Calculating planned value for EVM
Introduction
Planned Value, often abbreviated as PV, represents the authorized budget assigned to scheduled work in a project. It is the baseline value of the work scheduled to be completed up to a specific point in time.
Calculating Planned Value
The calculation of Planned Value depends on the project’s schedule and budget. A common approach is to assign planned values to individual project tasks or work packages based on the project schedule. The cumulative planned value over time forms the Planned Value (PV) S-curve, providing a visual representation of the planned project value over the project duration.
Using a very simple linear model to calculate Planned Value (PV)
Lets imagine a project’s with an budget of $100,000. Lets say the project runs for 10 months. If we plan to make 10% progress each month, then we would complete the project in 10 months on time and budget. In this case, we have assumed (or planned for) a linear progress and the formula to calculate PV curve in such case would be,
\[ PV = B \times \frac{t}{T} \]Where:
- \( PV \) = Planned Value at the given time period
- \( B \) = Total Budget for the project
- \( t \) = Elapsed time (in the same units as \( T \))
- \( T \) = Total project duration or time span
Using S-Curve Technique to calculate Planned Value (PV)
Empirically, teams in most projects tend to have a slow start during the initial phase, gradually picking up momentum as time progresses. It’s also essential to allocate time towards the end of the project for system stabilization, addressing bugs and enhancing performance, rather than solely focusing on new feature development. Consequently, the project’s progress rate typically exhibits a dip at both the beginning and end phases.
The calculation of the Planned Value (PV) S-curve relies on the specific methodology or model adopted for its development. However, a prevalent approach involves utilizing mathematical functions like the logistic function or cumulative normal distribution function to generate the S-curve.
One common formula for the Planned Value (PV) S-curve calculation is based on the logistic function:
\[ PV(t) = \frac{A}{1 + e^{-k(t - t_0)}} \]Where:
- \( PV(t) \) = Planned Value at time \( t \)
- \( A \) = Total project budget or final planned value
- \( k \) = Growth rate parameter (controls the steepness of the curve)
- \( t \) = Time period
- \( t_0 \) = Inflection point (the time at which the curve transitions from slow growth to rapid growth)
This formula generates an S-shaped curve that starts slowly, accelerates in the middle phase, and then levels off towards the end of the project. Adjusting the parameters \( A \), \( k \), and \( t_0 \) allows customization of the curve to match the project’s characteristics and timeline.
In the following simulator, you can get the S-Curve values using Logistic function for various values of “k”. The table should give you the actual values, and the graph should visualize the correspondig “S-Curve”.
As an exercise, check how for different project duration needs to be followed up with different values of “k” to get a desired S-Curve.
Conclusion
The value that has to be used for “S-Curve” depends on the Duration. Also, for shorter duration, the “S-Curve” is not suitable.