# Project Management Formulas

## Summary of Project Management Formulas:

- Earned Value
- Project Selection
- PERT
- Classes of Estimates
- SIGMA
- Communications
- Procurement
- Depreciation
- Network Diagram
- Important Values

## Earned Value Management

Budget At Completion BAC
BAC = Total budget
(What the project budget is)
Earned Value EV
EV= Actual % Complete * BAC
The value earned for the work actually completed to date. What the project is worth
Actual Cost AC
AC = Cost spent where cost spent = cost incurred.
What the project has spent so far

Cost Variance CV
CV = EV - AC
Positive = Under budget Negative = Over budget
Percent Complete PC
PC = EV / BAC *100%
Cost Performance Index CPI
CPI = EV/AC
Shows overall cost efficiency on the project. CPI >1: under budget CPI
Schedule Variance SV
SV = EV - PV
Negative = behind schedule

Schedule Performance Index SPI
SPI = EV/PV
SPI< than 1 : behind schedule
Project Future CPI (PP)
PP = Net investment / Average annual cash flow
Payback Period = Add up the projected cash inflow minus expenses until you reach the initial investment. Shorter is better
Variance At Completion VAC
VAC = BAC - EAC
Projection of being over or under budget based on current performance.
Positive: under budget
Negative : over budget

To Complete Performance Index - Utilizing BAC TCPI
TCPI =(BAC - EV)(BAC-AC)
Predicts likelihood of reaching BAC
TCPI >1, harder to complete & meet BAC TCPI
TCPI<1, Easier to complete and meet BAC
Utilizing EAC TCPI
TCPI =(BAC - EV)(EAC-AC)
Predicts likelihood of reaching EAC.
TCPI >1, harder to complete & meet EAC TCPI
TCPI<1, Easier to complete and meet EAC
Estimate at Completion - Standard formula EAC
EAC = BAC / CPI
Forecasts final project costs based on current performance. The CPI stays the same until the end of the project
Future work at planned costs formula EAC
EAC = AC+ BAC-EV
Forecasts final project costs based on current performance

Initial costs estimates flawed EAC
EAC= AC + Bottom-up ETC
Used when the initial plan no longer valid. Forecasts final project costs based on current performance
CPI and SPI affect remainder of project EAC
(EAC)=AC+{(BAC-EV)/(CPI*SPI)}
Used when both CPI & SPI influence the remaining work
Estimate To Complete ETC
ETC = EAC - AC
Predict how much more the remainder of the project will costs

## Project Selection

Present Value PV
PV = FV / (1+r)^n
What the project should be worth. Bigger result is better
Discounted Cash Flow DCF
Cash flow*DF
Future Value F
FV = PV * (1+r)^n
The value at specified date in the future that is equivalent in value to a specified sum today
Discount Rate r
Discount Factor DF
Number of Years n

Net Present Value NPV
Sum of PV of the individual cash flows
Used in Capital budgeting to analyze the profitability of a project or investment Bigger NPV is better, more precise than payback period
Return of Investment ROI
ROI = Net Income / total investment
ROI = Select biggest number.
Benefit Cost Ratio BCR
BCR = Benefit / Cost
Bigger is better. Represent return for every \$1
Cost Benefit Ratio CBR
CBR = Cost / Benefit

Internal Rate of Return IRR
The interest rate at which the PV equals the initial invst
Bigger IRR is better, more precise than NPV
Payback Period PP
PP = Net investment / Average annual cash flow
Payback Period = Add up the projected cash inflow minus expenses until you reach the initial investment. Shorter is better
Opportunity Cost OC
Opportunity Cost = The value of the project not chosen.
Smaller is better
Expected Monetary Value EMV
EMV = Probability * Impact

## PERT

PERT 3-point
PERT 3
PERT3=(Pessimistic+(4*Most Likely)+Optimistic)/6
PERT a
PERT a
PERT a = (Pessimistic-Optimistic) / 6
PERT Activity Variance PAV
PAV = ((Pessimistic - Optimistic) / 6)^2
PERT Variance all activities
(PVA)= sum((Pessimistic - Optimistic) / 6)^2

## Classes of Estimates

Order of Magnitude estimate
= -25% to +75%
The estimate cost at early stage, scope not defined yet
Preliminary estimate
= -15% to + 50%
Rough estimate made at the beginning of the project
Budget estimate
= -10% to +25%
Definitive estimate
= -5% to +10%
The most accurate, takes time to create
Final estimate
= 0%
Always zero

## SIGMA

1 sigma = 68.26%, 1 standard deviation, frequently used in analyzing data
2 sigma = 95.46%, 2 standard deviations, frequently used in analyzing data
3 sigma = 99.73% 3 standard deviations, frequently used in analyzing data
6 sigma = 99.99% 6 standard deviations, frequently used in analyzing data
Control Limits (CL) 3 sigma from mean, reflects the expected variation in the data

## Communications

Communication Channels: CC = n * (n-1) / 2
Communication Channels per member: (n-1)
Increased Channels: n * (n-1) / 2 After - n * (n-1) / 2 Before
Decreased Channels: n * (n-1) / 2 Before - n * (n-1) / 2 After
C: number of communications channels
n: number of stakeholders

## Procurement

Point of total assumption (PTA)
Determined by (FPIF) fixed price plus incentive fees contract. The seller bears all the lose of a coast overrun
Contract Savings (CS)
(CS)=Target Cost - Actual Coast
The saving that is divided between the seller and the buyer based on agreed ratio for the coast saved by the seller against the original estimated coast
Contract bounce (CB)
(CB)=Savings*percentage
The sum paid when the seller meets certain goals decided in the (CPIF) cost plus incentive contract
Contact Coast (CC)
Bonus + Fees
Total Coast (TC)
Actual coast+ Contact coast
Source selection criteria (SS)
(SS)=(weightage*Price)+( weightage + Quality)
Used to score seller proposals
CP: Ceiling price
TP: Target price
TC: Target cost

## Depreciation

Depreciation Expense (DE)
DE = Asset Cost / Useful Life
Calculated using Straight-line Depreciation
Depreciation Rate (DR)
(DR) = 100%Useful Life
Calculated using Straight-line Depreciation
Depreciation Rate (DR)
(DR) = 2*(100%Useful Life)
Calculated using Double Declining Balance Method

Depreciation Rate (DR)
(DR) = Useful Life + (Useful Life - 1) + (Useful Life - 2) + etc...
Calculated using Sum-of-Years' Digits Method
Book value (BV)
(BV) = Book value at the beginning of the year - Depreciation Expenses
Calculated using Double Declining Balance Method

## Network Diagram

Float (FLT)
(FLT) = LS -ES OR (FLT) = LF - EF
If FLT<0, Behind schedule
If FLT = 0, critical
If FLT >0, Under schedule
Free Float (FF) = ES -EF
Activity duration (AD) = EF - ES +1 OR (AD)= LF - LS + 1
Early Finish (EF) = (ES + Duration) - 1
Early Start (ES) = EF + 1
Late Finish (LF) = LS -1
Late Start (LS) = (LF - Duration) +1
Forward Pass ES = EF of the predecessor node EF = ES + Dur
Backward Pass LF = LS of the Successor LS = LF - Dur
Slack = LF - EF = LS - ES

## Important Values

Control Limits = 3 sigma from mean
Control Specifications = Defined by customer; less than the control limits
Float on the critical path = 0 days
Pareto Diagram = 80/20
Time a PM spends communicating = 90%
Crashing a project = Crash least expensive tasks on critical path.
JIT inventory = 0% (or very close to 0%.)
Lag: Waiting time between activities (positive time)

Lead: Activities are moved closer together or overlap (negative time).
Crashing: Adding resources to reduce the project duration. Crashing adds costs to the project.
Fast tracking: Allows project phases to overlap to reduce the project duration. Fast tracking adds risk to the project.
Free float: The amount of time an activity can be delayed without delaying the next activity’s start date.
Total float: The amount of time an activity can be delayed without delaying the project’s end date.