hedonic price method
A method for inferring the value of something not traded directly in the
market place based on market prices. The premise is that the prices of
goods traded in the market, such as houses, depend on internal factors
(e.g., house size, age, appearance) and external factors (distance to
schools, level of local air and water pollution). Price data for the
marketed good is analyzed (typically, via regression analysis) to determine
the contribution of each factor to price, thereby inferring a monetary
value for changes in that factor. The approach is often used to estimate
the monetary value of environmental outcomes for cost benefit analysis.
Helmsman complexity scale
A scale, developed by the Helmsman Institute of
Australia, for measuring the relative complexity of projects. The scale
ranges from 1 to 10 and is logarithmic, similar to the Richter scale for
measuring earthquake magnitude. Definitions are provided for various levels
of the scale. For example, the scale defines a moderate score between 4 and
5 as indicative of the complexity of projects typically performed in the
business units of large organizations, such as product maintenance and
competitive enhancements to ongoing business operations. A high score
between 8 to 9 is defined as the level of complexity associated with rare
and highly complex projects undertaken by countries that produce
significant impacts on the national economy, for example, conducting the
The scale is designed to be applied to assess project
complexity in five areas: (1) context complexity (complexity of the
project's leadership and the political environment), (2) people complexity
(how large and deep the sociological change will be for recipients of the
project), (3) ambiguity (in the approach and design of the project), (4)
technical challenge (of core systems and integration requirements), and (5)
project management challenge (such as contract complexity, risk sharing,
schedule and project structure, supplier complexity and external project
interdependencies). Since project complexity has been shown to relate to
project risk, the scale has been used as a proxy for assessing the level of
risk associated with complex projects. The approach may also be used to
provide guidance on where to focus efforts for risk mitigation.
Within the field of psychology, a simple mental rule
proposed to explain how people make decisions, come to judgments, or solve
problems, particularly when faced with more complex problems or incomplete
information. Although efficient, such rules may lead to systematic errors
or biases. Presumably, heuristics are the result of evolutionary processes
or learned behavior.
In computer science, a heuristic is a technique for
solving a complex problem that is faster or otherwise more practical than
an approach that results is a solution that is provably optimal.
A model with a top-down, tee-like structure, such that
each subsystem is linked to at most one "parent" subsystem. A hierarchical
model is distinct from a network
model, wherein each subsystem may have links to multiple parents.
To store (a website or other software) on a server or other computer so that it can be
accessed over the Internet or other network.
A specified rate of return for a project or other investment intended to
represent the minimum return that the organization will accept. The hurdle
rate is also often referred to as the required rate of return.
Typically, the hurdle rate is the risk adjusted discount rate
to be applied when computing the net present
value (NPV) of the cash flows anticipated from a project. If the NPV of
the cash flows using the hurdle rate is negative, the project is rejected.
Alternatively, the hurdle rate may refer to the minimum acceptable internal rate of return (IRR) for
projects—If a project's IRR is less than the hurdle rate, the project
According to investment theory, the hurdle rate should be
set equal to the rate of return that the organization could obtain by
investing in alternative investment opportunities having similar risks. If
the project generates a return greater than what the organization could
earn elsewhere (i.e., greater than the opportunity cost of the required
investment), the project will add value. In practice, hurdle rates for
projects are often specified by adding a risk premium to the risk free interest rate or by adding or
subtracting an incremental amount from organization's marginal cost of capital, so that a higher rate
is specified for project considered more risky.
Hurdle rates are generally a poor way to account for
risks when prioritizing projects. As explained in one of the papers, hurdle rates tend to produce a bias
toward short-term, quick payoff projects relative to projects of similar
risks whose benefits accrue over longer periods of time. Also, while hurdle
rates can be used to decrease the value of projects whose benefits are more
uncertain, they do not achieve the converse effect of increasing the value
of projects that, if not conducted or if delayed, would tend to increase
A weight (scaling
constant) assigned for multi-criteria
analysis based on the decision-maker's perception of how important a
criterion is relative to other
criteria. For example, if there are two criteria, 60% of the weight might
be assigned to the first and 40% to the second, based on a judgment that
the first criterion is one and one-half times as important as the second.
Importance weights should not be used as they result in flawed analysis and
indefensible results. The proper type of weights for multi-criteria
analysis are swing weights.
Despite the problem with importance weights, it is not uncommon to find
them used for project prioritization, though the documentation for such
systems typically refer to the flawed scaling factors as "weights" rather
than "importance weights."
The problem with importance weights is that they cannot
be meaningfully specified. To illustrate, suppose the context is
transportation projects and two criteria are relevant, costs and
safety. Suppose costs are measured in dollars, and the
metric for safety is number of
accidents avoided. If you were to be asked, "Which is more important,
accidents or costs?", you might answer "accidents." Does that mean that you
think avoiding one accident is more important that $1,000? Maybe so. Does
it mean that you think avoiding one accident is more important than $1
billion? Maybe not. The point is you must specify and consider the amounts
of the different metrics (their "swings," in order to logically judge and
compare importance. Weights assigned based on judged relative importance
are meaningless so any results produced through their use are not
Projects that are independent of one another in the sense that the choice to conduct or not to conduct
any project does not affect either the costs or benefits of conducting any other project. According to the
ranking theorem, if independent projects are ranked based on the ratio of value to cost
and then selected in rank order until the
budget is exhausted, the result will be the either the project set that would generate the greatest value or a project set that
comes very close to generating the greatest value. The only time that ranking may fail to identify the portfolio having the
most value is if ranking fails to spend all available funds. Then, if there are less costly projects with nearly the same ratio values
as the last projects funded, then substituting these may produce higher aggregate benefit. However, in practical settings, sorting
on benefit-cost ratios is a reasonable heuristic solution with only a small deviation from the aggregate value achievable through
constrained optimization. Constrainedoptimzation
is a solution approach that may apply if projects cannot be made independent.
A form of project dependency that arises in many settings is mutual exclusivity of project
choices. For instance, when considering alternative versions of the same project, choice is restricted to choosing at most one
version of the project. Another common form of project dependency occurs when projects are contingent, meaning that one project
can be chosen only when a second project is also selected. An example of project contingency is a computer software purchase
that is only feasible if necessary computer hardware components are acquired simultaneously. Oftentimes it is convenient to treat
contingent projects as a single project with combined costs and value. However, unless there is mutual contingency, this requires
introducing mutual exclusivity, to allow for scenarios where one wishes to acquire one project but not the other. For instance,
when considering constructing a new office building, one might consider a new parking garage as contingent on the construction of the
offices, if the garage would have no useful purpose without the new offices. Alternatively, one could consider “office building”
versus “office building plus garage” as mutually exclusive projects.
Also called risk-reward tradeoff curves, a curve identifying portfolios of investment assets with different
combinations of risk and return for which a decision maker is indifferent. Indifference curves are plotted on a two-dimensional
graph where the horizontal axis indicates risk, typically measured by the variance of the distribution over portfolio return, and
the vertical axis indicates reward, measured by expected return. Any portfolio combination of assets will have a risk,
represented by its variance, and an expected return. Typically, decision makers are assumed to be
risk averse, which means
that, to accept a portfolio with more risk, the decision maker would require greater expected return. If you were to plot
all the possible combinations of portfolio risks and returns for which the decision maker is indifferent is an indifference curve.
Since the decision maker is indifferent among the portfolios on the indifference curve, different indifference
curves have different utilities. The higher the curve and the furthest to the left, the higher the utility.
An influence diagram is a type of decision model that has a graphical
representation composed of nodes denoting model variables connected by
arrows. A rectangular node represents a decision variable, a choice that a
decision maker can make among various alternatives. An elliptical node
represents an uncertain variable, something relevant that is not directly
under the decision-maker's control. Sometimes another shape (e.g., a
rectangle with rounded corners, as shown below) is used to represent a
computed from other model variables indicating the degree to which a
decision objective is achieved.
Influence diagrams can be constructed in an informal way,
such that the arrows connecting nodes represent a generalized concept of
influence, or in a mathematically rigorous way, where
from an ellipse (an uncertainty) or a rectangle (a decision) pointing to an
ellipse (an uncertainty) means that the probabilities describing the
possible outcomes for the latter uncertainty depend on the choice made or
the outcome of the former variable. An arrow pointing from an ellipse or a
rectangle to a rectangle means that the latter decision can be made after
the outcome to the uncertainty is known or the prior choice is
made. Influence diagrams used in this rigorous fashion may be referred to
as Bayesian networks. Software tools for drawing influence diagrams
often provide algorithms for automating the conversion of an influence
diagram to a decision tree, and then solving the tree to identify
decision strategies that maximize expected utility and show
probability distributions over decision value.
A sample influence diagram (new drug project decision
The basic concepts underlying influence diagrams were
developed at SRI International in 1973, by Allen Miller, to analyze US
intelligence gathering strategies for the Persian Gulf. The diagrams allow
complicated decision situations involving many variables to be represented
by a compact graph. Because they are intuitive and can be constructed using
a top-down model building approach (What variable do you want to know? What
variables would you need to know in order to estimate what you want to
know?) influence diagrams support an efficient model building process that
can be conducted as a facilitated, team exercise. Also, software tools are
available that allow influence diagrams to be linked to other models (e.g.,
to a spreadsheet model for computing business outcomes) and analyzed to
calculate optimal decision strategies, risk, and the value of information. Along with decision trees, influence diagrams are
the most commonly used model forms for decision analysis.
information technology (IT)
Technology for managing information, especially computer
hardware and software systems for acquiring, storing, organizing,
analyzing, and communicating information. An IT project is a
projectt related to information
technology, such as a project to acquire, create, maintain, repair, or
replace IT assets.
Procedures for minimizing or maximizing an objective function when it is
required that one or more of the more of the decision variables be integers (whole
numbers such as -1, 0, 1, 2, etc.). If at the optimal solution some
decision variables must be integers and some need not be, the solution
procedure is often referred to as mixed integer programming. The use
of integer variables greatly expands the scope of useful optimization
problems that can be solved, since many real world problems require a
choice among a finite number of alternatives (e.g., you can choose to do or
not do option A, but you can't choose to do 1/6 of option A).
Unfortunately, finding the solution to an integer programming problem is in
general difficult. The most widely used algorithms for solving integer programming
problems are branch and bound, the cutting plan method, and
As in interdependent projects, a situation where
two or more projects are related to
each other in such a way that the costs and/or benefits of doing one project depend on
whether or not the other project is conducted.
Project interdependencies arise in a number of ways, for
- The same, scarce resource (e.g., an individual with unique skills) is
needed by several projects. If all of the projects requiring the resource
are initiated, resource conflicts can occur, increasing cost and
- A project cannot be started until another project is completed. For
example a project provides some knowledge or capability necessary to
conduct the other project.
- In the case of new product projects, market dependencies occur if a
new product enters a market served by an already existing product. The
success of the existing project may be harmed by the new product.
Interdependencies among projects complicates project
selection, a key task of project portfolio
management. Unless projects are independent of one another, the
value-maximizing project portfolio cannot be found by the simple technique
of ranking projects by the ratio of project value to project cost.
Portfolio optimization methods are
available for identifying the value-maximizing project portfolio, but the
methods require the user to mathematically describe the dependencies, which
is often difficult. Thus, the standard advice is to group interdependent
projects into larger projects (or programs) in such a way that the combined
projects are independent of each other.
internal rate of return (IRR)
rate that equates the present value of the income stream generated by a
project to the cost of that project.
In other words, the IRR is the value that satisfies the equation:
Equivalently, the IRR is the discount rate that causes
the project to have a zero net present value
The IRR is sometimes misunderstood to be the annual
profitability of a project investment. However, for this to be true, the
cash inflows derived from the project would have to be reinvested in
opportunities that produced a return equal to the project's IRR, which is
rarely the case.
Like NPV, the IRR is a commonly used criterion for
project-by-project selection decisions—all projects that have IRR's
greater than the cost of capital are recommended for funding.
When used as a ranking metric, IRR has an advantage over
NPV; it does not depend on the size or scale of the project (therefore, its
use is more consistent with the concept of ranking based on "bang-for-the
buck"). However, at best, the IRR is only a heuristic or approximate logic for
prioritizing projects. It creates predictable and significant biases in
project rankings and cannot be used to identify project portfolios that
create maximum value.
IRR analysis is popular because it compares projects
based on the familiar concept of rate of return (a metric analogous to
interest rates charged on capital markets). For this reason, it is for many
one of the easiest project evaluation methods to understand. Given two
investment alternatives of comparable costs, the investment with the higher
IRR should be selected. When used as a selection rule for
project-by-project decision making, IRR and NPV recommend the same projects
(provided that a unique IRR exists, see below). The IRR has a perceived
advantage over NPV and other methods that quantify project value in dollars
in that it downplays reliance on what might appear to be overly-precise
For several reasons, the IRR cannot be used to reliably
prioritize projects. First, like other purely financial metrics, the IRR
ignores the non-financial components of project value. Furthermore, IRR
cannot be used to correctly prioritize based on financial return alone.
Ranking projects based on IRR undervalues cash flows that occur late in a
project's life (assuming that the IRR is greater than the cost of capital).
It therefore creates a bias for projects with early positive returns
relative to projects whose returns tend to occur later. The significance of
this bias is greater the longer the duration of project cash flows and the
more severely constrained the capital budget (if the budget is highly
constrained then the IRR's of the projects being compared will tend to be
significantly higher than the cost of capital, meaning that future cash
flows will be very heavily discounted).
There are several additional disadvantages with IRR.
There is no specific formula that can be used to calculate the IRR; it must
be found by iteration and interpolation. Thus, computing the IRR
takes more computation than does the NPV (most spreadsheets do, however,
provide an IRR function). The IRR of the portfolio of projects cannot be
calculated from the IRR's of the individual projects, so there is no easy
way to quantify the performance of the portfolio based on the analysis of
the individual projects that make up the portfolio. IRR analysis cannot be
extended to account for consideration of project risks or project
interdependencies. Finally, there are situations of multiple solutions (no
unique IRR) when project cash flow changes direction more than once.
A solution process that involves approximating the value
of a function at points between which it has been evaluated.
investment review board
Term sometimes used to designate a decision-making group
composed of senior managers responsible for evaluating and prioritizing
projects or other investments. Organizations conducting information technology (IT) projects often
establish IRB's. Initiatives and supporting data are presented to the board
for review and discussion. Board members reach conclusions based on
comparisons and trade-offs among the competing projects, relying
substantially on their perceptions and judgments.
A solution process that requires repeating the execution
of a set of instructions, typically many times, with the goal of gradually
approaching a more accurate answer.
A probability distribution that
quantifies the simultaneous uncertain behavior of two or more random variables. Specifically, a joint
probability distribution expresses the likelihood of obtaining specified
outcomes for some number of random variables. If there are two random
variables, the joint distribution is called a bivariate
distribution. If there are more than two variables it is called a
multivariate distribution. A probability distribution over a single
random variable is called a univariate distribution.
Like single variable probability distributions, the
variables in a joint distribution can be discrete or continuous. If there are two discrete
random events A and B, the joint probability for A and B is the likelihood
that both events occur. The joint distribution for discrete random
variables may be called a joint probability mass function If there
are two continuous random variables X and Y, the joint probability
distribution gives the probability that X and Y each fall into a specified
range of values. In this case the joint probability distribution may be
called a joint density function. Like the case of a single-variable
probability distribution, a joint probability distribution can be specified
as a joint cumulative distribution, which gives the probability that
the value of each random variable is less than or equal to any specified
Joint probability distributions are useful for
quantifying the dependencies among uncertainties. Two events A and B are
independent if the probability of both A and B occurring equals the
probability that A occurs times the probability that B occurs. Likewise, if
X and Y are two continuous random variables, and the distribution of X is
not influenced by the value taken by Y, and vice versa, then the two random
variables are independent.
When dealing with
multiple random variables there are additional ways of expressing
uncertainty that are useful for exploring interdependencies. Once we know
the joint probability distribution for random variables, we can calculate
their individual distributions. The conditional probability assumes
that one event has taken place or will take place, and then asks for the
probability of the other (e.g., the likelihood of A occurring, given that B
has already occurred). Conditional probability distributions arise from
joint probability distributions where by we need to know that probability
of one event given that the other event has happened and the random
variables behind these events are joint. The marginal probability is the likelihood
of an event occurring (e.g., event A), irrespective of whether or not B
occurs. It may be thought of as an unconditional probability. The marginal
distribution of one of the variables is the probability distribution of
that variable considered by itself. Note that if the events are
independent, the conditional probability that A occurs given that B has
occur will exactly equal the marginal probability of A occurring, since
whether or not B occurs has no bearing on event A.
To provide an example, the bivariate normal
distribution is an often used joint probability distribution for two
random variables, X and Y, each of which is normally distributed. The
distribution is specified by 5 parameters, the means of the distribution
(μx,μy) the standard deviations of
the distributions (σx,σy), and the
ρ between X and Y. In the example, the conditional density
function for Y is more narrow than the marginal density function because
the variables are positively correlated. Thus, if the value of the random
variable X is known, that reduces the uncertainty over Y.
Joint, marginal, and conditional distributions for a
bivariate normal probability distribution