# Applying Earned Value

## Applying Earned Value

Presuming the project team has been initiated into the earned value system and the rules for claims and reporting have been established, the project manager is ready to apply earned value to the project. The following examples provide some of the situations likely to be encountered.

With the earned value equations in hand, we can now turn to applying them to project situations. We must first establish a ground rule for taking credit for accomplishment. For the moment, the rule is the simplest possible: 100% earned value is given for 100% task completion; else, no credit is given for a partial accomplishment. This is the rule we applied in the bicycle example.

Look now at Figure 6-1. The planned value for the two tasks, A and B, is \$50,000. Only Task A is completed, so under the "all-or-nothing" credit rule, no EV is claimed for Task B. Using the equations in Table 6-4, we calculate the report as shown in Figure 6-1. We see that we are \$30,000 behind schedule. This means that \$30,000 of work planned for the period was not accomplished and must be done at a later time. We are \$10,000 over cost, having worked on Task B and claimed no credit and finished Task A for an unspecified cost for a total actual cost of \$30,000.

Now in Figure 6-2, we see that we complete Task B, claim \$30,000 of earned value, and calculate the variances for Period 2. Of course since there was no planned value and a big earned value, we get a positive schedule variance. Overall from the two periods combined, we get the following performance record for Tasks A and B:

PV = \$50,000, EV = \$50,000, AC = \$60,000

Schedule variance at the end of Period 2: EV - PV = \$0

Cost variance at the end of Period 2: EV - AC = -\$10,000

We are on schedule at the end of Period 2 but carry a cost variance along for the rest of the project. The project manager now begins to analyze where in the project there might be a \$10,000 positive variance in another work package that could offset the cost variance from the Task A and B experience.

### Penalty Costs and Opportunity Costs in Earned Value

You might have observed from the bicycle project that the value variance to the project sponsor for the one-period delay as measured in earned value is \$0. By definition, the schedule variance is also \$0. But in calendar terms, the project is one period late. Is it not reasonable to assign a variance to a late delivery? If the late delivery has no dollar consequence, then the late delivery has no influence on the earned value metrics. But one of the principal objectives of the earned value method is to influence project manager decision making and performance. Without consequences, the project manager will focus elsewhere. If there are dollar consequences to the late delivery, then those dollar penalties are incorporated into the period earned value or the period cost, depending on whether the dollar penalty is an opportunity cost (value) or an expensed cost (cost).

Consider this project situation: delivery of the bicycle one period late requires payment of a late delivery penalty of \$500 to the ultimate customer. Such a payment is a "hard" cost expense. The \$500 is expensed to the project and becomes a part of the project cost. The value of the bicycle to the sponsor remains the same, PV = \$1,000. The variances now are for the whole project:

 PV of bicycle = \$1,000 AC = \$1,500 = \$1,000 cost + \$500 penalty EV = \$1,000 Cost variance = EV - AC = \$1,000 - \$1,500 = -\$500 Schedule or value variance = EV - PV = \$1,000 - \$1,000 = \$0

A late delivery also may present a depreciation of value requiring a discount to be applied to the earned value. We have studied the discount issues in prior chapters. Let us say that a one-period delay requires a 5% discount of value. No dollar penalties are involved. The 5% discount is an opportunity cost requiring an adjustment of the earned value. The bicycle project variances would then be:

 PV = \$1,000 (The performance baseline does not change) EV = (1 - 0.05) * \$1,000 = \$950 (Opportunity cost is applied to the EV) AC = \$1,000 Cost variance = EV - AC = \$950 - \$1,000 = -\$50 Schedule or value variance = EV - PV = \$950 - \$1,000 = -\$50

In subsequent tables and paragraphs the "value variance" will be called the "schedule variance." Make note that the schedule variance is dimensioned in dollars rather than hours, days, or weeks.

### Graphing Earned Value

Let's turn our attention from numbers to graphs. Sometimes the graphical depiction is very instructive and more quickly grasped than the numbers. For the moment, let us consider the project situation as depicted in Figure 6-4. The equations from Table 6-4 have been used to draw some curves. To make it simple, the curves are actually straight lines. There is no loss of generality for having straight lines for purposes of variances. However, the slope of the cumulative line at the point of evaluation affects the forecast, so just connecting some widely spaced points may create errors in the forecast.

Figure 6-4: Project Example 1.

In Figure 6-4, we see a project already under way with a vertical line drawn at the evaluation point. The curves are the aggregated sums of all the work packages in the WBS up to the evaluation point. The PMB extends for the whole project. Thus, these curves represent the project situation overall. At a glance, the experienced project manager can see that the earned value curve is below the actual cost curve, so there is a cumulative unfavorable cost variance to the earned value. The earned value curve is also below the PMB, so there is a schedule variance as well.

EV curve below AC means: unfavorable cost variance

EV curve below the PMB or PV means: unfavorable schedule variance

### Forecasting with Earned Value Measurements

Let us return to the bicycle now that we have a more complete set of equations to work with from Table 6-4. At the end of Period 1, we could make some forecasts:

 Schedule performance index (SPI) = EV1/PV1 = \$0/\$1,000 = 0 Forecast of schedule = (PMB - EV1)/SPI = indefinite (on account of divide-by-0) Cost performance index (CPI) = EV1/AC1 = \$0/(-\$900) = 0 Forecast of cost = (PMB - EV1)/CPI = indefinite

What to make of these forecasts? With no earnings, it is impossible to measure an earnings trend and therefore forecast the future from the past. What should the project manager do in such a case? With no guidance from the earned value forecast, the project manager could forecast the future or rebaseline by re-estimating the remaining work.

We can use the curves in Figure 6-4 to do some elementary forecasting. Doing so will give us a feel for the problem. Unlike the bicycle case, where the earned value was \$0 and the forecast was indefinite, there are cumulative earnings for the project shown in Figure 6-4. The project manager can make a prediction by extending the cumulative earned value line until it intersects with the dollar value of the planned value at completion. At this intersection, the cumulative project earned value equals the cumulative value of the project. The extended time on the horizontal axis at the point where the cumulative earned value equals the planned value at completion is the schedule at completion.

The project manager must be careful at this point. The slope of the extension must match the slope of the cumulative earned value curve at the point of evaluation. The slope is the ratio of a small increment of the vertical scale divided by a small increment of the horizontal scale. On the figure we are working with, the horizontal scale is time, so the slope is:

ΔEV/ΔT, where Δ means "small increment of

This slope, ΔEV/ΔT, tells us we are earning value at a certain rate of so many dollars, \$ΔEV, per time unit, AT. If the remaining value to be earned is PVremaining, then the time required to earn that much value is:

Remaining time = ΔT * PVremaining/ΔEV

A numerical example would probably be helpful at this point. Suppose there is \$10,000 of remaining value to be earned on a project in the remaining periods. Let us say that in the last reporting period the earned value was \$1,000, but that overall the earnings to date have been \$24,000 over six periods. On average, the \$EV/period is \$24,000/6 = \$4,000/period. Using this average, we could forecast that 2.5 periods remain to earn the remaining \$10,000. Using our formula: 2.5 = 6 * \$10,000/\$24,000.

However, in the last period, earnings have slowed to \$1,000/period. Thus, applying the formula to the performance as of the last period to find out how many remaining periods there are, we have: 10 = 1 * \$10,000/\$1,000. Which forecast is correct, 2.5 periods or 10 periods? It depends. It depends on the judgment of the project manager regarding whether or not the performance in the last period is representative of the future expectations. If the last period is not representative, then the overall average that uses much more information should be used. When working with statistics like average, in general the more information incorporated, the better is the forecast.

### Estimate at Completion, Estimate to Complete

There is a simple formula that ties the EAC and ETC together:

EAC = ETC + AC to date

The actual cost to date is obtained right off the P&L. However, the ETC is somewhat problematic. There are three ways to calculate ETC:

• Apply the earned value formula: ETC = PVremaining * ACto date/EVto date

• Re-estimate the ETC and then rebaseline the remaining planned value as described elsewhere

• ETC = PVremaining

Of course, all three methods will provide a different answer. Which to use is a decision to be made by the project manager considering the situation of the project.