# Capital Budgeting: Managing Efficient IT Project Portfolios

### The Devil Is in the Details

The major benefit that Evolver brings is its simplicity of use. The major downfall that it brings is also its simplicity of use. That's because this application is not immune to the venerable axiom: garbage in, garbage out!

In the capital budgeting process described above, you first need to estimate the expected rate of return (μ) and the standard deviation (σ) of the individual projects. Then, you need to estimate the way the returns on these projects interrelate (ρ_{ij}). With these data, you can construct the *efficient frontier* of all risky projects.

So, using these subjectively obtained values for, say, 40 projects can easily lead to unexpected results. That's because, for one reason, there will be almost 800 imprecisely known correlations between pairs of projects. (Recall the formula: number of relationships among n entities = (n^{2} - n)/2.

Furthermore, there is another significant shortcoming to the theory presented so far when it is applied to project portfolio management; namely, you have gone to all this trouble on the assumption that the element of time could be ignored. However, because capital budgeting typically deals with multi-period investments, some of which constitute mutually exclusive alternatives, expected net present value (NPV)—the discounted sum of the annual cash flows—should be substituted for expected return as your measure of a project's profitability, and by analogy the variance of net present value—the discounted sum of the annual variances—should be used as the risk indicator. NPV will be discussed at some length in the next article of this series. However, a brief introduction to this topic is given in Appendix A.

And, there's another catch. You've assumed for simplicity that the project's cashflows in successive years are statistically independent. In reality, this is not often the case. For example, when a firm invests in the development of a new software application, success in the first year is more likely to be followed by success in the second year. Similarly, a failure in the first year is often the harbinger of bad news in the second year. Thus, in general, you expect the cashflows of a project across years to be positively correlated. But, typically, this association yields a correlation between any pair of years of considerably less than + 1.

### Preference Theory, Utility Functions, and the Like

It may have already occurred to you that nothing in the discussion so far tells you which portfolio among the efficient set to pick. The selection of a particular optimal portfolio from among those on the efficient frontier has to be determined by a decision maker familiar with the firm's attitude about taking financial risk. And, like all human activity, this can be very inconsistent. However, Preference Theory, by taking information about this risk tolerance into account, can be used to modify the equations in Figure 1. Then, when implemented by an optimization tool, this model also serves as a proxy for the psychological makeup of the decision maker.

The modification of the equations in Figure 1 can be accomplished by utility functions; these are mathematical expressions that assign a value to all possible choices. In portfolio theory, the utility function expresses the preferences of economic entities (you or your firm) with respect to perceived risk and expected return.

Rational decision makers are usually willing to accept a lower return to reduce risk when large amounts of money are at stake. These risk-averse individuals or firms then maximize *expected utility (expected subjective satisfaction)* instead of expected monetary value. One position in the efficient frontier cannot be considered superior to another unless some decision-maker *utility* is incorporated. Adding *utility* to the equations in Figure 1 gives you a consistent way to pick the *best* point on the efficient frontier—you ask your optimization tool to maximize utility.

Established firms tend to be risk averse, for the most part, whereas startup firms are frequently risk seeking. There are no right or wrong answers. Thus, if you are asked what amount you will accept for certain instead of engaging in a lottery involving a 0.5 probability of losing $500 and 0.5 probability of winning $1000, the answer is a personal preference rather than a mathematical calculation. (In a group of fifty individuals it is likely that nearly fifty different answers will be obtained.)

Finding a utility function that leads to the best outcome possible for an individual or firm is a process requiring a good deal of knowledge and experience. Doing so for a group of individuals with different preferences (as in the case of a corporation) is even more difficult. Nonetheless, the decision maker must take both risk and attitudes toward risk into consideration.

Further discussion of preference theory and utility functions is beyond the scope of this article. However, the References include a good deal of material on this subject including how to incorporate utility functions into the equations of Figure 1.

### Conclusion

This article discussed the portfolio diversification approach for selecting projects (developed by Nobel-laureate Harry M. Markowitz in the 1950s) and how one implicitly or explicitly uses preference theory (developed by John von Neumann and Oskar Morgenstern in the 1940s) in the process. But, basing your decision on a single methodology is a little like a physician basing his or her diagnosis on just a single symptom (for example, fever, which accompanies both influenza and acute appendicitis). So, just as the physician should consider a number of symptoms when making a differential diagnosis, the corporate decision-maker might want to use the methodology presented above in combination with one or more other methodologies when deciding which projects to include in a portfolio (budget). Subsequent articles will examine some of the other methods commonly used for this purpose.

Finally, the small to medium-size project management office (PMO) may not have the resources to acquire the reliable input data needed for the methodology described above. However, you can sometimes gain valuable insights, after plugging very imperfect data into your spreadsheet/optimizer tools, by thinking about the outputs in *what-if* terms.

### Appendix A: Net Present Value

Net present value (NPV) is a project's net contribution to wealth (or, in the context of this article, the value of the firm). NPV is the *present value* of future cash returns, discounted at the appropriate interest rate, minus the present value of the cost of the investment. When this model is used in capital budgeting, it is applied to a single project (or portfolio) rather than to the firm as a whole. In brief, the procedure is as described below:

- Estimate the expected net cash flows from the project. Depending on the nature of the project, these estimates will have a greater or lesser degree of riskiness. For example, the benefits from replacing a database server used to host a pre-existing data warehouse can be estimated more accurately than those from an investment in a software-development project to produce a new and untried application.
- Estimate the expected cost, or investment outlay, of the project. This cost estimate will be quite accurate for purchased equipment because cost is equal to the invoice price plus delivery and installation charges; but cost estimates for other kinds of projects, particularly those involving human resources, may be highly uncertain or speculative.
- Determine an appropriate discount rate, or cost of capital, for the project. The cost of capital is considered in a later article of this series, but for now it may be thought of as being determined by the riskiness of the project; that is, by the uncertainty of the expected cash flows and the investment outlay.
- Find the present value of the expected cash flows and subtract the estimated cost of the project from this figure. The resulting figure is defined as the net present value of the project. If the NPV is greater than zero, the project should be accepted; if it is less that zero, the project should be rejected. However, as I'll discuss in a future article of this series, there are many exceptions to this rule! In equation form:
where CF

_{t}is the expected net cash flows at period t, and k is the project's periodic cost of capital. Cash outflows (expenditures on the project, such as the cost of buying hardware and software, salaries, and so on) are treated as*negative*cash flows.

Note:If the cost of capital is expected to vary over time, this fact could be taken into account by designating k as the cost of capital in the t^{th}year.

In the next article of this series, I'll take a look at how a Monte Carlo simulation can be used to improve on the NPV method, which is based on single-figure estimates of cash flows. I'll point out that the NPV method makes some very strong assumptions about the nature of the decision maker's preferences, which in some circumstances may not be justified.

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