’s investment rules against a benchmark investment strategy using Nelson and
Winter’s evolutionary economic model (Nelson & Winter, 1982). Using a technique
pioneered at the RAND corporation (Bankes, 1993), the relative performance of the
various BCG strategies was measured across several environmental contingencies to
discover regions where the BCG rules were dominant.
A secondary purpose of this study was to make a contribution to methodology by
demonstrating that any rule-based system can be tested using a computational approach.
Despite calls for a model-based organization science (McKelvey, 1997), computational
methods have not been widely adopted in strategic management research. We hope that
our approach will demonstrate that such studies can produce valid insights that can be
easily replicated and extended.
We begin the paper with an overview of the BCG matrix incorporating a discussion of
the theory underlying the BCG matrix leading to the development of several hypotheses.
This is followed by a description of the computational model, the experimental design,
and results. We conclude with a discussion of the findings and the implications of the
study for the ongoing relevance of the BCG matrix and future research.
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THEORY AND HYPOTHESES
Only three years after the foundation of The Boston Consulting Group consultancy,
Seymour Tilles outlined the main ideas of portfolio planning (Tilles, 1966). He labeled
the investments by divisions based on cash returns as “piecemeal” and called for a more
“strategic” resource allocation methodology. In his view, a company was seen as a
portfolio of businesses with a variety of risk and opportunities. Bruce Henderson first
outlined the shape, basic assumptions and key features of a ‘growth share’ matrix (see
Table 1) that would allow for a more strategic resource allocation (Henderson, 1968,
1973). In the following years, the BCG matrix received a lot of attention from academics
and managers and 1975, the growth share matrix had become one of the most commonly
used techniques in corporate planning (Lorange, 1975). An empirical study conducted by
Morrison and Wensley (1991) revealed that no other matrix was as widely utilized as the
BCG matrix. The proliferation of portfolio planning as a resource allocation tool was also
accelerated by competition from the likes of McKinsey, and Arthur D. Little who, in
conjunction with their corporate clients, developed matrices of their own.
Table 1. Prescriptions of the BCG Growth Share Matrix
Category
Star
Growth
High
Share
High
Cash
Cow
Low
High
Question
Mark
High
Low
Dog
Low
Low
Prescription
The main focus of star businesses is to protect their market shares and
thus get a bigger portion of the market growth than competitors. Star
businesses will ultimately turn into cash-cows
Characterized by high profit and cash generation. The remaining cash
after covering costs to run the business and to protect the share in a
mature market should be redistributed to other businesses.
These units have high cash needs and firms should therefore do whatever
is necessary to increase market share or divest quickly.
Often generate poor profits and cash needs are frequently higher than the
cash that is generated. To improve the overall performance, firms should
minimize the proportion of their assets that remain in this category by
focusing on a specialized segment, harvesting by cutting costs and
maximizing cash flow by divestment or liquidation.
Previous research
On the basis of his survey, Haspeslagh (1982) estimated that by 1979, some 36% of the
Fortune 1000 and 45% of the Fortune 500 industrial companies had introduced the
approach to some extent and nearly all of them believed that the new tool had a “positive
impact on management” (p. 67). Hambrick & MacMillan (1982) and Hambrick et al.
(1982) used PIMS data to confirm that the four business categories in the BCG matrix
had different tendencies to generate or consume cash. The study, however, did not
confirm the BCG’s advice that dogs should be promptly harvested, divested or liquidated.
The average dog generated even more cash than the cash needs of the average question
mark business.
Armstrong and Brodie (1994) provided a test on the effect of the BCG matrix on business
performance. In a series of laboratory experiments, Armstrong and Brodie tested whether
a sample of over 1000 practicing managers might be misled by portfolio methods when
making investment decisions. They discovered that information about the BCG matrix
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increased the subjects' likelihood of selecting a project that was clearly less profitable. Of
subjects exposed to the BCG matrix, 64% selected the unprofitable investment. Of
subjects who used the BCG matrix in their analysis, 87% selected the less profitable
investment. Armstrong and Brodie (1994) state: “Portfolio matrices have been widely
prescribed…yet they have not been tested in a scientific manner” (p. 91).
While Armstrong and Brodie’s results are very interesting, the study itself has several
limitations. First, the study only focused on a single investment decision (i.e. would
participants forego a profitable investment in a business unit that held ‘dog’ status). This
is hardly a complete test of the BCG model. For instance, in a corporate context, the
funds foregone may have been allocated to a business unit with even greater profit
opportunities. We believe such system-wide studies have not been attempted because of
the complexities inherent in gathering data on company decisions. Even determining if
companies are actually following BCG rules is problematic. No doubt, individual
companies tailor the use of the model to their own circumstances, combining it with other
decision-making tools as appropriate. Disentangling these effects would be no mean feat.
Hypothesis development
The BCG matrix has not lost popularity because it has been shown to under-perform rival
theories1, nor has it been shown to perform especially well in particular situations. In this
paper, we endeavor to conduct a systemic test of the BCG matrix as a portfolio
management system. Such studies are important if strategic management is to progress as
a science rather than by intuition (Hubbard, Vetter, & Little, 1998). Simply put, this
means discovering whether a sample of companies using the matrix’s recommendations
can outperform a sample of companies that uses some other resource allocation approach.
If success is anyway related to the scale and timing of investment flows, then any scheme
that pools and redistributes resources across multiple business units (such as the BCG
matrix) should outperform decentralized business units. As such, we expect that:
H1: Firms using the BCG matrix will outperform decentralized firms
Henderson’s contribution relied on two key theoretical assumptions. The first assumption
focused on the relationship between market share and the cost position of a business. Unit
cost was assumed to fall logarithmically with experience, and experience was assumed to
be a function of cumulative output. Thus, it followed that a market share leader should
have more experience, lower costs, and higher profits. It thus follows that:
H2: The BCG matrix should perform better as experience curve effects increase
Henderson’s second assumption relied on the relationship between stages in the product
life cycle stage and the cash needs of the business. Cash cows and dogs, being in the
mature stage of the product life cycle, were assumed to have low investment
requirements, whereas stars and question marks had high cash needs. The traditional
1
Although recommendations from a generalized (non-BCG) portfolio matrix were found
to under perform the stock market (Slater & Zwirlein, 1992)
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demarcation point to classify as high growth was a sales growth of 10% or more (Majluf
& Hax, 1983). Similarly, a relative market share of 1.0 or more denoted the delineation of
high and low relative market share. Assuming that these points were not arbitrarily
selected, we expect that:
H3: The best performance of the BCG matrix should occur at the traditional demarcation
points
In the traditional BCG logic, dogs should be promptly divested. However, we have
already seen that dogs can produce positive cash flow for a firm (MacMillan et al., 1982).
Morrison and Wensley (1991, p. 110) refer to the low share – low growth box as “pets”
(instead of “dogs”), which are “nice to have” because they deliver a constant, though
modest, flow of funds or contribute synergistically to other units. This suggests that:
H4: BCG firms will perform better if they harvest rather than divest dogs
MODEL
A computational model (or simulation) is a dynamic representation of reality used to
educate, entertain or explain. Simulation is often used when real-life experiments are
costly, time-consuming or dangerous. In other cases, such as economic policy and
warfare, real-life decisions are irreversible (and consequential) ensuring that decisions
cannot be re-run after an event. In these cases, simulation provides an opportunity to test
alternative theories and courses of action in a world without consequences.
The use of a computational model allows the researcher to create multiple microworlds
upon which to experiment. “The researcher is able to control all the variables under
consideration, manipulate them to uncover their effects on dependent variables over time,
examine all possible combinations and interactions of variables, and examine the
dynamic effects of the variables” (Lant, 1994, p. 144). In addition, input, process and
output variables can be measured with a high degree of accuracy and reliability. Thus, the
messiness of the real world is replaced by a pristine artificial world where the
experimenter has a high degree of control over the interactions that occur.
A simulation is also capable of producing novel theoretical insights because it is possible
to run the simulation across many different scenarios that may not have emerged in the
physical world. It may be possible that patterns and regularities will emerge from a
simulation study that have not been observed or recognized as a significant form of
behavior in the physical world. The fact that computational models have not been widely
used in strategic management to test existing theoretical propositions provides the overriding rationale for this study.
The BCG matrix is well-suited to exploratory policy modeling (Bankes, 1993; Phelan,
2004). Exploratory policy modeling seeks “…to discern patterns of outcomes across an
ensemble of plausible models” (Bankes, 1993: 444). The method calls for a number of
models to be tested because researchers are typically unclear about how the model might
behave under different contingencies or different operationalizations of key associations.
The use of computational methods forces the researcher “...to be precise about the
relationship among entities, to make implicit assumptions explicit, and to describe in
detail the mechanisms by which entities and relationships change” (Carley & Prietula,
1994, p.3).
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Operationalization of the Matrix
A simulated economy was constructed to test different operationalizations of the BCG
matrix. The equations for this economy were based on Nelson and Winter’s (1982, Part
V) model as implemented in Java by Yildizoglu (Yildizoglu, 2002, 2003).
The Nelson & Winter (hereafter NelWin) model was selected because of several
favorable characteristics. First, it conforms to Axelrod’s (1997) KISS2 principle by using
a simple model of the economy that makes its operations transparent to observers.
Second, the NelWin model is a neoclassical model, in the sense that price levels are
jointly determined by demand and supply considerations (something that is often missing
in simpler models). Finally, the model has been extensively studied and a considerable
body of work exists on its strengths and weaknesses (Andersen, Jensen, Madsen, &
Jørgensen, 1996). A detailed description of the equations underlying the NelWin model is
presented in the Appendix.
The model and investment behavior in the NelWin model had to be modified in several
ways to effectively test the BCG matrix as an investment system. The most obvious
requirement was to create a portfolio of business units (as the traditional NelWin model
dealt with only one industry). At the start of a simulation, each firm began with a single
business unit. All business units competed in the same industry, which followed the
NelWin dynamics outlined above. Every L rounds, a new industry was born and each
firm added a new business unit to compete in that industry. Thus, Kijt refers to the capital
stock of the ith business unit of the jth firm at time t. Once created, industries were never
removed from the simulation.
We believed it was important to stagger the introduction of business units because of the
underlying growth logic in the BCG matrix. If all business units were ‘in play’ at the start
of the simulation then they would all move through the various stages of the life cycle at
roughly the same time. This is not a good test of the underlying logic that cash-rich
mature businesses should fund cash-strapped growth businesses. The staggered approach
ensured that there would be a true portfolio of business units at different stages in the life
cycle.
The second requirement was to alter the investment behavior of the firm to incorporate
BCG investment rules. At the most basic level, we understood that cash cows should be
used to fund the growth of stars (and possibly question marks) and that dogs should be
left to languish but the challenge was to convert these general prescriptions into
actionable items in a NelWin setting.
The process was divided into four steps:
Step 1: Aggregate profits
2
KISS – Keep It Simple, Stupid. A reference to the fact that excessive complexity in a model diminishes, rather than enhances,
insight.
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All capital decisions are fully centralized in BCG firms. In contrast, firms following
traditional NelWin rules are fully decentralized, with all decisions determined at the
business unit (BU) level.
Step 2: Determine BCG Status of each unit
The classical BCG approach suggested a growth of 10% and a relative market share of
1.0 as the cutoff points in the matrix (Day, 1977). One of the objectives of the study was
to consider the effects of experimentally manipulating these cutoff points. Accordingly,
business units were classified by whether they exceeded or fell below the cutoffs for
growth (gcutoff) and relative market share (scutoff) used for that particular run. The exact
ranges used for these cutoff parameters are described in the method section below. Stars
exceeded both cutoffs, cash cows only exceeded the share cutoff, question marks only the
growth cutoff, and dogs failed to exceed either cutoff.
Step 3: Determine investment requests
Business units submitted their requests for funds to the corporate headquarters according
to the NelWin investment rules (see Appendix). However, the new investment received
by each business unit was determined at the corporate level according to their BCG
status.
Step 4: Allocate funds.
The total funds available to the corporation were equal to (1+b) times the combined
corporate profits, where b was the same bank lending factor used in the traditional
NelWin rules. If corporate profits were less than zero then no external funding was
available.
Perhaps the most critical decision in the whole computational model was determining
how to apply the BCG rules to fund allocation (see Table 2). A system of priorities was
developed. The business units with the highest priority were funded first. If insufficient
funds were available to meet all requests then the funds were split proportionally among
all business units at that priority level according to the size of their request. If funds
remained after all requests were fulfilled at a particular priority level then the next
priority level was considered.
Table 2. Priority Levels in Fund Allocation
Priority
Level
Action
1
Pay depreciation for cash cows
2
Fund stars
3
Fund question marks
4
Fund new investment for cash cows
For instance, the highest priority was assigned to paying depreciation for cash cows.
Without an allowance for depreciation, the capital stock (and free cash flow) of cash
cows would fall to zero over time. Maintaining the capital stock of cash cows was thus
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crucial to ensuring cash generation for the rest of the business. Once these requests were
met, a firm could then consider financing stars, question marks, and cash cows – in that
order. The long-standing issue of how to treat question marks in the matrix was resolved
by allowing them to be funded only after all star requests had been fully met. Cash cows,
as mature businesses, were ranked even further down the priority list.
Dogs were treated in one of two ways, depending on the experimental treatment. In the
first case, dogs were harvested. They had no access to new capital and their existing
capital was allowed to depreciate at the standard depreciation rate. Dogs were allowed to
enter and re-enter dog status and could be re-classified if their growth rate or share
improved. In the second treatment, dogs were divested immediately upon entering dog
status, with their capital assigned to the general corporate pool for reallocation.
The third requirement in operationalizing the matrix was to add an option for experience
curve effects into the model. We felt that the development of the BCG matrix was heavily
influenced by BCG’s earlier experience curve logic and that its effectiveness may require
that an industry display experience curve effects.
Following the traditional formulation of the learning curve (Andress, 1954; Hirschmann,
1964) the cost co-efficient (c) was calculated according to the formula:
ct = c 0 X b
(10)
where c0 is the initial cost parameter, X is the cumulative output of the business unit to
time t, and b equals log (learning rate)/log 2. A learning rate of 1 represents constant
returns to scale and no experience curve effect, while a learning rate of 80% would
represent an 80% decline in initial costs with every doubling of volume.
METHOD
The computational model described in the previous section was implemented in the Java
programming language using the Java 2 Software Development Kit v1.4.1 and the RealJ
development environment. Additional random number generation support was obtained
from CERN’s Colt open source library for high performance scientific and technical
computing in Java.
Design
This section outlines the design of experiments conducted with the simulation model. The
primary variable of interest, or independent variable, was the type of investment
behavior. In each run of the simulation, half of the firms used NelWin investment rules
while the other half used BCG investment rules.
Several contingency factors were varied in the model, including: experience curve
effects, investment inflation, treatment of dogs (harvest or liquidate), growth cutoff, and
share cutoff. A full factorial design was utilized using two or three levels for each
contingency factor (see Table 3 for a complete list of factors and their levels). This
generated 35 x 22= 972 experimental conditions. Each of the 972 experimental
conditions was tested 20 times generating 19,440 runs.
Table 3. Factors and levels
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Factor
Levels
Dog treatment (dog)
2 (harvest, liquidate)
Lag between new business
units (lag)
3 (every 3, 5, 7 rounds)
Learning rate (r)
3 (1, .9, .8)
Growth cutoff (gcutoff)
2 (0.05, 0.10)
Share cutoff (scutoff)
3 (1.0, 0.75, 0.5)
Elasticity (η)
3 (0.9, 1.0, 1.1)
Innovation rate (invrate)
3 (0.00, 0.01, 0.02)
Procedure
The parameters of each experimental condition were represented by a single tabdelimited line of text in the parameters file. Parameter files were generated using the
Design of Experiments module in the JMP statistics application.
At the start of each experiment, the conditions were loaded by the simulation software
and a new economy was created that was populated by fifty NelWin firms with one
business unit each. Half of these firms used standard NelWin investment rules and half
used BCG investment rules. Following Nelson and Winter’s (1982) original parameters,
each business unit started with the settings outlined in Table 4. Demand in each industry
was set at 3000 units.
Table 4. Initial Business Unit Settings
Parameter
Initial Value
Capital stock (K)
20
Cost of capital (c)
0.10
Productivity rate (A)
0.11
Depreciation (δ)
0.01
The computational model was iterated for 50 rounds on each run representing 50 years of
investment history. Each round included four phases:
1. New Industry Phase. Depending on the value of the lag variable, a new industry was
added every 3, 5 or 7 rounds. At this time, every firm received a new business unit to
compete in the new industry initialized with the values in Table 3.
2. Calculate Industry-Level Results. The industry specific results were calculated,
including supply, price, and industry growth rate.
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3. Calculate Business Unit Results. The industry level results (particularly price) were
passed to business unit in order to determine its performance. Relative market share and
BCG status were also determined at this stage.
4. Investment Phase. In the investment phase, firms added to their capital stock. Each
business unit in a NelWin firm added to its capital stock in accordance to the rules in
equation 9. All free cash flow from business units in BCG firms was pooled and reallocated to business units according to the investment rules discussed above.
Each experimental condition was tested 20 times. Following the conclusion of each
experimental run, dependent variables were calculated and outputted to a results file.
These variables included: the total profits for BCG and NelWin firms over the 50 rounds
of the simulation (All_P), the aggregate profit for BCG and NelWin firms in the final
round of the simulation (Last_P), the total ending capital for NelWin and BCG firms
(End_K), and the number of industries in which each firm competed at the end of the
simulation (i.e. business units with K>0). A fifth variable, return on capital (ROK), was
calculated by dividing final profit by ending capital. Comparisons were then made
between BCG and NelWin firms on all dependent variables by dividing the BCG value
by the NelWin value and subtracting 1 to indicate the percentage that the BCG was above
or below the NelWin value.
RESULTS
Descriptive statistics and Pearson correlation coefficients are presented in Table 5. The
BCG results are presented as a percentage of the NelWin results because profit levels
differ depending on the growth, innovation level, and number of business units in a
particular simulation. A score of 0% would indicate that the BCG firms averaged the
same level of profit as the NelWin firms. A score of -20% would indicate that the BCG
firms scored 20% lower than the NelWin firms. The table also includes the percentage of
cases in which the BCG firms outperformed NelWin firms. In general, the NelWin firms
managed to have a higher level of profit, both overall and in the final round. In fact, BCG
firms only outperformed the NelWin firms in less than 4% of cases. The NelWin profit
performance was also associated with much higher capital levels and a presence in more
industries. The BCG firms, on the other hand, were highly dominant in the return on
capital (ROK) category.
The conclusion from this information is that, in the aggregate, the BCG firms performed
very poorly vis-à-vis the NelWin rules in maximizing profit. On the other hand, they do
an excellent job of maximizing the profit per unit of capital utilized. Ceteris paribus,
higher economic profits are preferable to higher capital efficiency. The BCG matrix does
not appear to support the attainment of this objective. Hence, we find little support for
hypothesis 1 (that BCG firms should outperform NelWin firms).
Table 5. Descriptive Statistics and Pearson correlation coefficients (n=19,440)
Variable
Mean
SD
Max
Min
%>0
1. Total Profits
-54.5%
27.5%
2.7%
-89.5%
3.7%
2. Ending Profit
-60.0%
32.6%
8.5%
-97.5%
13.9%
0.98
3. Ending capital
-70.3%
34.2%
4.7%
-99.4%
7.4%
0.90
10
1
2
0.89
3
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4. Business units
5. Return on capital
-35.8%
36.5%
0.0%
-90.0%
-
0.52
0.49
0.75
332%
777%
7427%
-35%
78.7%
-0.12
-0.02
-0.33
-0.49
The dependent variables were then regressed on the independent variables to determine
the effect of key contingencies on the model outcomes. The results of this analysis are
presented in Table 6 using scaled estimates of the regression coefficients. These scaled
estimates enable us to compare the relative effect size of each variable directly as each
change of in the level of the independent variable changes the dependent variable by the
scale estimate. For instance, changing the lag (L) variable from 3 to 5 (or 5 to 7) years
results in a change in the all profit variable of 3.1%. Thus, a change in lag from 3 to 7
years (i.e. two levels) would place the BCG total profits 48.3% lower than those of the
NelWin firms (rather than the average value of 54.5% lower).
Table 6. Scaled Regression Estimates
Variable
Total Profit
Ending Profit
Ending
Capital
Business units
Return on
capital
Intercept
-54.5%
-60.0%
-70.3%
-35.8%
331.8%
Dog Treatment
-16.1%
-18.0%
-26.5%
-35.8%
331.1%
Growth Cutoff
2.4%
2.8%
1.2%
-2.6%
114.4%
Share Cutoff
0.0%
0.0%
0.0%
0.0%
0.0%
Learning Curve
23.8%
27.9%
18.0%
-4.2%
176.2%
Innovation Rate
0.0%
0.0%
0.0%
0.0%
0.0%
Elasticity
5.1%
5.1%
1.9%
-2.3%
120.4%
Lag
3.1%
5.3%
0.7%
-0.1%
188.6%
2
0.88
0.83
0.78
0.97
0.29
R
Note: all non-zero values are significant at p<0.001
While lag, elasticity, and growth cutoff had some effect on performance, the dominant
variables were the treatment of ‘dogs’ and experience curve effects. By choosing to
divest rather than harvest dogs, BCG firms decreased their profit and capital stocks while
greatly boosting their return on capital. This supported the predictions of hypothesis 4
(that harvesting dogs was better than divesting them). Curiously, as the experience curve
effect declined (i.e. approached 1), the profit differential between BCG firms and NelWin
firms narrowed. This was the opposite of what was predicted in hypothesis 2. This may
be because BCG business units tended to fall into dog status when a NelWin firm had an
early lead in an experience affected industry. This resulted in an early exit with a
concomitant loss of profit and capital.
Hypothesis 3 also received mixed support. Changing the share cutoff had no effect on
performance, while increasing the growth cutoff tended to improve performance
somewhat. However, the growth effect was nowhere near strong enough to lift BCG
performance to the level of NelWin firms.
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From these results, it is clear that when BCG firms do choose to compete, they perform
much better than NelWin firms (as measured by return on capital). The problem is that
BCG firms tend to underinvest in or even divest dogs while they are producing positive
profits. In the divest condition, dogs are also divested the instant they become dogs, thus
not allowing for any reversion to a more favorable state. Therefore, as predicted by
previous studies, the BCG rules force firms to forego potential profit opportunities in dog
industries. In fact, BCG firms have less than 30% of the capital of NelWin firms on
average (and less than 4% of NelWin capital when in the divest condition).
Model 2
On the basis of these results, it was decided to modify the BCG rules in an attempt to
produce better profit results, while attempting to maintain a respectable return on capital.
Two changes were made to the model. First, every BCG business unit attempted to meet
its investment requirements from its own funds. If excess funds were available then these
were made available to the corporate center for redistribution to business units who were
not able to meet their funding requirements. Funds were then allocated according to the
rules established in the first model. Second, dogs were always and only divested if they
were making a loss (defined as price below unit cost). Profit making dogs were retained
in Model 2 and could be re-classified to other categories if they met the necessary
conditions.
The results of these two relatively simple changes are displayed in Tables 7 and 8. On
average, the BCG profit performance jumped to 17% above the combined profits of the
NelWin firms (from 54% below NelWin combined profits in Model 1). BCG firms also
outperformed NelWin firms in over 90% of the trials and always had more capital than
NelWin firms. This success was offset by declining returns on capital, where BCG firms
averaged 25% less than NelWin firms.
The correlation matrix also shows some interesting reversals. Return on capital went
from being negatively associated with profits and the number of business units in Model
1 to a positive association in Model 2. Ending capital also went from a strong association
with ending profit in Model 1 (r=0.89) to a weak association (r=0.12) in Model 2.
Table 7. Descriptive Statistics and Pearson correlation coefficients (Model 2)
Variable
Mean
SD
Max
Min
%>0
1
2
3
1. Total Profits
17.4%
12.4%
33.1%
-4.6%
88.9%
2. Ending Profit
12.4%
23.7%
34.8%
-60.6%
85.2%
0.86
3. Ending capital
53.0%
20.3%
120.6%
18.9%
100.0%
0.09
0.12
4. Business units
-1.9%
5.2%
0.0%
-23.5%
-
0.59
0.80
0.23
5. Return on capital
-25.8%
16.5%
-10.5%
-73.1%
0.0%
0.74
0.88
-0.35
4
0.68
The regression analysis indicates that the learning curve (or experience curve) was the
most influential factor in Model 2. The sign was also in the expected direction. As the
learning factor reduced from unity, the volume of profits and invested capital increased.
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Increased elasticity also had the anticipated effect of reducing capital and increasing
returns to capital.
Table 8. Scaled Regression Estimates (Model 2)
Variable
Total Profit
Ending Profit
Ending
Capital
Business units
Return on
capital
Intercept
17.4%
12.4%
53.0%
-1.9%
-25.8%
Dog Treatment
0.0%
0.0%
0.0%
0.0%
0.0%
Growth Cutoff
0.0%
0.0%
0.0%
0.0%
0.0%
Share Cutoff
0.0%
0.0%
0.0%
0.0%
0.0%
Learning Curve
-12.0%
-19.1%
7.2%
-2.8%
-15.6%
Innovation Rate
0.0%
0.0%
0.0%
0.0%
0.0%
Elasticity
-4.5%
-4.0%
-16.0%
-1.0%
3.9%
Lag
-1.6%
2.2%
-4.6%
2.3%
3.9%
R2
0.72
0.46
0.53
0.35
0.66
DISCUSSION
In many ways, the environment in Model 1 provided ideal conditions for the BCG matrix.
Firms produced identical products on the same demand schedule and experience curve
effects were present. Nevertheless, the BCG model failed to outperform the NelWin rules
at every contingency. As predicted by many critics of the model, firms using the BCG
rules tended to divest too many profitable business units. BCG firms were able to achieve
significant returns on capital albeit with ridiculously low levels of capital and little
diversification.
When the BCG rules were altered in Model 2 by a) divesting only unprofitable dogs, b)
allowing all business units to fund their own growth, and c) making surplus cash
available to other business units, the results drastically improved. In fact, the firms using
Model 2 rules were able to outperform NelWin firms on most occasions. This suggests
that fund reallocation among business units has the potential to outperform decentralized
fund allocation but only if profitable units are not divested. It would also seem important
for business units to fund their own growth first, and then use any surpluses to fund
deficits in other units as required.
Critics of our approach might argue that a) the environment was not ideal for the BCG
matrix or was not realistic enough, b) the competition from the NelWin investment
strategy was too tough or not tough enough, or c) the matrix was not operationalized
correctly. We believe we have performed a very good test of the BCG matrix but we
recognize it is not a definitive test. We welcome additional studies that seek to modify the
assumptions presented here and are happy to provide the code to our model to facilitate
such studies. As Sir Karl Popper argued, science proceeds by conjecture and refutation.
Critics are welcome to build new models or gather new evidence to refute our results.
However, we believe that the results pertaining to Model 1 are quite robust. Adding
additional complexity would most likely see BCG firms perform even worse. There is
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also little doubt that altering some of the BCG rules dramatically improves its
effectiveness.
In conclusion, it would seem that the original BCG matrix presented a flawed investment
strategy and deserves its relegation to the history books. Most of the problems seem to lie
with dogs, which are divested or starved of funds despite offering profitable investment
opportunities. However, with some slight changes to the investment rules, the system is
capable of outperforming a fairly sophisticated decentralized investment strategy.
Some readers may be compelled to ask, “Why are you testing a technique from the 1970s
(BCG matrix) with a model from the 1980s (NelWin)?” The BCG matrix and NelWin
model were selected primarily for their simplicity and familiarity to scholars. In addition,
the BCG matrix has proven very difficult to study in the field. This paper constitutes one
of only a handful of tests of the BCG matrix and represents the first study to use
computational models to systematically study the efficacy of a strategic investment
model. Such tests were not feasible in the past because of the lack of computer power and
user-friendly, object-oriented programming languages.
Our hope is that other theories and models in strategic management can be studied using
agent-based techniques. As we have seen, these techniques allow us to explore the
systematic effects of different model interpretations under a wide range of contingencies.
As Armstrong and Brodie (1994) state: “We believe that a primary function of
management science should be to test widely prescribed procedures” (p. 91). We believe
computational modeling has come of age and represents a promising new tool to assist
the management scientist in this quest.
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APPENDIX. The NelWin Model
Following Yildizoglu’s (2002) presentation, the aggregate model can be summarized
using four basic equations. First, each firm produces the same homogenous good with the
following production function:
Q j = Aj K j
(1)
where j is the jth firm in an economy of N firms, A is the capital productivity of the
firm, and K is the firm’s capital stock. Firms are always assumed to produce at full
capacity. The base model also assumes constant returns to scale (although this
assumption is relaxed later in the paper).
The gross profit rate on capital for the jth firm is given by:
π j = pA j − c
( 2)
where p is the market price and c is the cost per unit of capital. The cost per unit of
output will thus fall as productivity rises and will be equal to c/Aj. Price (p) is determined
by:
 Q = ∑jQj

 p = p (Q) = D
1

Q η

(3)
In equation (3), Q is the total or aggregate supply, D is the demand co-efficient, and η is
the Marshallian demand elasticity. Note, that when η=1, the price simply reflects a
constant amount of money divided equally among all supplied units. Thus, D places a
limit on the total cash available in the economy.
Finally, the gross profits of the jth firm can be calculated as:
∏ j = π jK j
( 4)
In the original NelWin model, the state of each firm changed from one time period to the
next as a result of R&D and capital investment decisions. In the current paper, we restrict
our attention to capital investment decisions only. Innovations are assumed to arrive
randomly. Each round a firm’s productivity will increase using a random uniform draw in
the range (0, invrate). With an invrate of 5%, the average firm will increase its
productivity 2.5% per round. Thus, firm performance will change as a result of both
random productivity improvements and investment behavior that changes its initial
capital stock (K0).
Investment Behavior
Nelson and Winter (1982) describe their general investment formula as:
K jt +1 = I (
Pt A jt Q jt
,
, π jt , δ ) K jt
c
Qt
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(5)
BPSPAP12482
That is, investment (I) is a function of unit cost (P/(c/A)=PA/c),market share (λ=Qj/Q),
profitability (π) and depreciation (δ). Nelson and Winter (1982) also make a distinction
between desired (ID) and possible investment (IP). Yildizoglu (Yildizoglu, 2003)
operationalizes the desired investment as:
ID = δ +
mtη
η − λt
(6)
where:
mt =
Pt − (c / A jt )
( 7)
Pt
Thus, the desired investment increases with the firm’s margin (m), elasticity (η), and
market share (λ). However, the desired investment is constrained by the maximum
possible investment (IP):
δ + (1 + b)π j , when π j > 0
IP = 
 δ + π j , when π j ≤ 0
(8)
where b is the finance available from the bank to fund additional investment. The new
capital stock of the firm is therefore calculated as:
K jt +1 = (1 − δ + max{0, min{I D , I P }}).K jt (9)
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