We are now in a position to draw

the tracking Gantt chart that gives the status of the project at the end of week 10.

Note the revised estimate of project completion time is 15.

That is project is expected to be delayed by one week if no corrective action is taken.

We will next look at the earned value analysis in some detail,

and do the calculation for the example above.

For each activity at review time,

earned value is defined as the amount of the current budget that has been

earned by the work completed on that activity till the review of time.

The abbreviation EV, earned value is now involved,

but the abbreviation in the past for the same concept

was BCWP for budgeted cost of the work performed.

At review time, each of

the activities is in one of three mutually exclusive possible states.

The activity may have been completed some time on or before the review time,

or the activity is in progress and not yet completed,

or the activity has not yet started.

For activities that have been completed,

the earned value equals the planned value.

For activities not yet started,

the earned value is 0.

For activities that are in progress,

we need to calculate the earned value.

The popular approach is to estimate the percentage completion of the activity,

and multiply that by the total planned value for that activity,

to arrive at its earned value.

This rule is referred to as the percent complete rule.

A variant of the percent complete rule for long duration activities is to

first break up activity duration into two or more phases,

and the percent complete depends upon

the status of the activity in terms of which phase it is in,

and the percent complete within that phase.

For instance, suppose an activity duration is divided into three phases,

with the end of Phase 1 representing 30% complete of the activity,

while the end of Phase 2 represents 70% complete of the activity.

And the end of Phase 3 represents 100% complete of the activity.

Suppose the status of activity is that it is in Phase 2 and is in progress,

and 20% of Phase 2 has been completed.

Then the percent complete for that activity equals 30 + 0.2 into 70 - 30.

And this is equal to 38%.

There are other possible ad-hoc rules that may be used for

calculating the earned value for an activity in progress at review time.

The 0/100% rule is that earned value is 0 until the activity is completed,

at which time the earned value is 100% of the budget for that activity.

The 50/50 rule states that the earned value for an activity in

progress is 50% of the budget until it is completed,

at which point the earned value is 100% of the budget for that activity.

These ad-hoc rules may be reasonable for activities of short duration.

The only real advantage of these ad-hoc rules is that we need not

estimate the percent complete of an activity at review time.

Often, the percent completion of an activity is simply

estimated by someone who is familiar with such activities.

It should be borne in mind that as in the case of estimation or activity durations,

more elaborate procedures for estimating

the percent complete of an activity may not be worth the additional time,

effort, and cost in arriving at more accurate estimates.

Before we can calculate the different variances,

we need to run the data for each activity

that has been completed or in progress at review time.

This is the actual cost incurred for activities completed and

the actual costs incurred so far for activities in progress.

This data has to be obtained from the accounting department.

This implies that the accounts at least in terms of cost incurred are up to date.

The actual cost is abreviated as AC while in the past this was

referred to as the actual cost of work performed and abbreviated as ACWP.

Now with the activity level,

the definition of different variances are as follows.

The cost of cost variance,

CV for an activity is the difference between

the earned value and the actual cost for that activity.

That is CV equals earned value minus actual cost.

This variance is an assessment in monetary terms

of the progress of each activity at review time.

The schedule variance is the difference between EV and PV.

That is schedule variance equal to earned value minus planned value.

In the example above,

the two variances for each activity at the end of week 10 are shown in the next table.

For completed activities, the earned value equals planned value,

and the schedule variance SV equals 0.

Thus activities A, B and C have SV equal to 0.

Activity D is in progress and it has been estimated that activity D is 30% complete.

So its earned value equals 0.3 times 40 equals 12.

Similarly, for activity E,

earned value equals 0.4 into 60 equal to 24.

So CV and SV for activities D and E are -8 and -6 respectively.

The totals are given in the last row of the table.

These values will be used to calculate some variances of

the project level as we will see later in this module.

There are two other variances that have been defined.

The resource variance RV for an activity

is the difference between the cost that should have been

incurred as per the budget and the actual cost incurred as on the review date.

That is RV equals planned value minus actual cost.

Time variance, TV is the difference between the time schedule for work

that has been performed and the actual time used to perform the work, AT.

That is TV = ST - AT.

These variances provide some useful information,

although they're not as popular as CV and SV.

Next we will extend our analysis to the project level.

The baseline budget for the project is referred to as budget at

completion or abbreviated as BAC.

At review time, we need to calculate

the revised estimate of the total cost of completion of the project.

In order to do this,

we need to estimate the cost of completing the remaining work.

There are two approaches to this estimation,

one approach is to find out from experts and other persons associated with

the project what their estimate

is for the expected cost of completing the remaining work.

Suppose this estimate is denoted as ECR1,

then the revised estimate of the expected total cost at completion of the project

is ETC1 equals ECR1 plus TAC.

The TAC is the total actual cost as on review date.

Then the cost variance at completion of the project which is denoted as

VAC1 is BAC minus ETC1.

The second approach is to calculate the revised estimate of

the total cost of completion of the project is to use

the cumulative cost performance index and

the efficiency index to estimate the cost of completing the remaining work.

The cumulative cost performance index denoted as CPI is equal to TEV over TAC,

where TEV and TAC are the the total earned value and

the total actual cost respectively as on the review date.

Note that if TEV is less than TAC,

CPI is less than 1,

indicating that the performance to date is below expectation.

If CPI is greater than 1,

the performance to date is better than expectation.

Assuming that the remaining work will would be

performed at the same efficiency as on review date,

the estimated cost of completing the remaining work is

ECR2 equals work remaining over CPI,

which is equal to BAC minus TEV over TEV over AC.

Now the revised estimate of the expected total cost and completion is

ETC2 which is equal to ECR2 plus TAC,

and the cost variance VAC2 equals BAC minus ETC2.

Instead of defining variances as above

an alternate approaches is to define performance indices for monitoring the progress.

Now at the activity level, the cost performance index,

CPI for an activity is EV over AC,

where EV and AC are the earned value and the actual cost respectively for that activity.

Similarly, at the activity level schedule performance index

or SPI for an activity is EV over PV,

where EV and PV are the earned value and planned value respectively.

At the project level, we look at the total sales on review date for earned value,

planned value and actual cost which are denoted as TEV,

TPV and TAC respectively.

CPI at the project level is equal to TEV over TAC, and SPI is equal to TEV over TPV.

At the project level,

if CPI is less than one, it implies that there is a cost overrun.

But CPI greater than one implies that the cost incurred is less than the budget.

Similarly, SPI less than one implies that the project is behind schedule,

while SPI greater than one implies that the project is ahead of schedule.

The cost schedule index denoted as CSI is a product of CPI and SPI.

That is CSI equal to CPI multiplied by SPI,

which in turn equals TEV over TAC,

multiplied by TEV over TPV.

That is equal to TEV squared over TAC multiplied by TPV.

The rational for CSI is that if both CPI and SPI are greater than one,

then the product CSI is greater than one,

and the progress on the project is good.

If both CPI and SPI are less than one,

and the product CSI is less than one,

and the progress on the project is not adequate.

If one of them is greater than one and the other is less than one,

then the product CSI may be less than one hour greater than one.

In this case, if CSI is greater than one then progress on one dimension is good enough.

To review the overall progress is adequate,

although the progress on the other dimension is not really adequate.

On the other hand,

if CSI is less than one then the overall progress is not considered as adequate.

In the example, we have consider taking the values in the last row of the table.

We have TPV equals 340.

TEV equals 326, and TAC equals 310.

And CPI equals to TEV over TAC equals 326 by 310, which is equal to 1.052.

And SPI equal to TEV over TPV,

equals 326 by 340, equal to 0.959.

CSI then is TEV squared over TAC multiplied by TPV,

is equal to 326 squared divided by 310 into 340,

which is equal to 1.008.

So, the overall progress of the project is adequate,

although the project is slightly behind schedule as indicated by SPI.

At the activity level, to find the EV for an activity in progress at review time.

We have to estimate the percent complete of that activity.

At the project level,

we have three measures of percentage completion.

One measure is based on the budgeted cost of the project,

but ignoring the actual cost incurred till review time.

This percent complete index denoted as PCIB is simply equal to TEV over BAC.

The other two measures denoted as PCIC1 and PCIC2,

are based on the actual cost incurred till review time,

and the expected cost at completion of the project.

Recall that we had two ways of estimating the total cost at completion of the project.

These two estimates were denoted as ETC1 and ETC2.

So we had the percent complete index PCIC1 as equal to TAC over ETC1.

And PCIC2 is equal to TAC over ETC2.

In the example, we've have been considering PCIB equals 326 over 470,

which is equal to 0.694.

Suppose the experts estimated cost of completing the remaining work is 200,

that is ECR1 is 200, then the expected total cost at completion of

the project ETC1 equals TAC plus ECR1 equals to 310 plus 200, which is equal to 510.

So the cost variance at completion of the project,

VAC1 equals BAC minus ETC1, equal 470 minus 510, which is equal to minus 40.

And PCIC1 is 310 over 510, equals to 0.608.

If we use a cumulative performance index at review time,

CPI equals TEV over TAC,

which is equal to 326 over 310 equal to 1.052.

And the estimated cost of the remaining work ECR2 is equal to work remaining over CPI,

which is equal to BAC minus TEV divided by TEV over actual cost, AC.

This is equal to 470 minus 326 over 326 over 310,

which is equal to 144 divided by 326 over 310,

which gives us a value of 136.933.

Now ETC2 equals TAC plus ECR2 that is equal to

310 plus 136.933, equal to 446.933.

And the cost variance at completion of the project is VAC2 equals BAC minus ETC2,

equal to 470 minus 446.933 equals 23.067 which is positive.

While VAC1 was negative equal to -40.

Now, PCIC2 equals 310 over 446.933 which is equal to 0.694.

Finally, we have the two complete performance index,

TCPI which is the amount of value each unit of currency in

the remaining budget should earn to stay

within the total budget at the completion of the project.

The remaining budget is given by BAC minus TAC.

While the value still to be earned is BAC minus earned value, EB.

Hence, TCPI equals BAC minus TEV over BAC minus AC.

If TCPI is greater than 1,

then there's more work to be done than the available budget.

This would imply that the productivity has

to be increased if there has to be no cost overrun.

If TCPI is less than 1,

then there is less work to be done than the available budget.

This implies that the project may be completed without using all the budget,

and one may consider increasing the scope of the project while staying within the budget.

For the example we have been looking at,

TCPI equals 470 minus 326 over 470 minus 310,

which is equal to 144 over 160 which is 0.9.

Since TCPI is less than 1,

it is estimated that the project may be completed without using all the budget.

This completes our module on monitoring and control.