PMP Formulas

Formulas (turquoise)

 

 

Acronym	Terminology/Phrase	Formula(s)	Real Meaning /Reference
EV or BCWP	Earned Value or Budgeted[1] Cost of the Work Performed	EV = %completed * BAC	·         How much work was actually done as described in the budget ·         A method for measuring project performance.  It compares the amount of work planned with what was actually accomplished to determine if cost and schedule performance is as planned.   Earned  Value (EV), is a percentage of the total budget equal to the work actually performed.
PV or BCWS	Planned Value or Budget Cost of Work Scheduled		·         How Much work should be done (The estimated value of the planned work) ·         The budget that is part of the approved cost estimate planned to be spent on the activity during a given period
AC or ACWP	Actual Cost or Actual Cost of the Work Performed		·         What is the actual cost incurred?  ·         What have we spent to date? ·         The actual cost that is the total of direct and indirect costs incurred in accomplishing work on the activity during the given period
BAC	Budget At Completion	Budget at completion	·         How much did you budget for the job? The total budget.
	Variance	Variance = BAC – AC	·         Planned – actual (i.e. planned was three weeks, actual was two weeks – resulting in a one week variance)
	Percentage complete	%complete = EV/BAC
CV	Cost Variance	CV =   EV – AC	·         Any difference between the estimated cost of an activity and the actual cost of that activity
SV	Schedule Variance	SV =    EV – PV	·         Any difference between the scheduled completion of an activity and the actual completion of that activity
CPI	Cost Performance Index	CPI = EV/AC[2] CPI <1 means over budget CPI >1  cost are below budget CPI equal to 1 means costs equal benefits	·         Used to forecast project cost at completion ·        The ratio of budget cost to actual costs.
SPI	Schedule Performance Index	SPI = EV/PV   SPI <1  project will be late SPI  > 1`project is ahead of schedule SPI equal to 1 means costs equal means project is on scheule	·         Used to forecast project completion date ·        The SPI is used in some application areas to forecast the project completion date.
	Cumulative CPI	Sum of all individual EV divided by the sum of all individual AC
	Critical Ratio	SPI * CPI
	Critical Path uncertainty	The Critical Path uncertainty = the sum of the (square root of the variances)
EAC	Estimate At Completion		Several possible calculations depending upon the status of the project
EAC	Estimate At Completion	EAC = BAC  / CPI	·         Used if no variances from BAC or you will continue at the same rate of spending. ·         Most commonly used on PMP exams
EAC	Estimate At Completion	EAC=AC+ETC	·         Used when original estimate is flawed ·         Actual plus new estimate for remaining work.
EAC	Estimate At Completion	EAC=AC + (BAC –EV)	·         Used when current variances are atypical of the future. ·         Actual to date plus remaining budget.
EAC	Estimate At Completion	EAC=(AC + (BAC -EV))/CPI .	·         Used when variances are thought to be typical of the future ·         Actual to date plus remaining budget modified by performance
ETC	Estimate To Completion	ETC = EAC – AC	·         How much will the project cost
VAC	Variance At Completion	VAC  = BAC – EAC	·         How much over budget will we be at ten end of the project?
Slack		(LS-ES) or (LF-EF)
ES	Early Start	EF –  duration + 1
EF	Early Finish	ES + duration – 1
LS	Late Start	LF – duration + 1
LF	Late Finish	LS +  duration -1
FF	Free Float	ES (of successor) – EF (of current task) – 1	·         amount of time the current activity can be delayed without delaying the early start of the successor task
TF	Total Float	LF – EF (of current task)	·         amount of time the current activity can be delayed without delaying the LF of the entire project.
	Budget Burn Rate (linear)	BAC / planned duration	·         Example ($1,000 / 4 weeks = $250 per week)
	Actual Burn Rate (linear)	AC / Actual duration	·         Example ($1,200 / 5 weeks = $240 per week)
	Excepted Value	Probability (%) * consequences
	Simple Interest	Interest = Principle X Rate x Time
EMV	Expected Monetary Value	EMV = Odds of occurrence x amount at stake
	Present Value	Present Value = FV/(1+r)n	FV = Future Value r = Interest Rate n    = # of periods
	Future Value	FV = PV x (1 + i)	n = Number of time periods (years) PV = Present value (of money) i = interest rate
	Pay back	Pay back = period of time to recover investment through cash flow
BCR	Benefits Cost Ratio	BCR greater than 1 is good BCR less than 1 is bad BCR equal to 1 means costs equal benefits
	Opportunity cost	No calculation	·         Defines the opportunity given up by selecting one project over another
IRR	Internal Rate of Return	Complex calculations requiring computer	·         If a company has more than one project to invest, the company may look at projects’ return and then select the highest one.
	Fixed Cost		·         Resource constrained scheduling, end date may vary
	Fixed Time		·         Resource variable scheduling, end date fixed
NPV	Net Present Value	To calculate you need to calculate the present value of both income and revenue figures and then add up the present values	·         The present value of the total benefits (income or revenue) less the costs.

 

 

 

Valuable Hint NOT Written in Project Management Books About Costs

 

(Or more succinctly “How to know you’re in trouble”)

 

When EV (BWCP) is used in an equation, it always goes first:

 

CV = EV – AC

 

If you get a negative number, your project is over budget.

 

SV = EV – PV

 

Again, if you get a negative number, your project will overrun its schedule.

 

 

Communication channels (assuming a binary distribution)

 

N (N-1) / 2

 

 

 

Program Evaluation and Review Technique (PERT)

 

 

Other Notes

PERT assumes a beta distribution

Weighting –  Pessimistic = 1, Most likely = 2  and  Optimistic =3

 

Standard Deviation

(P-O)/6

Task Variance

[ (P-O) / 6]

 

 

Project Variance

Project Variance = Take the square root of the sum of the task variances

 

 

 

 

Conventional Critical Path Methodology

 

A to B
Finish to Start  (FS)	zero delay
Start to Start (SS)	implies delay on B after Start of A
Finish to Finish	A must finish before B
Start to Finish	A must start before B can finish

 

 

Measures of Central Tendency (Mean, Median, Mode)

 

Mean

The mean is the sum of the measures divided by the number of measurements

 

 

Mode

The mode is the most frequent occurring observation in the data under consideration.

 

If the observation has two modes, then the data is said to be bi-modal distribution.

 

If the observations have three or more modes, then the mode is no longer a viable measure of central tendancy.

 

2,2,2,3,3,5,7,10,12

 

mode = 2

 

 

Measures of Variability

 

Range

The range is the difference between the largest measure and the smallest measurement.

 

The range does not use all available observations.  It uses only the two extreme values.  It will have the same dimension, or unit of measure as the original data.

     

Standard Deviation

The standard deviation is the positive square root of the variance.

 

   12.67  = 3.56

 

Normal Distribution

  = 68.26

  = 94.36

  = 99.73

  = 99.99

 

Note   68.26/2 = 34.13   which is 50% above the one sigma mean and  50% below one sigma mena.

 

 

Other

 

·         UCL / LCL Upper Control Lime & Lower Control Limit on a control chart

·         Pareto:  80% of problems come from 20% of the work

·         Crashing:  Slope = Crash Cost – Normal Cost/Crash Time – Normal Time

·         Progress Reporting:  0/100; 50/50; 20/80

·         Standard Deviation of a project = Square Root of  Sum of Critical Path Variances

·         Slack = LST – EST (Latest Start Time – Earliest Start Time)

    = LFT – EFT (Latest Finish Time – Earliest Finish Time)

 

Histogram	Variance & Standard Deviation
Add up your number of observations. (N)	Find the mean (x-bar)
Determine the Range (R)	Subtract the mean from every observation (n)
Determine Classes (K)	Square each result
Determine Class Width (H) where H = R/K	Add up all the squares
Construct Frequency table	Divide that number by n-1 (for the sample) or N (for the population)     This is the Variance
Plot Data	Square root the answer This is the Standard Deviation

 

Binomial Distribution (Success or Failure)

·         A coin will be tossed 5 times but the coin is biased so that the probability of heads for each toss is 0.04. Heads is success, tails is failure.

·         N = number of items in the sample (the number of coin tosses)

·         X = number of items for which the probability is desired (number of Heads)

·         In Appendix A we go to column N and find where N = 5

·         In Appendix A we go to where p = 0.40

·         Each row represents the probability of 0, 1,2, 3, 4, and 5 successes

·         Add them up

 

Poisson Distribution

·         A light bulb manufacturer has a known defective rate of 4%. From a sample of 40, the probability of 4 or more defective light

·         µ = np = (40) (.04) = 1.6

·         Probability of 4 or more defective is = 1 – probability of 3 or less defective

·         In the table, find where µ = 1.6

·         Add up the numbers where x has a value of 0, 1, 2, or 3 (this is the P of 3 or less defectives)

·         Subtract that number from 1.0

·         Find np (sample x defective rate)

·         Calculate up to by going to the table, finding np, adding it up

·         Subtract that answer from 1 to x or greater probability

 

Normal Distribution (also known as Gaussian)

·         If process produces parts with mean of _ and standard Deviation of _, what is the P that one random part has a measurement of _?

·         Mean time of a bank transaction is 5.25 with a standard deviation of 0.75 minutes and the values are normally distributed. What is the probability that a transaction will occur between 4.0 and 5.25 minutes and below 4.0?

·         Z = 4.0 – 5.25/ 0.75 = -1.67

·         Go to Appendix A and find 1.67 = 0.4525

·         Because we know that µ is 5.25, the probability that a transaction will take less than 5.25 is .05 (1/2)

·         Therefore, the probability that a transaction will be less than 4 minutes = 0.5 – 0.4525 = 0.0475

 

Sampling Distributions (number of standard Deviations that a sample mean is away from the population mean)

·         If normal distribution with mean of _ and SD of _. From sample of _ what is P that the sample mean is >, <, =, or between _?

·         Hospital emergency room where it has a record waiting time of 30 minutes with a standard deviation of 5 minutes. If a sample of 35 is measured, what is the probability that the sample mean would be greater than 31.5 minutes?

·         Do the Z calculation to get 1.77

·         Find 1.77 in Appendix A (go to 1.7 and then across to 0.07)

·         Subtract that probability from the .5 probability = .50 – .4616 = .0384

·         This tells us that there is only a .0384 probability that, from the sample of 35, the sample mean will be greater than 31.5.

 

Measure of shapes (skewness)

 

Symmetrical (Bell sphere)

 

Positive skew (shift to right)

 

Negative skew (shift to left)

Beta Distribution = skewed in one direction

 

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[1]   Some of the literature refers to this as Basic rather than budgeted.

[2]    The simple way to remember CPI and SPI is these are ratios of the CV and SV.  If you know the CV and SV formulas, remember CPI and SPI are rations.