## 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

Positive = ahead schedule

Negative = behind schedule

**Schedule Performance Index SPI **

SPI = EV/PV

Shows overall schedule adherence.

SPI >1: ahead schedule

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Used when the initial plan no longer valid.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%

Made during the planning phase

**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) **

(PTA) = [(CP-TP)]/buyer’s share ratio]+TC

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.