The Use of Modern Portfolio Theory in Contexts Lacking Revenue
I. Public-Sector Inefficiency
II. Modern Portfolio Theory and its Limitations
III. Introducing the Market into the Realm of the Sub-Corporate
IV. From Sub-Corporate Entities to the Public Sector
In order to allocate resources effectively within an organization, one must know
the respective strengths of that organization’s components in the context of the whole.
Such a view explains the problems found in resource allocation in both the public and
private sectors: the unambiguous market indicator of value, revenue, cannot at first blush
be attributed to either the sub-corporate entities that comprise the business or to nonprofit agencies in their entirety. However, it is possible to determine optimal allocation
of resources for the former by introducing the mechanisms of the market, in conjunction
with the KVA methodology, and applying the findings of modern portfolio theory. The
extension of this approach into the public sector becomes clear with the implementation
of a market comparables approach.
I. The Problem of Public-Sector Inefficiency
While disagreements exist in the literature regarding the proper criteria for
measuring public sector inefficiency, there’s consensus that there is great deal of room
for improvement (Chao and Yu 2002). Recent studies drawing from stochastic frontier
analysis and data envelopment analysis (see IFS 2003, Chapter 8) are particularly
compelling, and doubts surrounding the methods for measuring efficiency do not
interfere with a consistent flow of proposals for improvement (as reviewed by Tuckman
1985). According to Nissen and Barrett (2006), “Bureaucratic organizations are known
well to excel in terms of efficiency when situated in stable, predictable environmental
contexts, but this classic organizational structure is also known well to be exceptionally poor
at anticipating and responding to change.” Many aspects of the public sector—including the
United States Department of Defense—are characteristically steeped in bureaucracy and an
environment of fast paced change, which puts them at risk of incurring greater inefficiencies
and misuse of taxpayer dollars. Ultimately, efficiencies can be heightened while meeting the
needs of the people through the introduction of market mechanisms which, “when
1
successful, breaks with some of the core institutions of hierarchical governance”
(Christiansen 2002).
Some basic differences between the public and private sectors are indicative of the
disparity in efficiencies often attributed to them:
Figure 1. Private and Public Sector Attributes (adapted from Sweeny, et. al.)
Private Sector
Public Sector
Single Constituency:
“Shareholders”
Multiple Constituencies:
“Stakeholders”
Singular Focus:
“Efficiency”
Mixed Focus:
“Efficiency” and “Equity”
Clear Measure of
Success: “Bottom Line”
No Clear Measure of
Success
The reputed inefficiencies of the public sector relative to the private are natural
byproducts of these differences: under the private-sector scheme, the focus is clear, the
basis for performance measurement self-evident, and the body on whose behalf
accountability is upheld is easily identifiable. In general, these are not features of the
public sector, and therefore the prospect of achieving an efficient public sector is
contingent upon change at a fundamental level. In the past, there have been scattered
instances of such change on a micro level: market-like conditions have been introduced
with success into very specific arms of the public sector, including education (e.g.,
Zuckerman and de Kadt 1997; Peterson 2007), electricity (e.g., Fabrizio 2007) and health
care (e.g., Klein 2006). In addition, isolated commercial practices have been imported
into the operations of various government entities (e.g., in Defense Acquisitions: Sweeny,
et. al. 1989; Cox, et. al 2001). However, these efforts that attempt to regulate when and
where market forces are used and corner them into particular facets of the public sector,
in reality tend to drive inefficient bureaucracy down more deeply into the system.
Furthermore, these changes on the surface do not alter the underlying motivations for a
2
workforce and therefore cannot align them optimally, as occurs in the ideal market
system.
This re-imagining of the public sector is centered around human tendencies as
built into market mechanisms; and central to its realization is the radical visualization of
public assets as ultimately an investment made by taxpaying citizens. If the public sector
is to be responsive to the needs of the taxpayers, then “the objective…is to give more
citizens a stake in reform” (Graham 1996). Further, recasting citizens as investors
introduces market forces that blur the lines between the private and public sectors; a
market-oriented public-sector and the efficiencies resulting from it can only arise given
“citizens who know that they have a stake in a better outcome and hold officials
accountable for achieving it” (Dohrmann 2004). However, the obstacle to full realization
of this framework is the practical concern of how public entities can be treated and
tracked as corporation-like entities without the benefit of revenue streams; the resolution
of which is addressed in a later portion of this paper.1
In visualizing the public sector in terms of the marketplace, we strive to break
away from the cost-based budgeting approaches associated with government agencies
attempting to simply break even, instead aiming for a model in which decision-makers
seek to accrue to themselves the highest possible revenue at feasible costs. Here, revenue
is the truest indicator of value and is measured in common units of money. By opening
up these operations to the influences of the market and establishing unambiguous
estimates for the value of non-profit services and products, leadership can effectively
gauge the impact of their investment decisions. Furthermore by treating the various
capabilities and processes as if they were independent entities within a market, we can
apply the tools of portfolio theory to better inform these leaders of the optimal investment
choices available to them. Effectively, the body of taxpayers asserts its investment
priorities. It then becomes the responsibility of public-sector leaders at the enterprise
level—with the aid of modern portfolio theory—to allocate the tax “investments”
effectively.
1
Some public sector activities, programs, institutions may not be amenable to a market forces based
approach due to their inherently unique purposes. We do not mean to imply that all public sector activites,
programs and institutions would benefit from our approach. However, there are a large number that have
common processes such as accounting. In these cases, it may be more prudent to conduct our analysis at the
process or function level rather than the whole entity level.
3
II. Modern Portfolio Theory
Modern Portfolio Theory, as initiated by Markowitz (1952), considers a method
of resource allocation for the investor in the for-profit sector, assuming that he/she desires
to maximize expected return over all feasible portfolios while keeping the risk/variance
constrained Starting here, Markowitz proceeds to formalize the intuition behind
investment diversification.
To apply MPT, one needs to be able to compute mean values of the return for
every stock in a portfolio as well as the correlation between the returns within a portfolio.
These values are estimated based on historical data. The capability provided by MPT can
be used to accommodate an investor’s preference in the tradeoff between return and risk
associated with every portfolio under consideration.
Thus, portfolio theory suggests a way of optimally allocating capital for the
investor in the private sector. However, we also believe it to be of utility as an
optimization tool for the allocation of resources within a firm among its constituent parts,
and ultimately as a method for resource allocation among the “portfolios” of capabilities
and process found in the public sector.
Detractors have perceived a number of flaws in MPT. These include:
1) MPT assumes that risk is synonymous with volatility. In fact, a number of
early empirical studies (e.g., Haugen and Heins, 1975) demonstrate little
correlation between risk (when defined as volatility) and returns. Murphy
(1977) concludes that “Efficiency is not an accurate description of the capital
markets and may not even be a very good description; there are serious
problems with the risk/reward relationship.” Fama and French (1992) find
that “the relation between β and average return for 1941-1990 is weak,
perhaps nonexistent, even when β is the only explanatory variable.” Logically
the strict correspondence between risk and volatility seems suspect: volatility,
4
in treating all motion indiscriminately, punishes upward trends just as much as
the downward ones investors wish to avoid. An adequate solution may be
simply to use “downside risk.” As Harlow (1991) explains, “Downside-risk
measures are attractive not only because they are consistent with investors'
perception of risk, but also because the theoretical assumptions required to
justify their use are very simple…a number of well known risk measures,
including the traditional variance (standard deviation) measure, are special
cases of the downside-risk approach.”
2) MPT assumes that portfolio returns can, in general, be adequately represented
by the normal distribution (reference [1]).
3) MPT assumes away all transaction costs and taxes.
The last point is certainly unrealistic in the private sector, but (presumably) in the
application to the public sector where the investor is represented by the leadership of an
agency and the “companies” in which investments are made, are controlled, this
assumption can be made. The downside-risk solution to the first problem and the
incorporation of the possibility of “skewness” (problem 2) are features of the so-called
Post-Modern Portfolio Theory, developments which are traced by Libby and Fishburn
(1977) and Rom and Ferguson (1993).
In addition to these noted drawbacks to MPT, there exists a central limitation, as
Markowitz himself acknowledges: it only purports to address the second half of the
resource allocation process. As mentioned above, MPT provides the investor with
efficient portfolios after he has chosen the investments to be considered. In DoD IT, for
instance, this would correspond to the allocation of resources throughout a given, existing
IT infrastructure. A reasonably worthwhile allocation of resources using MPT
presupposes a reasonably efficient investment structure. This limitation may be
resolvable using the attractors search algorithm (ASA).
An attractor is a set of n equities (n-attractor) such that the corresponding optimal
portfolio cannot be improved by replacing one of the n equities by any other equity
outside the n equities. For example, using MPT we allocate resources among 5 equities
(i.e., 1,2,3,4,5). If one of the five equities, e.g., 2, in this portfolio can be replaced by
another equity, e.g. 7, such that the performance of the corresponding optimal portfolio:
5
1,7,3,4,5 is better than the original portfolio, then the original portfolio is not an nattractor.
The properties of an n-attractor are:
1. Optimal portfolio of n stocks is an n-attractor
2. There may be more than one n-attractor given the same risk-reward parameters.
(biology references)
3. Given an efficient search algorithm, e.g. ASA, it may be possible to select the best
performing attractors from the set of n-attractors having common risk-reward
parameters
Kanevsky’s ASA [patent by VK] allows for an effective search through all equity subsets
of a given cardinality n. Since the computational complexity of the ASA is feasible, an
investor can extend the search to ever higher cardinalities until his risk-reward
expectations are met.
III. The Method in the Sub-Corporate Case
The firm faces the same fundamental problems in allocating resources to its
components as agencies do in the public sector. Just as non-profits have no revenue
streams, so do sub-corporate entities in the private sector lack information regarding their
true value. Opening up the internals of a firm to the voice of the market—acknowledging
that the boundary around the company is a permeable one—by inviting investment in
individual components of the firm structure can be for certain companies a way of
achieving the transparency needed to be able to allocate overall company resources
effectively. Some companies are in fact already doing this in essence through “tracking
stocks” (e.g., Disney). This system would benefit both sides of investment: increased
transparency will enable corporate leadership to identify inefficiencies and know where
investors are willing to place their capital, while investors will benefit by the additional
control over their investment.
Despite the potential advantages, selling stock in individual company components
does not exist under present equity market conditions. However, via the KVA
methodology, sub-corporate entities can at least be treated as members of a free market
6
with their own revenue streams. KVA is basically a method for describing all outputs in
common units which can then be priced at a given historical point in time based on
revenue generated at that same point in time. Assuming a direct relationship between
knowledge and the value stemming from it, knowledge value added delivers a capability
for allocating revenue to subcorporate-level entities by describing all process outputs in
common units. Value can be described as the knowledge needed to produce the common
units of output, a notion which can be operationalized in numerous ways (Housel and
Bell 2001), and has already been implemented in numerous for-profit (e.g., AT&T;
Housel et al. 2005) and non-profit organizations (e.g., to examine the return on
investment of intelligence information systems in the Department of Defense; Rios and
Housel 2005).
As demonstrated in Figure 2, applying KVA at the sub-corporate level transforms
the problem at hand into the same one that appertains to the corporate level. Given a
history of resource allocation, sub-organizations can be seen as members of a market for
such entities. Given a desired set of risk and reward characteristics, a portfolio of
suitable “equities” can be extracted from this market (a process represented here by the
“Kanevsky Attractor Prediction Algorithm”) and subjected to the tools of modern
portfolio theory just as is currently routine for the equities market on the company level.
This is done given the inputs of expected ROI, volatility in the history of the ROI, and the
correlations between the ROI histories of the different assets chosen. In this way,
optimization of even a portfolio of sub-corporate entities is possible.
Figure 2. The correspondence between the problems of corporate-level investment
optimization (currently practiced) and sub-corporate level optimization (enabled through
KVA).
7
Sub-Corporate Level
Corporate Level
KVA
ROI Over Time
Revenue Allocation
Equities Market
?
Theoretical Sub-Corporate Equities Market
Kanevsky Attractor
Prediction Algorithm
?
Kanevsky Attractor
Prediction Algorithm
Selected Equities
Portfolio of Selected Equities
Equities Earning Variables: Expected
earnings (mean), earnings volatility (standard
deviation), equity diversification (correlation)
Expected Earnings Variables: Expected ROI
(mean), ROI volatility (standard deviation),
equity diversification (correlations).
MPT
Optimal Portfolio: Allocation of capital that
provides the highest expected returns for a
given level of risk
8
Example for the Sub-Corporate Case: ABC Radiology, Inc
To illustrate the method, we have generated historical data for the fictitious ABC Radiology, Inc. This company provides services for
a wide variety of health professionals, including the operation and maintenance of X-ray, CAT scan, and MRI technologies as well as
the interpretation of the results from such devices. In addition, they manufacture such mechanisms at a high-quality level for sale in
many areas of the health care industry. The company operates under three major segments: testing services (including the operation of
radiological equipment and interpretation of results), technical services (specialized repairs the company is contracted to undertake),
and production and sales (the manufacture of such instrumentation is but a small component of the company’s aggregated operations
since it is so specialized). In addition, there are accounting and human resources departments. Table 1 shows the results of a typical
KVA analysis conducted for ABC Radiology, Inc. This analysis makes possible the allocation of REVENUE based on the amount of
knowledge embedded within each segment’s core processes. Given a periodic application of the KVA methodology, the company can
Table 1. KVA Analysis for ABC Radiology, Inc.
Learning
Department
Executions
Time
Total
Knowledge
Expenses
Revenues
ROK
ROI
STD
DEV
% of
Rev.
Accounting
15
800,000
12,000,000
$1,100,000
$1,200,000
109.09%
9.09%
4.0%
12.00%
Human Resources
10
1,000,000
10,000,000
$900,000
$1,000,000
111.11%
11.11%
3.2%
10.00%
Testing Services
0.5
110,000,000
55,000,000
$5,000,000
$5,500,000
110.00%
10.00%
3.0%
55.00%
Technical Services
30
500,000
15,000,000
$1,200,000
$1,500,000
125.00%
25.00%
8.5%
15.00%
Production and Sales
5
1,600,000
8,000,000
$650,000
$800,000
123.08%
23.08%
7.0%
8.00%
100,000,000
$8,850,000
$10,000,000
112.99%
12.99%
9.83%
100.00%
Totals
Revenue per
Knowledge Unit:
$0.10
9
build a historical record of sub-corporate revenues and arrive at a variance (shown as
standard deviation) and correlations between the earnings of the various segments. In
effect, we have all the information needed to extend the notion of portfolio theory as
applied to investments in companies down into a sub-corporate market. Since here we
are dealing with all the components in a given company, and not the optimal combination
of sub-corporate entities across companies, there is no need for the Kanevsky Attractor
Prediction Algorithm. We can now optimize this portfolio of five investments according
to the tenets of Markowitz’ portfolio theory (here we use the dynamic chart available at
http://www.spreadsheetmodeling.com/Portfolio%20Optimization%20%20Dynamic%20Chart.htm). Figure 3 below shows the allocation distribution for an
optimized portfolio given KVA data taken weekly over a period of fifteen weeks.
Portfolio Weights
Portfolio Weights in an
Optimal Portfolio
60%
50%
40%
30%
20%
10%
0%
1
2
3
4
5
Asset
Figure 3. Weights for ABC Radiology’s portfolio assets (1=accounting; 2=human
resources; 3=testing; 4=technical; 5=production and sales).
Armed with isolated KVA analyses, a company’s leadership can determine which parts
of the company are adding value and which need improvement, as well as map out the
direction for such improvement. However, the success of a given company’s components
relies not only on these improvements from within, but also on external market factors
10
(e.g., demand). Hence, we believe that the full potential of the KVA methodology on the
aggregate level can be achieved only with its coupling to the techniques of portfolio
theory, which takes into account—via historical volatility—the influences of the overall
market on each entity within the company. Figure 4 shows the plot of the ROI figures
over time for the five company segments, as well as for the company when allocating
based on the percentage of overall revenue represented by the respective segments in the
first KVA analysis (“company”). The ROI figures based on the optimized portfolio are
also shown. The results indicate the importance of applying MPT as the natural
completion of a KVA approach: as expected from the theory, the optimized portfolio
routinely outperforms the overall company portfolio based on the single KVA analysis,
which cannot take into account the dynamics that can drive optimum growth. KVA in
and of itself can reveal the inner workings of a company at a given moment in time, but it
is portfolio theory that keeps an eye on change and future earnings to guide investment,
with the help of inputs available through KVA.
ROI Data, with Overall Comapny and Optimal Portfolio
60.00%
50.00%
40.00%
Accounting
HR
30.00%
Testing
Technical
Production
20.00%
Company
Optimal
10.00%
0.00%
Week Week Week Week Week Week Week Week Week Week Week Week Week Week Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
-10.00%
Figure 4. ROI Data.
11
IV. Extending to the Public Sector
According to the Department of Defense Guide for Managing Information
Technology as an Investment and Measuring Performance (1997), “Congress has
determined that waste and inefficiency in Federal Information Technology (IT) programs
undermine the confidence of the American people and reduces the Federal Government’s
ability to adequately address vital public needs” (1-1). The Guide aims to outline the
“performance and results-based management” (1-2) required by federal legislation for IT
operations. However, it neglects to do so in the context of the “invisible hand” of the
market, which supports a results-based approach even on the lowest level of operation in
the for-profit sector. Instead, it offers intricate guidelines for organizing speculation and
prolific methods for measuring performance in hindsight—in other words, further
bureaucracy. The central problem is the attitude that “effectiveness” and “efficiency”
need to be balanced at every level of operation, which is typical of a “rule-intensive
organization” (Nissen and Barrett 2006) such as DoD. The authors of the Guide regard
“effectiveness” as the degree of success in which a government entity meets its predetermined goals and mission, and “efficiency” is the degree to which the resources that
work toward these goals are allocated well. Effectiveness is a passive measure seen
relative to static standards imposed by upper-level management, while efficiency is
intrinsic to the entity, apt for performance measures, and hence able to be optimized. The
model for DoD governance set forth in the Guide, and dominant currently in the
department, stresses the need to attach measures of both effectiveness and efficiency to
every level of organization, as illustrated in Figure 5.
12
Figure 5. A standard model for DoD governance. Adapted from Department of Defense,
1997.
r
Accountability
ENTERPRISE
Executive Information
Mission Results
Integration &
Planning
Resource
Allocation
FUNCTIONAL
Management Information
Unit Results
PROGRAM/PROJECT
Activity/Task Information
Workplace Results
This top-down structure is based around the premise that missions must be defined at
every level of DoD operations, a practice which stifles creative solutions to larger
problems that can only be achieved through collaboration between entities, and which is
prone to mass inefficiencies caused by the constant shifting of priorities within
government affairs. Introducing market forces into DoD would undermine this current
notion of “effectiveness”: supply and demand would come to define mission and goals at
lower levels, and they in turn would become more fluid. However, where conventional
notions of effectiveness change, efficiencies will abound once “output-based” and
13
“outcome-based” goals are realigned so as to allow for the natural market forces to work.
These projected efficiencies are apparent in the observation that the roles of
accountability and integration delegated in the above diagram are in fact end products of
the capitalistic market system in the for-profit sector (Davis 2007), and given the
methodology outlined above, more effective resource allocation is possible as well.
Introducing efficiencies into the public sector is a matter of pushing “outcome-based”
goals as far up the hierarchy as possible, to the level of the investor, embodied here in
the general body of taxpaying citizens. Hence, while the public defines the desired
outcomes expected of local and federal government agencies (e.g., emergency safety
services), the government agencies themselves focus on output, or producing the best
possible products or services under efficient use of the taxpayer resources. Leadership at
all levels of the government not only will be able to find creative solutions to overarching
problems by joining up with other public- or private-sector organizations where their
previous commitment to a specific “mission” could have precluded them from doing do,
but they must. Given the pressure of being responsible for profits, lower-level
management will have it in their best interests to integrate or realign with others where
they believe efficiency will result. Information at lower levels in the organization is more
readily available to lower-level management, and in deemphasizing specific missions at
these levels, we can allow this management to act on it. An organization with such
characteristics is modeled in Figure 6, to be held in contrast with Figure 5.
14
Figure 6. A less standard model for governance, is when the effective democratic
consensus is upheld by budgeting decisions made at the enterprise level, which is defined
as investments in members of relevant markets.
ENTERPRISE: Maintains taxpayer
“missions” through appropriate funding.
FUNCTIONAL
FUNCTIONAL
PROGRAM/PROJECT
FUNCTIONAL
PROGRAM/PROJECT
PROGRAM/PROJECT
Public/Private
Divide
Introducing the market into the public sector can be accomplished in a manner
akin to the methodology previously discussed. The additional problem in dealing with
the non-profit sector is that there exists no measure of revenue when taking the agency or
organization in the aggregate. The KVA analysis would provide common units, but there
would still be no manner of formulating a return on investment. The method we propose
of estimating non-profit sector revenue streams is a Market Comparables approach,
which assumes that “though the macro functions performed by governments are
monopolistic and centralized, many of the processes to accomplish those functions are
comparable to those in the private sector” (Cook and Housel 2005). Hence, subcorporate entities can provide revenues, with proper scaling, for similar segments in the
public sector, which in turn allows for a revenue breakdown for that segment’s core
processes, by which investments can be made. The method is further demonstrated in
Housel, et. al. (2007) and Joyce and Roosma (1991).
15
Corporate Level
Sub-Corporate Level
Public Sector
Revenue Streams on Process Level
KVA
KVA
ROI Over Time
ROI Over Time
Market
Comparables
Equities Market
?
Kanevsky Attractor
Prediction Algorithm
Revenue Allocation
Revenue Allocation on the Sub-Process
Level
Theoretical Sub-Corporate Equities Market
Theoretical Sub-Process Equities Market
?
?
Kanevsky Attractor
Prediction Algorithm
Kanevsky Attractor
Prediction Algorithm
Selected Equities
Portfolio of Selected Equities
Portfolio of Selected Equities
Equities Earning Variables: Expected
earnings (mean), earnings volatility
(standard deviation), equity diversification
(correlations)
Expected Earnings Variables: Expected
ROI (mean), ROI volatility (standard
deviation), equity diversification
(correlations).
Expected Earnings Variables: Expected
ROI (mean), ROI volatility (standard
deviation), equity diversification
(correlations).
MPT
Optimal Portfolio: Allocation of capital
that provides the highest expected returns
for a given level of risk
16
Example for the Public Sector Case: The XYZ County Healthcare System
The XYZ County Healthcare System is a fictional public network of healthcare programs, facilities, and services. The core
component of the system is the XYZ County Hospital, with other services offered through its cancer clinic and heart center. However,
all of these outlets rely on the system’s radiology division. Since the XYZ County Healthcare System is a public-sector organization,
it has no revenue streams to track and there is often difficulty allocating resources to its components, like the radiology division, on a
true value basis. The radiology division consists of three segments: testing services (using X-ray, CAT scan, and MRI tools in support
of operations across the system), analytical services (professional interpretation of results from the use of such technologies) and
technical services (including the maintenance and upgrading of radiological technologies throughout the system).
Table 2. Initial KVA Analysis for XYZ County Healthcare System—Radiology Division
Learning
Total
Department
Executions
Expenses
Time
Knowledge
Testing Services
0.5
5,000,000
2,500,000
$5,000,000
?
?
?
%
of
Rev.
?
Technical Services
20
75,000
1,500,000
$1,200,000
?
?
?
?
Analytical Services
4
5,000,000
20,000,000
$650,000
?
?
?
?
24.5
10,075,000
24,000,000
$6,850,000
?
?
?
?
Totals
Revenue per Knowledge Unit:
Revenues
ROK
ROI
STD
DEV
?
Table 2 shows a preliminary KVA analysis for the radiology division, and indicates that no new information is found, since the
(public) healthcare system has no overall revenues. At this point, a market comparables approach is pursued, between the division of
radiology in this public-sector organization and the for-profit ABC Radiology, Inc. (discussed above).
17
It should be noted, at this point the method diverges depending on the scope of the
problem being tackled. One possibility afforded by portfolio theory is a comparison
between the core processes of the for-profit radiology company’s core processes and
those of the public radiology division, with the aim of determining the best allocation of
resources among the components within the division. On the other hand, looking at
radiology as a component of the healthcare system as a whole, our task can be the proper
allocation between the various divisions and capabilities. In other words, KVA is
flexible in that it can be implemented on a variety of levels for the company or
organization under study. In addition, the latter task of valuing the radiology division in
the context of the whole is particularly prone to ambiguities without this methodology,
since the output of the division (i.e., radiological analysis) is used as the input in virtually
all other divisions.2
In comparing ABC Radiology, Inc. and the XYZ Radiology Division, we note
that their core processes are identical, only organized in different ways (“testing services”
for ABC corresponds to the combination of “testing services” and “analytical services” in
XYZ). The main difference lies in volume: ABC performs the same services as the XYZ
division, but on a larger scale. Thus, we will take the revenue figures from the
appropriate segments of ABC and, after adjusting for the disparity in volume, apply them
to XYZ. Revenues are assigned to XYZ segments after being scaled down based on a
ratio of executions. However, the KVA revenues given to each segment depend on the
amount of knowledge embedded in each segment, not in the volume of executions.
Therefore, the original revenues are summed to form an aggregate for XYZ, and then are
redistributed based on knowledge. Tables 3 and 4 present the results.
Table 3. Market Comparables Data
Volume Ratio
(XYZ/ABC)
Testing and
analysis
0.091
Technical
0.15
Revenues from
Comparable
$500,000
$225,000
2
Conventional methodologies tend to see such operations as essential and thereby overvalue them,
irregardless of actual performance. In this way, our radiology division is comparable to IT systems in the
DoD, whose output is simply supportive input for other aspects of the organization.
18
Table 4. KVA Analysis for XYZ Radiology Division
Learning
Department
Executions
Time
Total
Knowledge
Expenses
Revenues
ROK
ROI
STD
DEV
% of
Rev.
Testing Services
0.5
5,000,000
2,500,000
$70,000.00
$75,520.83
107.89%
7.89%
3.00%
10.42%
Technical Services
20
75,000
1,500,000
$40,000.00
$45,312.50
113.28%
13.28%
8.50%
6.25%
Analytical Services
4
5,000,000
20,000,000
$550,000.00
$604,166.67
109.85%
9.85%
7.00%
83.33%
24,000,000
$660,000.00
$725,000.00
109.85%
9.85%
6.68% 100.00%
Totals
Revenue per
Knowledge Unit:
$0.03
With a KVA history, the portfolio can be optimized as in the sub-corporate case. The resulting weights provide an optimized ROI
(Figure 8) that is consistent with the theory by overperforming on average, although this case differs slightly from the allocation
scheme derived from the first analysis’ revenue breakdown.
19
ROI Data, with Overall Company and Optimal Portfolio
35.00%
30.00%
25.00%
20.00%
Testing
15.00%
Technical
Analytical
10.00%
Company
Optimal
5.00%
0.00%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
-5.00%
-10.00%
Figure 8. ROI Data
20
V. Marginal Revenue
The relationship between marginal revenue and marginal cost is not helpful in the
present analysis, because equivalence of the two is only achieved under the condition of
maximized profit. In the case of non-profit organizations we are missing profits as well
as revenues, rendering the relationship pointless. In fact, if anything, this is an argument
against the notion that cost-based valuation in any way incorporates information about
true value as represented by revenue since we cannot assume the equivalence of revenue
and cost margins given the improbability of profit maximization. Further, even if we
could use marginal cost as marginal revenue, this would still only give changes in
revenue allocation. Finally, there is the monopoly factor, which plays a large role in the
non-profit sector, which also waters down the relationship between marginal costs and
revenues. (See equations.)
21
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