Project+ Formulas

PERT Estimate Formula and Definition

PERT Estimate = (O + 4M + P)/6

The project timing estimate, with adjustments for worst- and best-case scenarios.

Uses weighted average, meaning the most likely estimate is given 4 times the weight of the others. (4M)

Optimistic (O): Best case | Most Likely (M) | Pessimistic (P): Worst case

EMV

Expected Monetary Value (EMV) = $(Probability(%) x Cost of Impact)

There is a 30% chance that equipment will fail, causing a $20,000 cost.

EMV = 30% x -20,000 → -$6,000

Three point estimation formula

(most likely + optimistic + pessimistic) / 3

Formula to calculate team member’s available time on the project

Available working hours - Overhead hours

Available = EX. 40 hours per week

Overhead hours = Time spent outside project in meetings, training, etc

Formula for Lines of Communication

There are 4 Participants in your meeting. How many lines of communication are there? → 6

4 ( 4 - 1 ) / 2 = 6

P ( P - 1 ) / 2

ES Formula and Definition

Early Start (ES) = max Early Finish (EF) of direct predecessors

Max EF meaning some activities may be relying on the completion of other activities that have different length durations.

So if C relies on A and B, and A=3, B=5, and A and B start at the same time, then the ES for C is 5 because B has the longest duration.

The soonest an activity can start because of how long it will take to complete predecessor activities.

EF Formula and Definition

Early Finish (EF) = Early Start (ES) + Activity Duration

So if A=3, B=2, C=4, and C relies on A and B, and A and B start at the same time, the EF for C is 7

The earliest an activity can finish because of how long it takes to complete it

LS Formula and Definition

Late Start (LS) = Late Finish (LF) - Activity Duration

The latest an activity can start and still allow the project to finish on time

LF Formula and Definition

Late Finish (LF) = The latest an activity can finish and still allow the project to finish on time OR

LF = min ( LS of successors )

Late start (LS) is the latest an activity can start and still keep the project on time. If person A needs a report by 3 PM, and person B needs that same report by 5 PM, do you wait until 5 to send reports over? No, the min is 3, so you should send the reports by 3.

So if A=3, B=2, C=4, A and B start at the same time, C depends on A and B, project duration is 7 days, then the LF of C is 7 because C can finish on day 7 and still have the project be finished on time. A and B both have to be finished by the time C starts which is on day 3 (7-4=3). So A and B both have an LF of 3.

TF Formula and Definition

Total Float (TF) = Late Start (LS) - Early Start (ES)

or

TF = Late Finish (LF) - Early Finish (EF)

The amount of time an activity can wait to start without impacting the total project timeline. Also called Slack

FF Formula and Definition

Free Float (FF) = Early Start (ES) of Successor Activity - Early Finish (EF) of Current Activity

The amount of time an activity can be delayed without affecting the early start of any subsequent activities.

CP Formula

Critical Path (PA) = All activities where Total Float (TF) = 0

If TF = 0, add that activity to the Critical Path.

The sequence of events with zero TF that cannot afford any delays at all.

PV Formula and Definition

Planned Value (PV) = (Planned % Completed) * BAC

A project has BAC = $100,000, Project schedule says that after 3 months, 40% of the work should be complete.

Formula: PV = 40% * $100,000 → $40,000

What you should have spent at this point in the schedule.

BAC Definition

Budget at Completion (BAC). How much the project should have cost

EV Formula and Definition

Earned Value (EV) = $(Actual % Complete) * BAC

Measures the monetary value of the percentage of work completed

AC

Actual Cost (AC). How much the project has actually cost so far.

CV Formula

Cost Variance (CV) = Earned Value (EV) - Actual Cost (AC)

How above or below budget the project is.

CPI Formula and Definition

Cost Performance Index (CPI) = Earned Value (EV) / Actual Cost (AC)

Whether the project is within budget.

CPI < 1 = Over budget

CPI = 1 = On budget

CPI > 1 = Under budget

SV Formula and Definition

Schedule Variance (SV) = $Earned Value (EV) - Planned Value (PV)

How far ahead or behind schedule the project is.

Measured in dollars

Negative SV = Behind schedule

Zero SV = On schedule

Positive SV = Ahead of schedule

SPI Formula and Definition

Schedule Performance Index (SPI) = Earned Value (EV) / Planned Value (PV)

Will likely be a decimal value

Whether the project is ahead of or behind schedule

SPI > 1 Ahead of schedule

SPI = 1 On schedule

SPI < 1 Behind schedule

Bottom-Up ETC Formula, Definition and Use when?

Estimate to Complete (ETC) = sum of the cost of all remaining activities

Used when the original BAC estimates end up incorrect. The team goes back through the remaining work and creates a new cost estimate from the ground up

The cost needed to finish the remaining work.

Budgeted Rate ETC Formula, Definition and Use when?

Estimate to Complete (ETC) = $Budget at Completion (BAC) - Earned Value (EV)

or

ETC = $Remaining Work (Units/Hours left) x Budgeted Rate (Cost per unit/hour)

Use when the source of variance is eliminated. I.E the reason you were over/under budget is no longer happening, so you expect future work to return to the original planned cost rate.

Measured in dollars.

The cost needed to finish the remaining work.

ETC CPI Formula, Definition and Use when?

Estimate to Complete (ETC) = $(Budget at Completion (BAC) - Earned Value (EV)) / CPI]

Cost Performance Index (CPI) = EV / Actual Cost (AC)

Used to determine the cost needed to finish the remaining work when you expect the current cost variance to continue for the rest of the project.

ETC CPI and SPI Formula, Definition and Use when?

Estimate to Complete (ETC) = $[(BAC - EV) / (CPI * SPI)]

Cost Performance Index (CPI) = EV / Actual Cost (AC)

Schedule Performance Index (SPI) = EV / Planned Value (PV)

Used to determine the cost needed to complete the remaining project work when you expect both cost variance and schedule variance to affect it.

EAC Formula and Definition

Estimate at Completion (EAC) = $Actual Cost (AC) + Estimate to Complete (ETC)

Measured in dollars.

Based on what we know now in the current state of the project what the total project will probably cost.

BAC = What was planned the project would cost

EAC = What the project will probably cost now

VAC Formula and Definition

Variance at Completion (VAC) = $Budget at Completion (BAC) - Estimate at Completion (EAC)

How much the total project will be above or below budget.

Measured in dollars.