There are a number of project management formulas to perform quantitative analysis, but from pmp exam point of view there are a few important ones. Key areas such as Earned Value Analysis, Critical Path Analysis, and Procurement Management require use of Quantitative skills. Hence, this post enumerates important mathematical formulas used in the field of Project Management.
Table of Contents
Project Management Formulas for PMP Certification Examination
Project Selection Methods
Net Present Value (NPV) Project Management Formulas
Present Value (PV) = Future Value (FV) / (1+k)N
![\[PV=\frac{FV}{(1+k)^N}\]](https://i0.wp.com/milestonetask.com/wp-content/ql-cache/quicklatex.com-9dc38095e616199e1c42651857321e30_l3.png?resize=129%2C42&ssl=1 "Rendered by QuickLaTeX.com")
- Where k = discounting factor / interest rate and N = Number of time periods
NPV = [Sum of present value of all future cash inflows] – [Cash outflow]
![\[NPV=\sum_{t=1}^{N} \frac{FV_t}{(1+k)^t} - PV\]](https://i0.wp.com/milestonetask.com/wp-content/ql-cache/quicklatex.com-f0bbbe6fd56c368dae72c5e2f2a34ad2_l3.png?resize=223%2C56&ssl=1 "Rendered by QuickLaTeX.com")
While evaluating two or more projects select the project with greater NPV
Internal Rate of Return (IRR)
- IRR is the discount rate at which NPV = 0
Benefit Cost Ratio (BCR) / Cost Benefit Analysis (CBA)
Ratio of sum of present value of all cash inflows to project cash outflow.
![\[CBA=\frac{\sum_{t=1}^{N} \frac{FV_t}{(1 + k)^t}} {PV}\]](https://i0.wp.com/milestonetask.com/wp-content/ql-cache/quicklatex.com-2decdb8d35c203ac1724d953d53164fc_l3.png?resize=167%2C49&ssl=1 "Rendered by QuickLaTeX.com")
Return on Investment (ROI)
ROI = Average Income / Average Investment
Payback Period
Payback Period (PB) = Initial Investment / Annual Cash Inflow
Project Selection Acceptance Criteria Summary
| Project Selection Method | Project Selection Criteria | Project Selection Decision |
|---|---|---|
| Net Present Value (NPV) | if NPV is greater than zero | Accept |
| if NPV is less than zero | Reject | |
| Internal Rate of Return (IRR) | Greater than threshold | Accept |
| Less than threshold | Reject | |
| Cost Benefit Analysis (CBA) | if CBA is greater than one | Accept |
| if CBA is less than one | Reject | |
| Return on Investment (ROI) | Greater than threshold | Accept |
| Less than threshold | Reject | |
| Payback period | Less than threshold | Accept |
| Greater than threshold | Reject | |
Also read: Project Selection Methods
Project Management Formulas for PERT Analysis
Following are the project management formulas for Program Evaluation and Review Technique (PERT)
Three Point Estimates (Beta Distribution)
- Activity Duration / Cost Estimates = (P + 4M +O) / 6
![\[Estimates = \frac{(P+4\times M+O)}{6}\]](https://i0.wp.com/milestonetask.com/wp-content/ql-cache/quicklatex.com-3f868b381a6a1b488de62b92affc3bef_l3.png?resize=258%2C40&ssl=1 "Rendered by QuickLaTeX.com")
Where P = Pessimistic Value; M = Most Likely Value; O = Optimistic Value
- Standard Deviation (σ)= (P – O) / 6
![\[\sigma = \frac{P-O}{6}\]](https://i0.wp.com/milestonetask.com/wp-content/ql-cache/quicklatex.com-4aff8edb7d30caebaee50963ff0781cd_l3.png?resize=91%2C38&ssl=1 "Rendered by QuickLaTeX.com")
- Variance = (σ)2 = (P – O)2 / 36
![\[\sigma^2 = \frac{(P-O)^2}{36}\]](https://i0.wp.com/milestonetask.com/wp-content/ql-cache/quicklatex.com-2bff4ef6f6a876d2e08e8bda9a268126_l3.png?resize=122%2C41&ssl=1 "Rendered by QuickLaTeX.com")
Three Point Estimates (Triangular Distribution)
- Activity Duration / Cost Estimates = (P + M + O) / 3
![\[Estimates=\frac{(P+M+O)}{3}\]](https://i0.wp.com/milestonetask.com/wp-content/ql-cache/quicklatex.com-6d47b7a0b9154867dc45eba4914f8ccf_l3.png?resize=226%2C40&ssl=1 "Rendered by QuickLaTeX.com")
Also read: Program Evaluation And Review Technique
Critical Path Analysis Formulas
Early Start (ES)
Project management formulas for Early Start (ES) if the convention that project starts on day one is adopted.
Early Start (ES) =
- 1 for the first activity
- ES of the next node is the earliest finish time of the immediately preceding activity plus 1 = EF + 1
For activities with more than one preceding activity ES is latest of the earliest finish times of the preceding activities.
Early Finish (EF)
Project management formula for Early Finish (EF) if the convention that project starts on day one is adopted.
- Early Finish (EF) = ES + Activity Duration (D) – 1
Late Finish (LF)
Project management formula for Late Finish (LF) if the convention that project starts on day one is adopted.
Late Finish (LF) =
- On Critical Path LF of the last activity is equal to the EF of that activity
- The latest start time of the activity of previous node minus 1 = LS -1
For activities with more than one previous node, LF is the earliest of the latest start times of those activities.
Late Start (LS)
Project management formulas for Late Finish (LS) if the convention that project starts on day one is adopted.
- Late Start (LS) = LF – Activity Duration (D) + 1
Project Management Formulas for Critical Path Analysis
- For Critical Path ES = LS and EF = LF
- For Critical Path Total Float = 0
Total / Free Float
Project management formulas to calculate total float / free float.
- Total Float = LS – ES or LF – EF
- Free Float = (ES)S – (EF)C – 1 [When Start = 1] Where S = Successor Activity and C = Current Activity
Critical Path Analysis Forward and Backward Pass Calculations
Also Read Post Related to Critical Path Analysis
Read the following post to know about Critical Path Analysis formulas if the convention that project starts on day Zero is selected.
Cost to Crash
The following equation gives project management formula to calculate cost to crash.
- Cost to crash per period = (CC – NC) / (NT – CT)
- CC = The activity cost associated with the crash time
- NC = The activity cost associated with the normal time
- NT = The time necessary to complete the activity under normal conditions
- CT = The shortest possible time necessary to complete an activity
Cost Estimates
The following are the two types of cost estimates.
- Rough Order of Magnitude (ROM) Estimates = -25% to +75%
- Definitive Estimates = -5% to +10%
Also Read: Wrong Cost Estimates Implications Solutions
Project Budget
The following paragraph lists project management formulas to compute project budget.
- Work Package Cost Estimates = Activity Cost Estimates + Activity Contingency Reserve
- Control Accounts = Work Package Cost Estimates + Contingency Reserve
- Cost Baseline = Summation of Control Accounts
- Project Budget = Cost Baseline + Management Reserve
Number of Communication Channels
Project management formulas to calculate total number of communication channels
- Number of communication channels = N(N – 1) / 2 ; Where N = Number of stakeholders
Project Management Formulas for Expected Monetary Value (EMV)
The following paragraphs lists various formulas in expected monetary value calculations.
- EMV = Probability X Net Path Value
- Net Path Value = Pay offs – Costs along the path
- EMV of opportunities = Positive Value
- EMV of risks = Negative Value
Project Management Formulas for Procurement Management
The following paragraphs lists various formulas in project procurement management.
- Target Price = Target Cost + Target Fee
- Final Fee = [(Target Cost – Actual Cost)*Sellers ratio] + Target Fee
- Final Price = Actual Cost + Final Fee
- Point of Total Assumption (PTA) = [(Ceiling Price – Target price) / Buyer’s Ratio] + Target Cost
Earned Value Analysis Project Management Formulas
Earned Value Measurement
Fixed Formula
- 25 / 75 Method
- 50 / 50 Method
- EV = (% ) X Work package BAC
Percent Complete
- EV = % Work Complete Estimate X Work Package BAC
Project Management Formulas Earned Value Variance Analysis
The following table enumerates the list of earned value variances formulas in project management.
| Earned Value Analysis Indicator | Earned Value Analysis Formula | Earned Value Analysis Criteria | Earned Value Analysis Interpretation |
|---|---|---|---|
| Schedule Variance (SV) | SV = EV - PV | Positive Value SV > 0 | Ahead of schedule |
| Equal to Zero SV = 0 | On schedule | ||
| Negative Value SV < 0 | Behind Schedule | ||
| Cost Variance (CV) | CV = EV – AC | Positive Value CV > 0 | Under planned cost |
| Equal To Zero CV = 0 | On planned cost | ||
| Negative Value CV < 0 | Over planned cost | ||
| Variance at Completion (VAC) | VAC = BAC – EAC | Positive VAC > 0 | Under planned cost |
| Equal To Zero VAC = 0 | On planned cost | ||
| Negative VAC < 0 | Over planned cost |
Also read: Variance Analysis In Project Management
Project Management Formulas Earned Value Performance Indices
The other name for earned value analysis performance indices is efficiency indicators. The following table enumerates the list of formulas for earned value analysis performance indicators.
| Earned Value Analysis Indicator | Earned Value Analysis Formula | Earned Value Analysis Criteria | Earned Value Analysis Interpretation |
|---|---|---|---|
| Schedule performance Index (SPI) | SPI = EV / PV | Greater than 1 SPI > 1 | Ahead of schedule |
| Equal to One SPI = 1 | On schedule | ||
| Less than one SPI < 1 | Behind Schedule | ||
| Cost Performance Index (CPI) | CPI = EV / AC | Greater than 1 CPI > 1 | Under planned cost |
| Equal to One CPI = 1 | On planned cost | ||
| Less than one CPI < 1 | Over planned cost |
Also read: Earned Value Analysis Project Management
Earned Value Analysis Forecasting Project Performance
Estimate To Complete (ETC)
Project management formulas to calculate Estimate to complete (ETC) to complete the balance work.
- Method 1 to calculate ETC
- ETC = Re-estimate manually
- Method 2 using mathematical equation
- ETC = (BAC-EV)/CPI
- Method 3 if EAC is valid then;
- ETC = EAC – AC
Estimate At Completion (EAC)
Project management formulas to compute Estimate at Completion (EAC) for the balance work.
- If future work will be accomplished at the planned rate (EAC at budgeted rate)
- EAC = AC + BAC – EV
- If the CPI is expected to be the same (EAC at current CPI)
- EAC = BAC/CPI
- Considering impact of both CPI and SPI
- EAC = AC + [(BAC – EV) / (CPI x SPI)]
- If the initial plan is no longer valid then
- EAC = AC + Bottom-up ETC
Also read: Forecast Project Cost Earned Value Method
To Complete Performance Index (TCPI)
Project management formulas to calculate TCPI
- TCPI = (BAC – EV) / (BAC-AC)
- TCPI = (BAC-EV) / (EAC-AC)
- Work Remaining = BAC – EV
- Funds Remaining = BAC – AC
- Also, Funds Remaining = EAC – AC
- Greater than 1.0 = Harder to complete
- Exactly 1.0 = Same to complete
- Less than 1.0 = Easier to complete
Also read: Earned Value Formulas
Earned Value Management Quiz
Take the Earned Value Management Quiz
Statistics
Mean
- Mean (µ) = ∑ X / N = (X1 + X2 + X3 + . . . . XN) / N
Variance
- Variance (σ2) = ∑ (X – µ)2/ N
Standard Deviation
Standard deviation (σ) is square root of variance.
If a set of data is normally distributed then 68% of the data values fall within one standard deviation (µ ± 1σ) of the mean, 95% are within (µ ± 2σ ) and 99.7% with in (µ ± 3σ).
Also read: PMP Certification Exam Changes 2019
Summary
I hope I have compiled as many formulas as possible. In case I have missed any important formula please do let me know.
Using the objectivity of time and costs, you can assign small yet measurable chunks of work to your teams and pick up the pace. Project managers are notified in case of deviation to take necessary proactive steps to bring the project back on track.
I wanted to leave a little comment to support you and wish you a good continuation. Wishing you the best of luck for all your blogging efforts.
Thank you
Please expalin formulas in detail.
Hi, Mangesh, This post is intended to act a quick reference for important formulas used for PMP certification. Explanation and use of these formulas is covered in different post. Underneath every formula I have included a link to the post where usage of these formulas is covered in detail.