## Cost Estimating

A cost estimate is a prediction of the likely cost of the resources that will be required to complete all of the work of the project.

Cost estimating is done throughout the project. In the beginning of the project proof of concept estimates must be done to allow the project to go on. An ''order of magnitude'' estimate is performed at this stage of the project. Order of magnitude estimates can have an accuracy of — 50 percent to +100 percent. As the project progresses, more accurate estimates are required. From company to company the specified range of values for a given estimate may vary as well as the name that is used to describe it. For example, conceptual estimates are those that have an accuracy of — 30 percent to + 50 percent. Preliminary estimates are those that have an accuracy of — 20 percent to + 30 percent. Definitive estimates are those that have an accuracy of — 15 percent to + 20 percent. Finally, the control estimate of — 10 percent to +15 percent is done. Early in the project there is much uncertainty about what work is actually to be done in the project. There is no point in expending the effort to make a more accurate estimate than the accuracy needed at the particular stage that the project is in.

### Types of Estimates

Several types of estimates are in common use. Depending on the accuracy required for the estimate and the cost and effort that can be expended, there are several choices.

### Top-Down Estimates

Top-down estimates are used to estimate cost early in the project when information about the project is very limited. The term top down comes from the idea that the estimate is made at the top level of the project. That is, the project itself is estimated with one single estimate. The advantage of this type of estimate is that it requires little effort and time to produce. The disadvantage is that the accuracy of the estimate is not as good as it would be with a more detailed effort.

### Bottom-Up Estimates

Bottom-up estimates are used when the project baselines are required or a control type of estimate is needed. These types of estimates are called ''bottom up'' because they begin by estimating the details of the project and then summarizing the details into summary levels. The WBS can be used for this ''roll up.'' The advantage of this kind of estimate is that it will produce accurate results. The accuracy of the bottom-up estimate depends on the level of detail that is considered. Statistically, convergence takes place as more and more detail is added. The disadvantage of this type of estimate is that the cost of doing detailed estimating is higher, and the time to produce the estimate is considerably longer.

### Analogous Estimates

Analogous estimates are a form of top-down estimate. This process uses the actual cost of previously completed projects to predict the cost of the project that is being estimated. Thus, there is an analogy between one project and another. If the project being used in the analogy and the project being estimated are very similar, the estimates could be quite accurate. If the projects are not very similar, then the estimates might not be very accurate at all.

For example, a new software development project is to be done. The modules to be designed are very similar to modules that were used on another project, but they require more lines of code. The difficulty of the project is quite similar to the previous project. If the new project is 30 percent larger than the previous project, the analogy might predict a project cost of 30 percent greater than that of the previous project.

### Parametric Estimates

Parametric estimates are similar to analogous estimates in that they are also top-down estimates. Their inherent accuracy is no better or worse than analogous estimates.

The process of parametric estimating is accomplished by finding a parameter of the project being estimated that changes proportionately with project cost. Mathematically, a model is built based on one or more parameters. When the values of the parameters are entered into the model, the cost of the project results.

Resource cost rates must be known for most types of estimates. This is the amount that things cost per unit. For example, gasoline has a unit cost of \$1.95 per gallon; labor of a certain type has a cost of \$150.00 per hour, and concrete has a cost of \$25.00 per cubic yard. With these figures known, adjustments in the parameter will allow revising of the estimate.

If there is a close relationship between the parameters and cost, and if the parameters are easy to quantify, the accuracy can be improved. If there are historical projects that are both more costly and less costly than the project being estimated, and the parametric relationship is true for both of those historical projects, the estimating accuracy and the reliability of the parameter for this project will be better.

Multiple parameter estimates can be produced as well. In multiple parameter esti mates various weights are given to each parameter to allow for the calculation of cost by several parameters simultaneously.

For example, houses cost \$115 per square foot, software development cost is \$2 per line of code produced, an office building costs \$254 per square foot plus \$54 per cubic foot plus \$2,000 per acre of land, and so on.

### Control Estimates

Control estimates are of the bottom-up variety. This is the type of estimate that is used to establish a project baseline or any other important estimate. In a project, the WBS can be used as the level of detail for the estimate. The accuracy of this estimate can be made to be quite high, but the cost of developing the estimate can be quite high and the time to produce it can be lengthy as well.

Control estimates are based on the statistical central limit theorem, which explains statistical convergence. If we have a group of details that can be summarized, the variance of the sum of the details will be less significant than the significance of the variance of the details themselves. All that this means is that the more details we have in an estimate, the more accurate the sum of the details will be. This is because some of the estimates of the details will be overestimated, and some will be underestimated. The overestimates and underestimates will cancel each other out. If we have enough detail, the average overestimates and underestimates will approach a zero difference.

If we flip a coin one time, we can say it comes up 100 percent heads or 100 percent tails. If we continue flipping the coin a large number of times, and the coin is a fair coin, then 50 percent of the flips will be heads and 50 percent of the flips will be tails. It may be that there are more heads than tails at one time or another, but if we flip the coin long enough, there will be 50 percent heads and 50 percent tails at the end of the coin flipping.

If we know the mean or expected values and the standard deviations for a group of detailed estimates, we can calculate the expected value and the standard deviation of the sum. If we are also willing to accept that the probability of the estimate being correct follows a normal probability distribution, then we can predict the range of values and the probability of the actual cost.

Using the same estimates for the expected value and the standard deviation that we used in the PERT method for schedules, we can make these calculations. These are only approximations of these values, but they are close enough to be used in our estimating work.

Expected Value = [Optimistic + Pessimistic + (4 X Most Likely)]/6 Standard Deviation = (Pessimistic - Optimistic) / 6

Where do these values come from? Most estimators report a single value when they complete a cost estimate. However, they think about what the cost will be if things go badly, and they think about what the cost will be if things go well. These thoughts are really the optimistic and pessimistic values that we need for our calculations. They do not cost us a thing to get. All we have to do is to get the estimator to report them to us.

For control estimates we are usually happy to get a 5 percent probability of being correct. As luck would have it, this happens to be the range of values that is plus or minus 2 standard deviations from the mean or expected value.

For example, suppose we want to estimate the cost of a printed circuit board for an electrical device of some sort. In Table 3-1, the optimistic, pessimistic, and most likely values that were estimated are entered in columns 3, 4, and 5. From these estimated values the expected value of the individual components can be calculated. This is shown in column 6. The expected value of the assembly can be reached by adding the expected values.

The standard deviation for each component is calculated and shown in column 7. In order to add the standard deviations they must first be squared. These values are shown in column 8. Next, the square of each of the standard deviations for each component is added, and the square root is taken of the total. This is the standard deviation of the assembly.

The expected value of the assembly is \$5.54, and the standard deviation is 7.4 cents. We are interested in the range of values that have a probability of containing the actual cost of the assembly when it is produced. The range of values that would have a 95 percent probability of occurring is plus or minus 2 standard deviations from the expected value. In our example we can say that the assembly has a 95 percent probability of costing between \$5.39 and \$5.67.