# Earned Value Management for the PMP Exam!

What are the Math Concepts of the earned value management included in the PMP Exam?

- Cost / Schedule Variance (SV, CV) .
- Cost/ Schedule Performance Index (CPI, SPI).
- Estimate at completion (EAC).
- To Complete Performance Index (TCPI).
- Estimate To Complete (ETC).
- Variance at Completion (VAC).

Earned value is used in performance reviews to measure project performance against the scope , schedule and cost baselines , it integrates Cost , time and scope ( work done ) and can be used to forecast future performance and project completion dates and costs , Earned Value measurements may also result in change requests to the project ,measurements are performed in Monitor and control process group .

**Terms you need to know :**

- Planned Value (PV) , As of today , what is the estimated value of the work planned to be done .
- Earned Value (EV), As of today , what is the estimated value of the work actually accomplished.
- Actual Cost (AC) , As of today , what is the actual cost incurred for the work accomplished.
- Budget at completion (BAC), How much did we budget for the total project effort .
- Estimate at completion (EAC) , What do we currently expect the total project to cost …. Forecast .
- Estimate to Complete (ETC) , From this point on , how much more do we expect it to cost to finish this project … Forecast
- Variance at Completion (EAC) , As of today , how much over or under budget do we expect to be at the end of the project… Forecast

__Cost / Schedule Variances __

Variances: Difference between planned and actual , target value is 0 , positive is good , Negative is bad

Cost Variance (CV) = EV – AC

Schedule Variance (SV) = EV – PV

Variances :

If Cost Variance is Positive , Project under Budget

If Cost Variance is Negative , Project Above Budget

If Schedule Variance is Positive , Project ahead of schedule

If Schedule Variance is Negative , Project behind schedule

**Cost / Schedule Performance Indexes **

Ratio of planned to actual , target value is 1 , greater than one is good , less than 1 is bad

Cost Performance Index (CPI) = EV/AC

Schedule Performance Index (SPI) = EV/PV

Performance Indexes :

If Cost Performance index is above 1 , Project under budget

If Cost Performance index is below 1 , Project above budget

If schedule Performance Index is above 1 , Project ahead of schedule

If schedule Performance Index is below 1 , Project behind schedule

**Estimate At Completion ( EAC )**

As of today , How much we expect the total project to cost ?

**Estimate To Complete ( ETC) **

How much more will the project cost ?

**Variance at Completion ( VAC) **

As of today , how much over or under budget do we expect to be at the end of the project

- Majority of Earned Value Measurement exam questions refers to this topic , there are many ways to calculate EAC depending on the assumptions made ,you should pay attention to information provided in the question to decide which formula to use
- In this lecture we will discuss 2 Formulas , the Next lecture will contain more 2 Formulas .
- Note that EAC , ETC & VAC looks forward , It forecast future performance based on what has actually occurred on the project .
- Once you have the EAC , It is easy to calculate the Variance at Completion

**VAC = BAC-EAC**

- It is the same formula used if you were asked to calculate ETC

**ETC = EAC – AC**

**Formula 1 **

- EAC = AC + ETC
- This formula calculate the actual costs to date plus a new estimate for the remaining work . It is used when the original estimates assumptions are no longer valid .

**Formula 2 **

EAC = BAC / CPI

This formula is used if there is no variances from BAC .have occurred or you will continue in the same rate of spending .

**Formula 3 **

EAC = AC + ( BAC-EV)

This formula calculate the actual costs to date plus remaining budget , it is used when current variances are through to be atypical of the future , It is the actual cost plus the remaining value of work to perform .

**Formula 4 **

EAC = AC + ( BAC-EV)/(CPI*SPI)

This formula calculate the actual costs to date plus remaining budget modified by performance , it is used when current variances are through to be typical of the future .

**To Complete Performance Index ( TCPI) **

The Formula divides the work remaining to be done by the money remaining to do it .

The only index with below 1 is good , above 1 is bad !!

TCPI = ( BAC-EV)/(BAC-AC)

= Work/Money

**Question # 1 :**

You have been managing a project to build a new football complex , you want to forecast the new EAC to check if there is any variances , calculate TCPI of your project based on the new EAC , actual cost is $200,000 , Cost variance is $25,000 ,and the Budget at completion of your project is $350,000

Choice 1 : 1.125

Choice 2 : -1.4

Choice 3 : 1

Choice 4 : -1

**Solution :**

TCPI = (BAC-EV)/(BAC-AC)

But the Question is asking to consider the New EAC , So the formula becomes

TCPI = ( BAC-EV)/( EAC-AC )

= ( 350,000 – EV ) / ( EAC – 200,

CV = EV-AC

25,000 = EV – 200,000

EV = $225,000

EAC = BAC/CPI …….. As if there is no variances from BAC

CPI = EV/AC

= 225,000/200,000

= 1.125

EAC = BAC/CPI = 350,000/1.125

= 311.111

TCPI = (BAC-EV)/(EAC-AC)

= ( 350,000-225,000)/(311,111-200,000)

= 1.125

**Choice 1**

**Question # 2 : **

The actual cost of your project is $200,000 , budget at completion is $325,000 and the cost variance is -$25,000 , from this data calculate To complete performance index , given that senior management did not agree to revise the estimate at completion based on current performance .

Choice 1 : 1.0

Choice 2 : 1.1

Choice 3 : 1.2

Choice 4 : 1.3

**Solution : **

TCPI = ( BAC-EV)/(BAC-AC)

= ( 325,000-EV)/(325,000-200,000)

So we need to determine the EV

CV = EV-AC

-25,000 = EV – 200,000

EV = $ 175,000

TCPI = (325,000-175,000) / ( 325,000-200,000)

= 1.2

**Question # 3 :**

Assuming that the current variances are atypical and remaining work will be completed using original estimates , your project team prepared a forecast report for you with the following data , Variance at completion – $70 , Actual cost of $350 and total project budget of $500 , the report doesn’t include Earned value , using this information , what is the project EV ?

Choice 1 : 280

Choice 2 : 300

Choice 3 : 320

Choice 4 : 340

**Solution :**

VAC=BAC-EAC

-70 = 500 – EAC …… So EAC= $570

Based on the assumption made of current variances are atypical and remaining work will be completed using original estimates we will use formula # 3

EAC = AC + (BAC-EV)

570 = 350 + (500-EV)

220 = 500 – EV

EV = $ 280

**Question # 4 :**

In your project , there have been several changes in the cost and schedule estimates , the original estimations are no longer valid , calculate the EAC for your project based on the following information :

BAC = $300,000

AC = $100,000

EV = $150,000

CPI = 1.2

ETC = $120,000

Choice 1 : $250,000

Choice 2 : $220,000

Choice 3 : $280,000

Choice 4 : $300,000

**Solution :**

Key word ; Original estimating assumptions no longer valid

So the equation we are willing to use

Original estimating assumptions are no longer valid

EAC = AC + ETC

Current variances are atypical , similar variances will not occur

EAC = AC + BAC – EV

Current Variances are typical of future variations

EAC = AC + ( BAC-AC ) / (CPI*SPI)

As if there is no variances from BAC

EAC = BAC/CPI

EAC=AC+ETC

= 100,000 + 120,000

= $220,000

**Question # 5 :**

As a project manager , you have 2 projects to select from , project A that has an initial budget of $1,000 out of which $800 has already been spent , to complete this project , you need an additional $500 , Project B will requires $1,200 only for completion , which project would you prefer to manage and what will be the ETC

Choice 1 : Project A , ETC of $800

Choice 2 : Project B , ETC of $2,200

Choice 3 : Project A , ETC of $500

Choice 4 : Project B , ETC of $ 1,200

**Solution :**

Project A , $800 is sunk cost and it’s not considered in making decisions , so Project A ETC is $500

Project B , ETC is $1,200

So it’s more beneficial to select Project A

** **

**Question # 6 :**

While performing variance analysis for your project , you refer to your status reports which show the following information :

PV = $100,000

AC = $125,000

EV = $90,000

In this context , which of the following is incorrect ?

Choice 1 : Schedule variance is -$10,000 and you are behind schedule

Choice 2 : Cost variance is -$35,000 and you are over budget

Choice 3 : CPI is 0.5 and you are over budget

Choice 4 : SPI is 0.9 and you are behind schedule

**Solution :**

CV = EV-AC = 90,000 – 125,000

= -$35,000 , over budget

SV = EV – PV = 90,000 – 100,000

= -$10,000 , behind schedule

CPI = EV/AC = 90,000/125,000 = 0.75 , above budget

SPI = EV/PV = 90,000/100,000 = 0.9 , behind schedule

So all options are correct except option 3

**Question # 7 :**

Your project manager asked you for a status report , you are required to include estimate at completion information at the report , based on the following data , what would be the EAC ?

AC = $350,000

BAC = $500,000

EV = $250,000

Choice 1 : $700,000

Choice 2 : $155,000

Choice 3 : $525,000

Choice 4 : $850,000

**Solution :**

Nothing is mentioned about any variances , so we are going to use the formula EAC = BAC/CPI

CPI = EV/AC

= 250,000/350,000

= 0.714

EAC = 500,000/0.714

= $ 700,000

**Question # 8 :**

As a project manager , you are required to produce project performance reports on a regular basis , your project BAC is $750,000 , planned value is $100,000 , Schedule variance is $30,000 and cost variance is $50,000 , what is the percent complete and the estimate at completion of your project

- Choice 1 : 18% , $500,000
- Choice 2 : 17.33 % , $461,538
- Choice 3 : 17.8% , $437,500
- Choice 4 : 18% , $ 521,451
**Solution :**

SV = EV- PV

30,000 = EV – 100,000

Percentage Completed = EV/BAC * 100

= 130,000/750,000 * 100 = 17.33%

EAC = BAC/CPI ….. As there is no variances mentioned

CPI = EV/AC

CV= EV-AC

50,000 = 130,000 – AC

AC = $ 80,000

CPI = EV/AC = 130,000/80,000 = 1.625

= 750,000/1.625

= $461,538

**Question # 9 :**

For your project , find To Complete Performance Index based on the given data :

BAC = $700,000

CV = $25,000

EV = $200,000

ETC has now been revised to $425,000

Choice 1 : 1.176

Choice 2 : 0.9

Choice 3 : 1.5

Choice 4 : 0.65

**Solution : **

TCPI = ( BAC-EV)/(BAC-AC)

But Notice that ETC is revised … so EAC will be used in the formula down below instead of BAC after it is calculated

TCPI = ( BAC-EV)/(EAC-AC)

= ( 700,000 – 200,000 ) / ( EAC – AC )

CV = EV-AC

25,000 = 200,000 – AC

AC = $175,000

EAC = AC + ETC … As original estimates are no longer valid

EAC = 175,000 + 425,000 = $600,000

TCPI = (700,000-200,000 ) / ( 600,000 – 175,000 )

= 500,000 / 425,000

= 1.176

**Question # 10 :**

You are managing a project when your sponsor has asked you to forecast for the cost of project completion, the project has a total budget of $80,000 and CPI 0.95 , the project has spent $25,000 of it’s budget so far, how much more money do you plan to spend on this project ?

Choice 1 : $59,210

Choice 2 : $81,450

Choice 3 : $94,220

Choice 4 : $72,980

**Solution : **

The question is asking about ETC = EAC-AC

Nothing is showing that the original estimates are not valid , so we will use the Formula

EAC=BAC/CPI

= 80,000/0.95

= $84,210

ETC = 84,210-25,000

= $59,210

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