# Practical calculation of delays and cost overruns

**Abstract**

This paper provides examples of practical calculations of delays and cost overruns in Earned Value Management (EVM). Project managers (PM) use EVM to determine cost and schedule variances between planned and accomplished work for a project at any given time. It is a valuable tool and both the PM and the customer can use it to estimate the final costs at completion and the possible date for completion. In this paper, we briefly visit EVM history and key methods, and present the limitations of the existing models and methods. We then focus on the new EVM calculations as presented in *A Guide to the Project Management Body of Knowledge (PMBOK ^{®} Guide)—Fourth Edition.* Using two scenarios from a case study, we explore the new To-Complete-Performance-Index (TCPI) calculations and suggest how it can be used to calculate cost overruns practically. One case study is based on exact estimates while a second case study explores the same calculations when large uncertainties are involved in the underlying estimates.

**EVM and its Importance**

The EVM concept was introduced to industry almost five decades ago. What is EVM? According to *PMBOK ^{®} Guide*, “EVM integrates project scope, cost, and schedule measures to help the project management team assess and measure project performance and progress. It is a project management technique that requires the formation of an integrated baseline against which performance can be measured for the duration of the project” (Project Management Institute, 2008). It has been successfully used in projects associated with the various agencies of the United States and other governments, but not widely adopted in the private sector. It has been said that the resistance to the universal adoption of the earned value concept is not the fault of the technique itself, but rather of the implementation requirements, the terminology employed, and the countless rules and interpretations that have been perceived by many PMs to be overly restrictive (Fleming & Koppelman, 2005). Details of the emerging earned value body of knowledge that has been accumulated by individuals working within the Department of Defense (DOD) Pentagon and the individual branches of the military has been synthesized to 10 findings, the details of which can be found in several books and articles, including “

*The Earned Value Body of Knowledge*” from Project Management Institute (PMI) by Fleming and Koppelman (2005).

EVM provides PMs with early warning signals of project trouble, and such indicators were found to be reliable as early as 15% into a project (Christensen & Heise, 1992). This was later validated using contracts from the Defense Acquisition Executive Database (DAES):

DOD experience in more than 400 programs since 1977 indicates without exception that the cumulative Consumer Price Index (CPI) does not significantly improve during the period of 15% through 85% of the contract performance; in fact it tends to decline.

This was true regardless of the type or phase of the defense contract, weapon system, or the military service involved. Therefore, a significant overrun, which continues more than 20% into a project, indicates that it is unlikely to meet its budgetary goals, and customers can reliably conclude the project is in trouble. However, the sting is in the tail: On most contracts the CPI tends to decline so that things will only get worse! This indicates that time dependence is a property of the CPI, and so a goal of this paper is to improve EVM by including in the definitions of all EVM quantities the additional aspect of time dependence.

The EVM Practice Standard provides a guide to the principles of EVM and its role in facilitating effective project management (PMI, 2005). Marshall (2006) suggests that EVM is an effective project management methodology, and that EVM principles can be significant positive predictors of project success. EVM metrics were also shown to be important contributors to the successful administration of contracts (Marshall, Ruiz, & Bredillet, 2008). Christensen (1994) demonstrated that performance measurement data are relevant and have predictive value, as well as the general accuracy of the estimate at completion (EAC). On the other hand, Kim (2000) found that the main reasons for non-adoption of EVM were that it was “not needed on small projects and that it was hard to apply.” However, Kim also pointed out that computer tools and training significantly improved the acceptance and performance of EVM, and that “the literature suffers from an over reliance on anecdotal data.”

The key concept is the earned value *(EV)*, which converts project accomplishments from physical units of measure (e.g., miles of roadway or deliverables completed) to financial units (e.g., dollars or labor hours). EVM defines the planned value *(PV)*, as the time-phased budget baseline, and the actual cost *(AC)*, as the cumulative cost spent to a given point in time to accomplish an activity, work package, or project.

Whether a project is on schedule at a particular date is determined by comparing the planned value to the earned value, where value is typically considered to be “earned” by the completion of measurable deliverables. For example, if at some time, four deliverables were planned and three were actually completed (earning value), then the ratio of earned to planned value is 0.75. This is known as the schedule performance index, *SPI* = *EV/PV*, and it is intuitively obvious that a value of *SPI < 1.0* represents a project that is behind schedule. The schedule variance (*SV*) is another measure of the conformance of the earned progress to the planned progress: *SV* = *EV* − *PV*.

Graphs of the variances and performance indices over time provide valuable information about trends in project performance (Vanhouckel & Vandevoorde, 2007). When corrective actions are implemented, the changes in the behavior of the indices are assumed to reflect the impact of management actions. Such graphs can be very effective in project reviews (Anbari, 2002, 2003). Anbari provides detailed, worked examples of EVM, presenting graphical tools for assessing the performance trends, and generally enhancing the effectiveness of the approach. However, according to Anbari, “EVM has not been widely used to estimate the total time at completion, total project duration, or schedule.”

**Criticisms of EVM**

A general criticism of EVM is that it is difficult to find a proper balance between the utility of the *EV* technique…vs. the effort it takes to implement the concept (Quentin & Koppelman, 2005).

There are a number of specific issues associated with EVM as it is currently practiced.

*1) Time Dependence*

*SPI* and *SV* are inherently functions of time, but the form of the time dependence is unknown. This can be most easily seen by examining the behavior of *SPI* toward the end of the project. As activities are completed, the *EV* approaches the planned value, i.e., *EV* → *PV*, and therefore, *SPI* = *EV/PV* → 1.0 (Kerzner, 2006; Vanhouckel & Vandevoorde, 2007). This is true even if the project is late, in which case the *SPI* → 1.0 after the planned completion date. A similar argument shows that *SV* → 0.

If we measure *SPI*(*t*) < 1.0 at some point in time, we would like to know how late the project is going to be by decoding the behavior of *SPI(t)* over time. The challenging question is, therefore: Exactly *how* does *SPI(t)* change over time? If the form of the time-dependence of *SPI(t)* were known, it would allow a PM to compare the actual, measured time-dependent performance to the projected performance.

*2)SV is in Cost Units*

Another criticism of the standard EVM methodology is that the schedule variance is measured in cost units, not time units. A negative schedule variance indicates that the project is behind schedule, but how does one relate a schedule variance, say, *SV* = −$1,000, to a true schedule delay measured in weeks or months? This issue has been addressed in two ways:

*3.Converting SV into time units* (Anbari, 2003).

This involves defining the average actual costs spent per time period, called the spend rate (*ACRate*), and the average planned value per time period, called the planned value rate, (*PVRate*). *PVRate* is defined as the baseline budget at completion (*BAC*) divided by the baseline schedule at completion (*SAC*):

Now, one can divide *SV* by *PVRate* to convert it into time units, which is referred to as the time variance (*TV*):

The usefulness of *PVRate* is that it translates *SV*, which is in currency units, into *TV*, which is in time units.

*4.Measuring the time delay on the cumulative planned and earned value cost curves* (Fleming & Koppelman, 2005).

In this approach, *TV* is measured graphically by drawing a horizontal line from the intersection of the *EV* curve to the *PV* curve, and interpreting the distance on the horizontal time axis as a measure of the schedule delay (or acceleration).

*5.The Schedule Variance Method.*

The Schedule Variance Method (SVM) calculates a project's time delay (or acceleration) as the horizontal distance from the *EV* curve to the *PV* curve (Lipke, 2003). SVM provides an estimate of the current project delay directly in time units. While SVM claims to give the correct signal along the entire life of the project (i.e., whether the project is ahead or behind schedule), SVM does not provide an estimate of the final total project delay from a value determined at the current time.

*6)Constancy Assumption for CPI and SPI*

Another difficulty with making projections about the final cost and schedule is that they assume that values for *CPI* and *SPI* remain constant over time. However, Christensen and Heise (1992) clearly established that graphs of *CPI* and *SPI* change over time. In fact, a measure of the deficiency of the current state of the art is that in attempting to calculate the time estimate at completion, (*TEAC*), Anbari (2003) provides six different formulae for *TEAC.* In this paper we will address this deficiency by explicitly calculating the time dependence of all of quantities, and in particular, *CPI(t)* and *SPI(t).*

**Cost and Schedule Performance Indices**

The cost performance index (*CPI*) is a measure of the conformance of the actual work completed (measured by its earned value) to the actual cost incurred. The schedule performance index (*SPI*) is a measure of the conformance of actual progress (earned value) to the planned progress:

In both of the above formulae, a value of 1.0 indicates that the project performance is on target.

**Estimates of Cost and Time to Complete**

The estimated cost to complete the remainder of the activities is called the estimate to complete (*ETC*), while the estimate of the final cost at completion is called the estimate at completion (*EAC*). The inverse of the *CPI* formula (equation 5) is used in forecasting (Anbari, 2003; Fleming & Koppelman, 2005). For example, dividing the remaining budget by the current *CPI* gives a prediction of the remaining expenditures, if performance continues at the same rate. Adding this to the actual costs to date gives a prediction of the final budget. Methods for calculating *EAC* depend on the assumptions made about the future performance of the project vs. the historical, established performance to date. The *PMBOK ^{®} Guide* provides three approaches, based on three different sets of assumptions (PMI, 2008):

- When the assumptions underlying the original estimate are flawed,
- When past performance is not a good predictor of future performance, and
- When past performance is a good predictor of future performance.

**Proposed Approach to Applying EVM**

In this section we introduce two case studies that illustrate our practical approach to EVM using the TCPI. This index is the calculated projection of cost performance that must be achieved on the remaining work to meet the financial goals as set by the management's current authorized budget, and the PM's estimate at completion (EAC). We present our analysis using two case studies both involving a simple “book contract” project from a publisher.

**Case Study I: Book Contract with Deterministic Estimates**

The book contract project involves 10 clear deliverables or work packages—10 chapters negotiated to be delivered at an estimated cost of $100 each, and delivered one per month. The project should therefore be completed in 10 months. The BAC is therefore $1,000 and PV is $100 each month.

In this first case study we illustrate our approach using deterministic estimates; that is the budgeted costs are based on estimates with zero uncertainty. Note: In the second case study, we elaborate a specific scenario where there is large uncertainty, which happens typically when the scope is not very clear.

The new *PMBOK ^{®} Guide—Fourth Edition* has new information on the topic of EVM. The newly added formula is:

The trouble with the EVM literature is that there are hundreds of formulae floating around. Why pick TCPI? We've got CPI and SPI, so what else do we need? Here are the key features about this index: The TCPI focuses on the remaining project tasks. It is effectively the mirror opposite of the cumulative CPI, in that it reflects what it will take in future performance to recover from a negative actual cost position.

The TCPI takes the work remaining (the total budget less the Earned Value accomplished) and divides that amount by the funds remaining (the latest management financial goal less funds spent) to determine what performance results it will take to meet such goals. The TCPI can be an effective indicator for management at all levels to monitor the remaining project tasks. (Fleming, & Koppelman, 2005).

But it's not just another formula; TCPI is a revolution waiting to happen. But surprisingly, it's a political and ethical revolution.

We've all been there. You're a few months into a project and the first few deliverables have been completed. You diligently calculate the CPI = 0.9. Your customer asks you about your plans for the cost overrun. “No problem, we'll make it up,” you say.

Once our customers start computing the TCPI, that answer is not going to work anymore. Let us show you why.

Consider the above book project where you propose to deliver 10 chapters, one per month. You negotiated the cost and schedule with the customer: The cost of each chapter is $100, and you will deliver one chapter per month. The Budget at Completion (BAC) = $1,000, the projected cost of the book.

**Exhibit 1: The status of the book project after month three.**

You start the project and dutifully deliver the first three chapters on time. But you have to put in some over-time to complete the work. Exhibit 1 shows the status of the project at the end of month three.

We delivered the first three chapters on time, so we “earn” the credit for those (the second line of the table), however, we earn the planned value, not the actual cost. We see that the ** CPI = 0.89.** Ok, so we are running a little over in costs, but at this stage we might just shrug it off.

Now let's add the TCPI calculation. The work remaining is BAC − EV = $1,000 - $300. This is actually an estimate of the earned value remaining: the total earned value for the project is $1,000 (the BAC), while we have completed three deliverables, and so earned the value of $300.

The funds remaining are BAC − AC = $1,000 − $330. This is the remaining budget if we are to deliver as promised. We now calculate the TCPI:

The TCPI says that to complete the project within budget, we have to work at a rate 4% greater than we proposed. So far we are working at an 89% rate (CPI = 0.89), and we need to get our production up to 1.04. We need a 15% improvement (from 89% to 104%). No big deal.

We write three more chapters and our status is now shown in Exhibit 2.

**Exhibit 2: The status of the book project after month six.**

We delivered the next three chapters on time, so we again “earn” the credit for those (the second line of the table. We see that once again the ** CPI = 0.89.** Our production rate is pretty constant. In reality, this is not an uncommon occurrence.

Let's again add the TCPI calculation. The work remaining is BAC − EV = $1,000 - $600. The funds remaining are BAC − AC = $1,000 − $6600, so the TCPI is:

To complete the project within budget, we now have to work at a rate 18% greater than we proposed. In fact, we need a 29% improvement in our expenditure rate (from 89% to 118%)!

At this point, it is getting extremely difficult to justify our position that we can “make it up” and finish on budget. If our customer computes the TCPI, they will have every reason to be concerned.

**Exhibit 3: The TCPI is the efficiency required to complete the project on time. It rises dramatically, clearly demonstrating the project is in trouble. The CPI (dot-dash) shows the current cost efficiency.**

The story does not end here, it gets even more interesting and very quickly. Exhibit 3 shows a plot of the TCPI for the book project if things continue along the same path. Only a quarter of the way through month seven, we must more than double our productivity to stay on budget!

It is interesting to explore the shape of the TCPI in Exhibit 3. Divide the formula for TCPI by AC:

The term *AC/B AC* is the percentage of the budget already spent, which we will call *P(t).* The second term in the numerator is the CPI, so we have:

This formula explains why the TCPI explodes. As *P*(t)→ 1, the TCPI goes to infinity! However optimistic you are as a PM, and no matter what miracle you think you can perform, your project will reach a point where you just cannot deliver on time.

A much better approach is just to admit early on that your project is over budget. The *PMBOK ^{®} Guide* teaches us how to do this. The estimate at completion (EAC) is defined as:

This says that if our cost efficiency is 89% (CPI = 0.89), then we should admit that the final cost will be around $1,123. The *PMBOK ^{®} Guide* 4

^{th}Edition says that when the PM finally owns up to the cost overrun, the TCPI formula changes to:

Note that the *BAC* in the denominator of the TCPI equation is replaced by *EAC.* If we follow the same process as in equations (4-5), we find:

We again use *P*(t) = *AC/BAC*, and *CPI* = *EV/AC*. We also use the fact that *EAC* = *BAC/CPI* to give:

If we now multiply by *P*(t) *× CPI*, we get:

What this says is that if we own up to the cost overran and calculate the new EAC (BAC = BAC/CPI = $1,128), then the TCPI, the efficiency that is required for the rest of the project, is simply the CPI. That is, the TCPI has the remarkable property that if we own up to the cost overrun and use the TCPI with the EAC in the denominator, then we can proceed at our current efficiency (defined by our current CPI) and hit the new cost target.

One of Albert Einstein's favorite sayings was, “Insanity is doing the same thing over and over and expecting a different result.” As PMs, we are often guilty of this kind of insanity when we measure a few values for CPI < 1, and then tell ourselves (and even worse, our customers!) that all will be well.

PM: “We've run into some problems, and our CPI = 0.9, but we believe that we can still deliver on budget.”

Customer: “Oh Yeah? I've computed the TCPI = 1.2. How are you going to get 30% increase in productivity?”

See what we mean? If our customers start computing the TCPI, it is going to change the world-no more cheating.

**Case Study II: Book Contract with Large Uncertainties in Cost Estimates**

In this second case study we briefly elaborate the EVM approach using budgeted costs that have large variances in estimates. This is typical in situations where the scope is not very clear and there is a risk associated with scope creep. The PM could use the three-point estimate technique to come up with the expected value for the budgeted numbers. This is illustrated below.

**Exhibit 4: The status of the book project after month three. (Milestone 1)**

The complexity with this case study arises when the variance is calculated for the above packages. Let us use the same case study to illustrate the complexity.

**Exhibit 5: The status of the book project after month three. (Milestone 1)**

Let us focus on the first work package (chapter 1 deliverable). A PM or customer could view the results from two perspectives.

Bad News: Actual Cost is greater than the planned value.

Good News: Actual Cost is comfortably within the upper boundary of the estimated range of $300 using the three-point method.

**Exhibit 5: Three point method for chapter one**

The same reasoning could apply for the remaining two packages. But once again we have to be honest and conclude that at the given productivity rate we are going to go over the budget and use the TCPI formula illustrated in equation 7 as the new yardstick. To determine when we should own up to the cost overrun and use the TCPI with the EAC in the denominator, the following three stages are proposed.

1) Identify expected values for the project budget,

2) For the various milestones, determine the standard deviation that is acceptable to the customer,

and

3) If the CPI is outside the acceptable standard deviation, equation 7 will be used for computation.

The calculations for the above are similar to the Case Study 1, but we use the expected value instead of the mean. To save space in this research paper we avoid duplication in presenting the results here.

**Conclusions**

EVM provides PMs with early warning indicators of project trouble. It has been widely used in government projects as it is a good tool for a wide variety of application domains. Its adoption is lagging in private industry for a variety of reasons, as explained in this paper. The latest edition of The *PMBOK ^{®} Guide* has introduced a new index, the TCPI. In this paper, we illustrate why TCPI is useful index and illustrate its adoption within the context of two scenarios in a case study. We provide some meaningful guidelines when TCPI (EAC) should be used.

**References**

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© 2009, Kanabar, Leybourne & Warburton

Originally published as a part of 2009 PMI Global Congress Proceedings – Orlando, Florida

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