Project Management Formulas

Actual Cost

Actual cost (AC) is the realized cost incurred for the work performed on an activity during a specific time period. It’s the total cost incurred in accomplishing the work that the EV measured.

Consider a project to paint a room where the budget at completion (BAC) is $100. If one wall is completely finished, 25% of the project is complete. 25% of $100.00 is $25.00. The earned value (EV) is $25.00. What if it actually cost more than that to paint the wall? That's what actual cost is. If the total cost realized when painting that room totals $27.50, then the actual cost (AC) is $27.50.

CPI = EV / AC

EV stands for earned value and AC stands for actual value. The result of this formula will give you an number. An answer of 1 means on budget. Less than 1 means over budget and greater than 1 means under budget. So, the higher the number, the greater the cost efficiency.

The purpose of this formula is to calculate the cost efficiency on a project, or how well the money is being spent. It's perhaps the most critical earned value management (EVM) metric.

CBR=Net Present Value of Investment/Initial Investment Cost

The cost-benefit ratio compares the money invested in a project to the value that has come out of the project. It is a financial measure of project success.

If the initial investment in a project is $10,000 and the Net Present Value is $20,000, then the Cost Benefit Ratio is

$20,000/$10,000 = 2

A Cost Benefit Ratio of 2 indicates that every dollar invested in the project is now worth $2.

CV = EV - AC

EV stands for earned value and AC stands for actual cost. An answer of 0 means on budget. Less than 0 means over budget and greater than 0 means under budget.

Cost variance (CV) is the amount of budget deficit or surplus at any given time. It's a measure of cost performance on the project.

CP = The path with the longest duration.

To calculate the critical path on a project network schedule, simply determine the path with the longest duration. In other words, add together the durations of each activity on every path. The longest path is the critical path.
 
To begin, assign an estimated duration for every project activity. Next, establish the dependencies between all the activities. For example, walls must be framed before plumbing can begin. Once all the dependencies are established, you will see different paths because not all activities will be related to each other. One activity will be dependent upon the completion of five others with another activity being dependent upon 20 on a different path.

Add together the durations of every activity on each path. The path with the longest total duration is the critical path. Note that it is not necessarily the path with the most activities.

The critical path methodology is simply a technique used to identify all the tasks that will directly impact the project end date. If any task on the critical path is delayed, the project will be behind schedule. That's why it's so important to carefully monitor activities along the critical path.

ES = The earliest date the activity can start.

ES of the current activity + duration of current activity = ES of the successor activity.

This is the forward pass formula for calculating early start (ES). ES is the earliest an activity can possibly start.

EV = The measure of work performed.

Earned Value (EV) is the measure of work performed expressed in terms of the budget authorized for that work. It’s the same thing as Budgeted Cost of Work Performed (BCWP).
 
Consider a project to paint a room where the budget at completion (BAC) is $100. If one wall is completely finished, 25% of the project is complete. 25% of $100.00 is $25.00. The EV is $25.00.

ETC = EAC - AC

EAC means estimate at completion and AC means actual cost.

Estimate to Complete (ETC) is the expected cost to finish all the remaining project work.

EAC = AC + (BAC - EV)

AC stands for actual cost and BAC stands for budget at completion and EV stands for earned value.
 

The EAC is the expected total cost of completing all work expressed as the sum of the actual cost to date and estimate to complete.

This method for calculating EAC accepts the actual project performance to date and predicts that all future ETC work will be accomplished at the budgeted rate.

EMV  for  A  =  V  x  PEMV  for  B  =  V  x  PA + B

Expected Monetary Value (EMV) analysis calculates the average outcome when the future includes events that might not occur. EMV for a project is calculated by multiplying the value of each possible outcome by its probability of occurrence and adding the products together.

The “A” and “B”, above are risks on same project. “V” is the Value of the impact when it occurs. “P” is the probability of occurrence.

Positive numbers represent positive opportunities while negative numbers represent negative risk or threats.

An excellent illustration of this can be found in a decision tree diagram located in A Guide to the Project Management Body of Knowledge, Fifth Edition, (PMBOK® Guide). Newtown Square, PA : Project Management Institute, Inc., 2013. p. 339, Figure 11-16.

Float = Late Start (LS) – Early Start (ES)

also: Float = Late Finish (LF) – Early Finish (EF)

Float is the amount of time an activity can be delayed without delaying the project end date. There are two ways to calculate it using the critical path method. Both ways are set forth above.

Free float is the amount of time that a schedule activity can be delayed without delaying the early start day of any successor or violating a schedule constraint.

Total float is the amount of time that a schedule activity can be delayed or extended from its early start date without delaying the project finish date or violating a schedule constraint.

When calculating float, know that zero (0) float means that if one delay occurs, the project will fall behind schedule. Remember that the activities on the critical path (critical activities) have a float of zero.

FV=I×(1+(R×T))

FV=Future Value
I=Investment amount
R=Interest rate
T=Number of years


The Future Value formula is used to estimate how much today’s asset or investment will be worth in the future, based on an assumed growth rate.

LS = The latest an activity can start.

LS of the current activity minus duration of predecessor activity= LS of predecessor activity.

This is the backward pass formula for calculating late start (LS).

LS is the latest an activity can possibly start. Where paths join, use the path with the lowest duration.

PV = The authorized budget that is assigned to scheduled work.

Planned value (PV) is the amount of budget that’s planned for an activity or WBS component, not including management reserve.

At any given moment, planned value defines the work that should have been accomplished. The total planned value for the project is also known as the budget at completion (BAC).

Consider a project to paint a room where the budget at completion (BAC) is $100. Painting one wall equates to 25% of the project being complete. The planned value for that work is $25.00. The total planned value for the project is $100.

PTA = [(Ceiling Price - Target Price) / Buyer's Share Ratio] + Target Cost

PTA is a concept associated with fixed price incentive fee (FPIF) contracts. It represents costs above the established price ceiling that are the responsibility of the seller.

FPIF contracts specify the target cost, the target profit, the target price, the ceiling price, and one or more share ratios. Note that FPIF contracts can create win/win situations where sellers receive a bonus for finishing early or exceeding other performance metrics.

PV = FV/(1+i)^n

Present Value represents the current value of future money or a future money stream. It's based on the concept that an amount of money today is worth more than the same amount in the future.

With the present value formula,
• PV = present value
• FV = future value
• i = interest rate per period in decimal form
• n = number of periods
(Note that "n" indicates that (1+i) must be raised to the "nth" power. A common mistake is to multiple (1+i) times "n".

PERT Estimation = (Optimistic + (4 x Most Likely) + Pessimistic)/6

PERT is a three-point estimating technique used to approximate an activity cost or duration.

Most likely (M) - The activity cost/duration based on a realistic assessment of effort for the required work and any predicted expenses.
Optimistic(O) - The activity cost/duration based on an analysis of the best-case scenario.
Pessimistic(P) - The activity cost/duration based on an analysis of the worst-case scenario.

n (n-1)/2

This formula is used to calculate the total number of potential communication channels. When calculating, "n" represents the number of stakeholders. Don't forget to include the project manager as a stakeholder.

RPN = Severity x Probability x Detection

Risk Priority Numbers are calculated by multiplying three values:
1. Severity - regards the severity of the risk.
2. Probability - indicates how likely it is to experience the severity.
3. Detection - represents the ease with which the risk can be detected.

Once RPNs are assigned to risks, the risks can be sorted from highest to lowest.

ROI = [(Financial Value - Project Cost) / Project Cost] x 100

This ROI formula is used to justify a project. The ROI is expressed as a percentage to reflect the gain/loss from an investment in relation to the initial investment. Low or negative percentages may indicate that the project is not worth the investment.

SPI = EV/PV

EV stands for earned value and PV stands for planned value. An answer of 1 means on schedule. Less than 1 means behind schedule and greater than 1 means ahead of schedule.

The SPI is a measure of schedule efficiency. It measures how efficiently the project team is using its time. It can be used in conjunction with the CPI to make forecasts regarding final project completion estimates.

SV = EV - PV

EV stands for earned value and PV stands for planned value. An answer of 0 means on schedule. Less than 0 means behind schedule and greater than 0 means ahead of schedule.

Schedule variance is a measure of schedule performance expressed as the difference between the earned value and the planned value. It's the amount that the project is ahead or behind schedule at a given time.

tE = (tO + tM + tP) / 3

Where there is uncertainty with an individual activity estimate, a three-point estimate can be used to estimate cost or duration by applying an average of optimistic, pessimistic and most likely estimates.

cE = (cO + cM + cP) / 3

Where there is uncertainty with an individual activity estimate, a three-point estimate can be used to estimate cost or duration by applying an average of optimistic, pessimistic and most likely estimates. By considering uncertainty and risk, we look to improve our estimates.

This concept originated with the program evaluation and review technique (PERT). Two commonly used formulas are triangular and beta distributions.

tE = (tO + 4tM + tP) / 6

The beta distribution formula is from the traditional PERT technique.

cE = (cO + 4cM + cP) / 6

The beta distribution formula is from the traditional PERT technique.

TCPI = Work Remaining (BAC - EV) / Funds Remaining (BAC - AC)

1 means on budget. Less than 1 is under budget. Greater than 1 is over budget.

TCPI is a measure of the cost performance that's required to be achieved with the remaining resources in order to meet a specified management goal.

VAC = BAC - EAC

0 means on budget. Less than 0 means under budget. More than 0 means over budget.

Variance at completion (VAC) is a projection of the amount of budget deficit or surplus.