Lee Merkhofer Consulting Priority Systems

Technical Terms Used in Project Portfolio Management (Continued)





























natural logarithm

A logarithm taken to the base of the mathematical constant e. The natural logarithm of a number x is typically written ln(x). Like all logarithms, ln(x) is the power to which a number must be raised to get the number x. A natural logarithm ln(x) is the power to which e would have to be raised to equal x.

Plot of the natural logarithm

A normal probability distribution

The natural logarithm function is the inverse of the exponential function:

eln(x) = x

ln(ex) = x

natural measure

Also called natural scale, a commonly used measure or scale for an attribute, expressed in original or natural units. For example, project cost is commonly measured in dollars (or other currency), and time to complete may be measured in months.

net present value (NPV)

The traditional method for quantifying the financial attractiveness of a project based on equating project value to the present value (PV) of the project's present and future cash flows. NPV, also called discounted cash flow (DCF), represents the amount in today's dollars by which all income projected from the project exceeds all costs.

Formula for computing NPV

Basically, NPV attempts to answer the question, "What is the equivalent, lump-sum worth of this project?" According to NPV logic, given two projects, the one with the larger NPV should be preferred. Also, any project with a positive NPV should be viewed as a good investment.

NPV computes the present value for a project by discounting estimated future incremental cash inflows and outflows. The discount rate is chosen to represent a required rate of return or target yield for the capital invested, which is often chosen to the company's weighted average cost of capital (WACC).

To accurately calculate a project's NPV, it is necessary to estimate the life-cycle cash flows that would result from doing the project— not just the project costs, but also all of the financial benefits that would result from the project. For example, if a project improves productivity, the future cost savings that would result should be included in the estimated cash stream. Cost estimates must reflect the total cost of ownership (TCO) perspective. Thus, costs include project investment costs, future operating costs, and any "exit" costs associated with ultimately phasing out whatever it is that the project produces. Since taxes and the capital structure of the firm can have a significant impact, cash flows should ideally be calculated "after-tax," accounting for depreciation, working capital, and other considerations. More precisely, what should be estimated is the impact of the project on the company's so-called free cash flow, the value actually available to shareholders and debt holders.

NPV cannot be used directly as a reasonable metric for ranking projects because it ignores the size of the projects being compared. Larger projects tend to have larger NPV's. Thus, projects with large NPV's tend to consume greater portions of the available budget. However, NPV can be used to translate the financial benefits expected from a project into an equivalent dollar value which, if divided by the project cost, can be a useful metric for ranking projects (assuming the projects are independent).

By requiring that a single, nominal cash flow be identified for the project, NPV ignores uncertainty. This limitation may be addressed by using NPV in conjunction with simulation. If alternative project cash flows are simulated, they may be used to generate a range or probability distribution of possible project NPV's. This distribution may be interpreted as describing the uncertainty over the actual value that the project will generate. See expected net present value (ENPV) for more discussion.

The major limitation of NPV for project prioritization is that it underestimates the true value of projects (e.g., the impact of a project on shareholder value) because it leaves out "intangible" project benefits that are difficult to express as incremental cash flows. One such omitted component of value is "option value," the value associated with options embedded in or created by the project which may allow management to better respond to future risks and take advantage of future opportunities. See real options analysis for an explanation of option value. One method for addressing this bias is to add to the estimated project cash flows additional dollar amounts that represent the equivalent dollar value of the non-financial project benefits. See multi-attribute utility analysis for a method for doing this.

Another problem with NPV is that it is not always clear what discount rate should be chosen. According to finance theory, the correct rate is a risk adjusted discount rate equal to the return available from investing in securities equivalent to the risk of the project being evaluated. Research on real options shows that the discount rate ought to be adjusted over time depending on how uncertainties are resolved and on the project-management strategy. Using a constant discount rate for a project implicitly assumes that uncertainty increases over time in a specific way (geometrically). If the discount rate is adjusted upwards to account for the risk of the project, there will be a bias toward short-term, quick payoff projects because project benefits that occur in the more distant future will be severely discounted.

network model

A model composed of multiple, relatively independent sub-models linked or interact in specified ways. Thus, network models are often used to represent systems composed of multiple, interacting components or subsystems.

A network model is distinct from a hierarchical model. The latter has a top-down, tree structure such that each subsystem is linked to at most one "parent" subsystem. With a network, each sub-model may have links to multiple parents.

The term network model is also used to describe a database structured as a collection of records with relationships among the data represented by links.

nominal group technique

A group decision-making method, developed originally by Andre Delbecq and Andrew Vandeven, that helps prevent the domination of discussion by a single person, encourages more passive group members to participate, and results in a set of prioritized solutions or recommendations.

The basic process begins with each participant suggesting possible solutions or choices, typically recorded on a flip chart. After duplicate ideas are eliminated, each person ranks the solutions and then anonymously votes points according to his or her ranking (e.g., 5 points to the first choice, 4 points to the second choice, etc.). The total points each solution receives determines the group ranking, and the top ranked alternative is assumed to be the group's choice.

non-compensatory method

A multi-criteria decision making method (MCA) that is not compensatory, meaning that poor performance of an alternative against one criterion may not be compensated for by good performance relative to other criteria. A lexicographic method is an example of a noncompensatory method.

Noncompensatory methods are based on the premise that certain preference attributes are not compensatory by nature, that is, certain attributes cannot be traded off with, or compensated by, other attributes even if they are objectively considered "good" attributes. For example, when purchasing food you may reject any products that contain a substance to which you are allergic.

The advantage of non-compensatory methods is that performance with respect to criteria having a disqualifying threshold can be evaluated sequentially. Whenever you find an alternative that fails the test you can disqualify it, there is no need to expend the effort to consider its performance relative to any other criteria. People often employ non-compensatory rules over compensatory methods for making purchase decisions. For example, when purchasing a car you might be concerned with acceleration, gas mileage, and cost, but you won't bother even considering cars whose price is above a level set by your budget. The reason being that evaluating performance against all relevant criteria and then mentally trading off the alternative's perceived weakness on one or more attributes with its perceived strength on other attributes collecting and comparing all of the necessary data is simply too difficult or mentally labor intensive.

While most project portfolio management tools with capability to prioritize projects employ compensatory methods, a few incorporate non-compensatory methods. Such methods gradually eliminate projects from consideration based on identifying alternatives with less attractive attributes.

normal distribution

An often used probability distribution with a symmetrical bell shape. It has been found to approximate the frequency distributions for many economic, natural, social and other real world phenomenon.

The normal distribution has two parameters—the mean, denoted μ, and the standard deviation, denoted σ. The mean of the distribution determines the location of the center of the graph, and the standard deviation determines the spread and height of the graph. When the standard deviation is large, the curve is short and wide; when the standard deviation is small, the curve is tall and narrow.

Example normal distribution

A normal probability distribution

With the normal distribution, roughly 68 percent of all values lie within one standard deviation, 95 percent within two standard deviations, and 99 percent lie within three standard deviations of the mean.


As used here and in multi-criteria analysis, the process of multiplying a function, series, or other mathematical item by a factor that makes it achieve some associated "normal" property, such as summing to one unit. In the case of weihts, for example, it is just a matter of dividing each weight by the sum of the weights.

Another common usage is for the process of converting a performance measure for an relative to a criterion into a unitless measure (a score) on a zero-to-one scale. In this case, the purpose of normalization is to allow performance measures expressed using different units to be converted into a common, unitless measure, thereby allowing direct comparisons across criteria.

Different normalization methods are used, although most often the transformation is a linear one. If the performance measure is to be maximized, the two most common transformations are (1) the fraction of the maximum value of the performance measure and (2) the fraction of the difference between the minimum and maximum values of the performance measure. Mathematically, let the level of performance achieved by an alternative with respect to the i'th criterion is denoted xi. The units for xi will be whatever unit is most natural for measuring performance relative to the criterion. To normalize this measure, identify the best (maximum) and worst (minimum) levels of performance attained by any alternative, denoted ximax and ximin respectively. The transformation of the performance measure to a score indicating the fraction of the maximum value is:

Transformation to fraction of maximum value

The transformation of the performance measure to a score indicating the fraction of the difference between the maximum and minimum value is:

Transformation of performance measure to score

To illustrate, suppose that you are deciding which of several automobile models to purchase. One criterion might be engine power—you want a car with sufficient power to safety pass slower vehicles. The natural unit of measurement for a car's power is brake horsepower (bph). Of the several cars that you are considering, 200 bhp and 360 bhp are the least and most horsepowers. Suppose one particular car has a horsepower of 300 bhp. Its normalized horse power, based on the second formula above, is 0.625 (=100/160); it is 62.5% of the difference between the most and least horse powers of the cars you are considering.

Normalization is useful because it allows performance against all criteria to be expressed on the same, unitless scale.


According to an ideal standard; that is, what would be considered the correct way of doing something based on norms of behavior. The terms normative and descriptive are often used to contrast two types of models. A normative model describes idealized behavior whereas a description model describes typical or actual behavior. Vendors of project portfolio management software sometimes say their tool prioritizes projects based on a normative model for project selection.