## Mastering the PMP Calculations, one formula at a time

The PMP calculations are linked to each other.

That’s why learning all of them is vital to passing the PMP.

That’s why learning all of them is vital to passing the PMP.

**Actual Cost (AC)**

Actual Cost is one of the easiest calculations that you’ll need to know for the PMP. Well there’s no formula involved so that makes it pretty easy right? AC is used to answer the question - “How much have we spent on the project as of today?”

Tip – AC is also known as Actual Cost of Work Performed (ACWP).

As we already said, there’s no formula for AC. But that doesn’t mean there’s no math involved.

To calculate the AC for a project, you add up all the costs incurred by the project as of the point in time you are measuring. Usually this means adding all the costs incurred by the project as of today.

__Example of Calculating Actual Cost__

Let’s see an example.

Tom is working on a project to install a new Wi-Fi network on the campus of a Palo Alto Smartphone manufacturer.

The project has a budget of $2.5 million and involves numerous contractors. The expected value of the work (e.g. the Wi-Fi network) is $3.6 million dollars. Tom has budgeted $1.2 million for Wi-Fi equipment, $1.1 million for installation costs, employee laptop updates and training. He has also budgeted $200,000 for miscellaneous costs.

The project team has just begun installing the equipment needed – starting with the Wi-Fi antennas. The project has spent $400,000 on Wi-Fi equipment, $50,000 on site surveys, $3,000 on team meetings and team building sessions. Tom will be signing a contract for an extra ten Wi-Fi antenna tomorrow for $30,000.

What is the AC of the project?

Answer: $453,000. How did we calculate this? $400,000 + $50,000 + $3,000 = $453,000.

**Budget At Completion (BAC)**

Budget At Completion (BAC) is a measure of how much you estimate the project will cost at its completion.

Tip – BAC is an estimate and is determined at the start of the project.

How is BAC calculated? Usually for the PMP exam you won’t need to calculate it. You will normally be given the BAC in the question as part of figuring out another value. For example, the question may want you to calculate the To-Complete Performance Index. To do that, the BAC could be included in the question text. However, if you do need to calculate the BAC here’s how to do it. BAC is estimated by calculating how much money you believe you will need to complete the project. (There is no formula).

__Example of Calculating BAC__

Let’s see an example.Dave is the project manager on a project to install a new privacy fence around a five-star hotel.

The materials for the fence are estimated to cost $230,000. The labor is estimated at $95,000. Miscellaneous costs are estimated at $15,000. And training is estimated at $3,000. Ongoing maintenance is estimated at $20,000.

What is the BAC?

Answer: $343,000. How did we calculate this? $230,000 + $95,000 + $15,000 + $3,000 = $343,000.

**Planned Value (PV)**

Planned Value (PV) is the estimated value of the work to be completed by your project within a specific time period.

PV is also used to calculate Schedule Variance.

Tip – PV is also known as Budgeted Cost of Work Scheduled – BCWS.PV Formula: Planned Value = Planned % Complete X BAC

__Example of Calculating PV__

Let’s see an example. Jenny is the project manager on a project to build a new smart-phone browser. The project is expected to last 10 months. The estimated total cost is $2,300,000. What is the PV after 5 months?

Answer: $1,150,000. How did we calculate this? Planned % Complete is the percentage of the project that is planned to be complete. In this case, 5 months / 10 months = 0.5 (or 50% in other words). We know that BAC is the estimated total cost of the project. So in this case, BAC = $2,300,000. With these figures we can calculate that PV = 0.5 x $2,300,000 = $1,150,000.

**Earned Value (EV)**

EV is the estimated value of the work completed by your project as of today.So if the project stopped today, the EV would show the value that it has produced. Understanding EV is vital as it’s used in many of the other calculations that you will need to know to master the PMP exam.

It’s used to calculate:

Cost Variance (CV)

Schedule Variance (SV)

Cost Performance Index (CPI)

Schedule Performance Index (SPI)

To-Complete Performance Index (TCPI)

Tip – EV is also known as Budgeted Cost of Work Performed (BCWP).

EV Formula : Example of Calculating EV : Earned Value = Percent Complete * Budget At Completion

Rohit is the project manager on a project to build a new cricket stadium in Mumbai, India. After six months of work, the project is 27% complete. The estimated total cost of the project is expected to be $50,000.000. What is the EV?

Answer: $13,500,000. How did we calculate this? The Percent Complete = 27%.

We know that BAC is the estimated total cost of the project. So in this case, BAC = $50,000,000. With these figures we can calculate that the EV = 27% * $50,000,000 = $13,500,000.

**Cost Variance (CV)**

CV Formula : As the name suggests the CV calculation shows if there are any variations in the costs of the project.

In other words, CV shows if your project is under or over budget.

Cost Variance = Earned Value – Actual Cost

Tip – EV is also known as Budgeted Cost of Work Performed (BCWP). And AC is also known as Actual Cost of Work Performed (ACWP).

So you may see the formula written as:

CV = BCWP – AC

CV = BCWP - ACWP

CV = EV – ACWP

The formula produces a dollar amount (or pounds, rupees etc). But what does this mean? A negative number is over budget. And a positive number is under budget. An important point to remember is that on a perfect project, the CV is $0. This because a CV of $0 is neither over budget or under budget. Most people understand instinctively why being over budget is bad. But why is being under budget bad?

It could be a sign that the team has missed a requirement, forgot to install a piece of equipment etc. Anytime the CV isn’t $0 – you need to investigate.

__Example of Calculating CV__

Chris is the project manager on a project to build a new photo sharing app for the iPhone and Android smart phones.

The value earned by the project is $2,300,000. The costs incurred by the project are $2,560,000. What is the CV? And what does it tell us about the project?

Answer: The CV is -$260,000. And this tells us that the project is over budget. How did we calculate this? The EV is $2,300,000 (“value earned by the project” is another way of saying Earned Value).

The AC is $2,560,000 (The project’s costs are “the costs incurred by the project”). Knowing this we can calculate that the CV = $2,300,000 – $2,560,000 = -$260,000.

**Schedule Variance (SV)**

Just like with CV, Schedule Variance shows if there is a variance on the project. In this case, it shows if there is a variance in the scheduling of the project. Simply put, Schedule Variance is your project is behind or ahead of schedule.

SV Formula: Schedule Variance = Earned Value – Planned Value

Tip – EV is also known as Budgeted Cost of Work Performed (BCWP). And PV is also known as Budgeted Cost of Work Scheduled (BCWS). So you may seen the formula written as: SV = BCWP - BCWS

A value of less than zero means the project is behind schedule. And a value greater than zero means the project is ahead of schedule. A value of zero means the project is exactly on schedule but this is very rare.

__Example of Calculating SV__

Doug is the project manager for a software company based in San Francisco. He is working on a project to build a new inventory management system. The project has been underway for six months. Doug has estimated that the project should have a planned value of $825,000 at this point. The value earned by the project is $815,000. What is the Schedule Variance? And what does this tell us about Doug’s project?

Answer: The Schedule Variance is -10,000. This tells us that the project is behind schedule. How did we calculate this? Well we know that Schedule Variance = Earned Value – Planned. The Earned Value is $815,000. The Planned Value is $825,000. Knowing this we can calculate that the SV = $815,000 – $825,000 = -$10,000

**Cost Performance Index (CPI)**

Cost Performance Index is used to show the efficiency of the money being spent by the project. In other words, the Cost Performance Index shows how much value you are getting for each dollar spent on the project (or pounds, rupees or riyals – you get the point).

CPI Formula: Cost Performance Index = Earned Value / Actual Cost

The result of the Cost Performance Index formula is a number. So what does this number mean? A value of less than one means that money is being spent inefficiently on the project. So if your CPI is 0.75, this means that for every $1 spent on the project you are getting $0.75 of value. A CPI of one means that your project is exactly on track. You spent $1 on the project and got $1 Investment Return of value in return.

And a value of greater than one means that money is being spent efficiently on the project. So if your CPI is 1.4, this means that for every $1 spent on the project you are getting $1.40 of value. Cost Performance Index answers the question “We’re investing in this project, but what is the return?”

Brian is the project manager for a food manufacturing company based in Dallas, Texas. He is working on a project to implement a new inventory management system. The estimated value of the work completed by the project so far is $405,000. The total cost of the project is expected to be $650,000. So far the project has cost $325,000. What is the Cost Performance Index? And what does this tell us about Brian’s project?

Answer: Knowing this we can calculate that the CPI = $405,000 / $325,000 = 1.25

The Cost Performance Index is 1.25. This means that for every $1 spent on the project $1.25 of value is being produced. How did we calculate this? Well we know that Cost Performance Index = Earned Value / Actual Cost.

The AC is $325,000. Knowing this we can calculate that the CPI = $405,000 / $325,000 = 1.25

__Example of Calculating CPI__Brian is the project manager for a food manufacturing company based in Dallas, Texas. He is working on a project to implement a new inventory management system. The estimated value of the work completed by the project so far is $405,000. The total cost of the project is expected to be $650,000. So far the project has cost $325,000. What is the Cost Performance Index? And what does this tell us about Brian’s project?

Answer: Knowing this we can calculate that the CPI = $405,000 / $325,000 = 1.25

The Cost Performance Index is 1.25. This means that for every $1 spent on the project $1.25 of value is being produced. How did we calculate this? Well we know that Cost Performance Index = Earned Value / Actual Cost.

The AC is $325,000. Knowing this we can calculate that the CPI = $405,000 / $325,000 = 1.25

**Schedule Performance Index (SPI)**

Schedule Performance Index is used to show whether a project is behind or ahead of schedule. In other words, the Schedule Performance Index shows whether your project will deliver late, on time or early.

SPI Formula : Schedule Performance Index = Earned Value / Planned Value

A value of less than one means that the project is potentially behind schedule. So if your SPI is 0.8, the project will not finish on time. An SPI of one means that your project will be finish exactly when the plan predicts. And a value of greater than one means that the project will be completed early. So if your SPI is 1.2, the project will be completed sooner than the plan predicts. Schedule Performance Index answers the question “When will the project be completed?”.

__Example of Calculating SPI__

Frank is the project manager for a software development company based in London. He is managing a project to create a new mobile photo sharing app. The estimated value of the work completed by the project so far is $116,000. The planned value of the project is $125,000. What is the Schedule Performance Index? And what does this tell us about Frank’s project?

Answer: The Schedule Performance Index is 0.93. This means that Frank’s project is behind schedule. How did we calculate this? We know that Schedule Performance Index = Earned Value / Planned Value.

The Earned Value is $116,000. Knowing this we can calculate: Schedule Performance Index= $116,000 / $125,000 = 0.093

**Estimate At Completion (EAC)**

Estimate At Completion (EAC) is used to predict the cost of the project at its completion. In other words, the EAC predicts the total cost of your project. Why is this different to BAC? EAC is used once the project has started and uses actual results from the project not just estimates. If you have been working on a project for six months and the PMO ask for an estimate of what the project will cost. You would have to give them the EAC and not BAC.

EAC Formula

The Estimate At Completion formula is more complicated than most. This is because there are actually four formulas. Each formula tackles a different scenario that you may face on your project.

**Scenario 1 – Original estimate is no longer valid**

You might discover that the original estimates for your project were fundamentally floored. Or circumstances may have changed so much that the estimates you have are no longer valid. In this case you would use the following formula:

Estimate At Completion = Actual Cost + Bottom-up Estimate To Complete

You might be wondering how you calculate the Bottom-up Estimate To Complete. According to the PMBOK® there is no formula. Instead this is a prediction by the team of how much work is left to complete the project.

**Scenario 2 – CPI will stay the same for the rest of the project**

This scenario assumes that the Cost Performance Index (CPI) experienced by the project will stay the same until the project is completed. In this case you would use the following formula:

Estimate At Completion = Budget At Completion / Cost Performance Index

**Scenario 3 – Current CPI is abnormal**

In this case you need to calculate the Estimate At Completion but discover that your current CPI is abnormal. Why could the current CPI be abnormal? An example might be that you have estimated $50,000 to install a new generator. During the installation the generator is accidentally damaged and $5,000 has is spent on repairs.

You have three more generators to install but you are confident that the accident won’t happen again as you have a risk mitigation plan (and you yelled at the people who caused the damage!). In this case it is appropriate to believe that your original estimates for installing the generators are still good. It’s also appropriate that the current CPI (which reflects the accidental damage) does not reflect how the project will progress.

In this case you should use a formula that ignores the CPI. The formula is:

Estimate At Completion = Actual Cost + (Budget At Completion – Earned Value)

**Scenario 4 – Project has to meet a deadline**

We’ve all worked on projects where the boss or a customer demands that a project be delivered by a certain date.

To calculate the Estimate At Completion for such a project you need to take into account the

Schedule Performance Index and Cost Performance Index. The formula is:

Actual Cost + [(Budget At Completion - Earned Value) /(Cost Performance Index X Schedule Performance Index)]

__Examples of Calculating EAC Example 1__

Frank is the project manager for a software development company based in London. He is managing a project to create a new recipe sharing social network. The project recently hit problems when the development team discovered that the software architecture they were going to use is not valid. After discussions the team has decided on a new approach. The PMO has asked for a new estimate of the total cost of the project. The project has already spent $210,000 and has a CPI of 1.1. After talking with the teams on the project, he determined that the remaining costs are development – $50,000, quality assurance – $30,000 and documentation – $10,000.

What is the Estimate At Completion?

Answer: The Estimate At Completion is $300,000.How did we calculate this? In this example, the original estimates are bad because they are based on a flawed architecture approach. Therefore, we will calculate Estimate At Completion using the formula from scenario one: Estimate At Completion = Actual Cost + Bottom-up Estimate To Complete

Knowing this we can calculate: $210,000 + ($50,000 + $30,000 + $10,000) = $300,000

__Example 2__

Tim is the project manager for an undersea cable company based in Cyprus. He is managing a project to lay an optical fiber cable from Naples to Palermo. The PMO has asked for an updated estimate of the total cost of the project. At the start of the project, the costs of the project were estimated as $1,600,000 for design and permitting, $18,750,000 for optical fiber costs, $4,500,000 for installation and $2,300,000 for testing of the cable. The Cost Performance Index of the project is currently 1.08. What is the Estimate At Completion?

Answer: The Estimate At Completion is $25,138,888.89 How did we calculate this? In this example, the CPI is not considered abnormal. Therefore, a formula using CPI can be used. So we will calculate Estimate At Completion using the formula from scenario two: Estimate At Completion = Budget At Completion / Cost Performance Index

Knowing this we can calculate: ($1,600,000 + $18,750,000 + $4,500,000 + $2,300,000) / 1.08 = $25,138,888.89

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