# PMP – Notes-Formulas (EVM, PERT, etc)

## Earned value calculation:

Formulas here will provide the Earned value of the project at a given time. There by one can easy understand how far the project is over and how much is spent to achieve this outcome.

### Earned value – EV

The measure of work completed expressed in terms of the budget authorized for that work. If you substitute Value with money then, then the total value of the project is equal to the total cost (budget) of the project. To calculate the earned value you should know the % of work done and total project cost.

EV = BAC * % complete
BAC – Budget at completion is the total cost budgeted for the project.

Example1:

```Project is to build a mobile application with 10 features, within
6 months and budgeted cost is \$10000.
Assume the each features takes same effort to develop, and team has
successfully accomplished 4 features in 3 months of time.
Customer now wants to know, how much of work is one.

Calculations: First of all % of work done should be determined,
if 4 features out of 10 is completed then % of work done
will be 4/10 = 40%. So the earned value at this moment is

EV = 40% * \$10000, i.e. \$4000```

Panned value – PV

So just by looking at the EV it’s difficult to know if the project is on time or on budget. In above example assume the each features takes a different effort to complete, then to determine the EV becomes next to impossible without knowing the budgeted amount to each features.

Planned value is the authorized budget assigned to scheduled work. In simple terms it’s an approved budget for a task.

Example2:

```Project is to build a mobile application with 10 features, within
6 months and budgeted cost is \$10000. Assume that each features
takes different amount of effort to develop, and team has
successfully accomplished 4 features in 3 months of time.
Planned value of the features completed is a) \$1000, \$500, \$1500 & \$200.
Customer now wants to know, how much of work is one.

Calculations: EV is sum of all the PV of the completed tasks.
In this case

EV = \$1000 + \$500 + \$1500 + \$200 i.e. \$3200```

### Actual cost – AC

Another important factor in earned value management is the actual cost. This is amount that is been spent to date. This factor is important to determine the cost variance of the project.

### Schedule variance – SV

A measure of schedule performance on the project, expressed as the difference between project’s earned value and planned value. This tells us if the project is ahead, behind or on time.

SV = EV –PV

Example3:

```Project is to build a mobile application with 10 features, within
6 months and budgeted cost is \$10000. 3 months have passed buy and
\$6000 is been spent, and features delivered until now is only 4.
Customer now wants to know, if the project is lagging or on track?

Calculations:
EV is \$4000 (refer example 1)

PV is 50% (since the project is mid-way) * total budget
i.e 50% * \$10000 = \$5000

SV = EV – PV i.e. \$4000 - \$5000 = -\$1000
This means the project is behind schedule```

A negative SV means you are behind schedule (that’s bad). A positive SV means you are ahead of schedule (which is good).

### Cost variance – CV

Is the difference between the actual cost and the budgeted cost. This tells us if the project is over, under or on budget.

CV = EC – AC

Example4:

```Project is to build a mobile application with 10 features, within
6 months and budgeted cost is \$10000. 3 months have passed buy and
\$6000 is been spent, and features delivered until now is only 4.
Customer now wants to know, if the project is on budget?

Calculations:
EV is \$4000 (refer example 1)

AC is \$6000, this is the amount spent until now

CV = EV – AC i.e. \$4000 - \$6000 = -\$2000
This means the project is over budget.```

A negative CV means you are over budget. A positive CV means you are under budget.

### Schedule performance index – SPI

The Schedule Performance Index indicates how efficiently you are actually progressing compared to the planned project schedule. It is the efficiency of the time utilized on the project.

SPI= EV / PV

With SPI, once can find out if more or less work has been completed against the planned work.

Example5:

```Project is to build a mobile application with 10 features, within
6 months and budgeted cost is \$10000. 3 months have passed buy and
\$6000 is been spent, and features delivered until now is only 4.
Customer now wants to know, if the project is lagging or on track?

Calculations:
EV is \$4000 (refer example 1)

PV is 50% (since the project is mid-way) * total budget
i.e 50% * \$10000 = \$5000

SPI = EV /PV i.e. \$4000/\$5000 = 0.8
This means the project is behind schedule```

### Cost performance index – CPI

The Cost Performance Index specifies how much you are earning for each dollar spent on the project. CPI in project management measures the cost efficiency of a project.

CPI = EV/AC

Example6:

```Project is to build a mobile application with 10 features,
within 6 months and budgeted cost is \$10000.
3 months have passed buy and \$6000 is been spent, and features
delivered until now is only 4.  Customer now wants to know, if the
project is lagging or on track?

Calculations:
EV is \$4000 (refer example 1)

AC is \$6000, this is the amount spent until now

CPI = EV /AC i.e. \$4000/\$6000 = 0.66
Project is over budget, which means for every
\$1 Spent only \$0.66 is the earned value.```

If the number is greater than one, it means you are getting more for every \$1 spent which is good. If the number is less than 1, then it’s bad because for every \$1 spent less value is realized. If the number is 1, then the spending is on track.

Table below from PMBOK describes few more formulas related to earned value management.

## Communication channels

Effective communication is the most important success factor of a project. Communication complexity depends on how many stakeholders communicate to each other. To determine such communication below formulas is used.

N*(N-1)/2

Example7:

```There are 10 people in project including sponsor, project manager
and team. How many communication channel project manger
should be aware of?

Calculations:
Communication channel: N * (N-1)/2 i.e. 10*(10-1)/2 = 45```

## Standard Deviation

PMBOK defines standard deviation as (P – O)/6. Standard deviation is simply a reflection of the uncertainty in the estimates.

Example8:

```The pessimistic estimate to develop and app is 12 months.
The optimistic estimate by expert is 5 months. What is the risk involved
in the estimation of the effort to develop the app?

Calculations:
Standard deviation = (P - O)/6 i.e. (12-5)/6 = 1.16
Since the deviation value is less, the risk level is low of this project.```

A low standard deviation means that most of the numbers are close to the mean. A high standard deviation means that the numbers are more spread out and the risk level is high.

## PERT

Program Evaluation and Review Technique  is used to estimate the activity when there is no exact estimation of activity is known. Its a statistical tool to estimate the effort of a one time projects where usually no historical records are available and time is an important factor than the cost.

PERT =  (O+4M+P)/6

Optimistic – Best case estimation

Pessimistic – worst case estimation

Median – Most likely, high portability estimation

Example9:

```Team members told that an activity can be most likely be completed
in 15 days. However, in the worst case you think it might take 35 days,
and if all conditions are favorable, it might be completed in 10 days.
What is the PERT based estimate and standard deviation for this activity?

Calculations:
PERT = (O+4M+P)/6 i.e. (10+4*15+35)/6 = 17.5 days
Standard deviation = (P-O)/6 i.e. (35-10)/6 = 4.16 day```
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