Tổng hợp tất cả 39 công thức luyện thi PMP và 18 giá trị cần phải nhớ
I – PMP Formulas
|Cost Variance (CV)
Provides cost performance of the project. Helps determine if the project is proceeding as planned
|CV = EV – AC||Negative = over budget = bad
Positive = under budget = good
|Cost Performance Index (CPI)
Measure of cost efficiency on a project. Ratio of earned value to actual cost.
|CPI = EV / AC||1 = good. We are getting 1$ for every $1 spent. Funds are used as planned.
>1 = good. We are getting >1$ for every $1 spent. Funds are used better than planned.
<1 = bad. We are getting <1$ for every 1$ spent. Funds are not used as planned.
|Schedule Variance (SV)
Provides schedule performance of the project. Helps determine if the project work is proceedding as planned
|SV = EV – PV||Negative = behind schedule = bad
Positive = ahead of schedule = good
|Schedule Performance Index (SPI)
Measure of schedule efficiency on a project. Ratio of earned value to planned value. Used to determine if a project is behind, on or ahead of schedule. Can be used to help predict when a project will be completed.
|SPI = EV / PV||1 = good. We are progressing at the originally planned rate.
>1 = good. We are progressing at a faster rate than originally planned.
<1 = bad. We are progressing at a slower rate than originally planned
|Estimate at Completion (EAC)
Expected final and total cost of an activity or project based on project performance. Helps determine an estimate of the total costs of a project based on actual costs to date. There are several ways to calculate EAC depending on the current project situation and how the actual work is progressing as compared to the budget. Look for certain keywords to determine what assumptions were made.
|EAC = BAC / CPI
Assumption: use formula if current variances are thought to be typical in the future. This is the formula most often required on the exam
|Original budget modified by the cost performance. The result is a monetary value|
|EAC = AC + ETC
Assumption: use formula if original estimate was fundamentally flawed or conditions have changed and invalidated original estimating assumptions
|Actual Cost plus a new estimate for the remaining work. Result is a monetary value|
|EAC = AC + BAC – EV
Assumption: use formula if current variances are thought to be atypical in the future and the original budget is more reliable.
|Actual cost to date (AC) plus remaining budget (BAC – EV). Result is a monetary value|
|EAC = AC + ((BAC – EV) / (CPI * SPI)) Assumption: use formula if project is over budget but still needs to meet a schedule deadline||Actual cost to date (AC) plus remaining budget (BAC – EV) modified by both cost performance and schedule performance. Result is a monetary value|
|Estimate to Complete (ETC)
Expected cost needed to complete all the remaining work for a schedule activity, a group of activities or the project. Helps predict what the final cost of the project will be upon completion. There are many ways to calculate ETC depending on the assumptions made
|ETC = EAC – AC
Inversion of the same formula from the EAC calculations.
Note: This ETC formula is listed in only one (the “most famous”) PMP prep workbook. No others list it. We recommend using it, if no keywords are given
|Expected total cost minus actual cost to date. Result is a monetary value that will tell us how much more the project will cost|
|ETC = BAC – EV
Assumption: use formula if current variances are thought to be atypical in the future
|The planned budget minus the earned value. Result is a monetary value that will tell us how much more the project will cost.|
|ETC = (BAC – EV) / CPI Assumption: use formula if current variances are thought to be typical in the future||The planned budget minus the earned value modified by project performance. Result is a monetary value that will tell us how much more the project will cost|
|ETC = We create a new estimate when it is thought that the original estimate was flawed||This is not the result of a calculation or formula, but simply a new estimate of the remaining cost|
How much of the planned budget do we have completed?
|Percent Complete = EV / BAC * 100||The result is a percentage. What is currently completed divided by the original budget times 100.|
|To-Complete Performance Index (TCPI)
The calculated project of cost performance that must be achieved on the remaining work to meet a specific management goal (e.g. BAC or EAC).
It is the work remaining divided by the funds remaining.
|Based on BAC:
TCPI = (BAC – EV) / (BAC – AC)
Based on EAC:
TCPI = (BAC – EV) / (EAC – AC)
|The TCPI is compared to the cumulative CPI to determine if a target EAC is reasonable. A target EAC is assumed to be reasonable if the TCPI is within plus or minus 0.05 of the cumulative CPI EVM metric.|
|Variance at Completion (VAC)
Anticipates the difference between the originally estimated BAC and a newly calculated EAC. In other words, the cost we originally planned minus the cost that we now expect.
|VAC = BAC – EAC||Result is a monetary value that estimates how much over or under budget (the variance) we will be at the end of the project.
<0 = over budget 0 = on budget
>0 under budget
|Earned Value (EV)
A quick formula for calculating the Earned Value on a project.
|EV = % complete * BAC||The result is the EV, a monetary value|
|Program Evaluation and Review Technique (PERT (Program Evaluation and Review Technique))
Three point estimate for the expected duration of a schedule activity using pessimistic, optimistic and most likely durations. A probabilistic approach, using statistical estimates of durations
|(Pessimistic + (4 * Most Likely) + Optimistic) / 6||The result is the estimated duration of a schedule activity expressed as a weighted average.|
|PERT Standard Deviation (Single Activity)
The standard deviation (σ) is a reflection of the uncertainty in the estimates. It is a good measure of the statistical variability of an activity.
|σ = (Pessimistic – Optimistic) / 6||The result is the standard deviation from the mean of a schedule activity. For instance, the duration +/- 1 standard deviation will give you a 68.26% confidence that you can meet the estimated duration|
|PERT Activity Variance
Every activity has a variance, which is a statistical dispersion. Here is an example: The PERT three point estimate gives a 15-day duration. The variance formula tells you that you have a two-day variance. Therefore the activity duration is 15 days +/- 2 days.
|Variance = ((Pessimistic – Optimistic) / 6)^2||The Activity Variance will give you the expected variance in the activity’s duration. For instance: +/- 3 days.|
|PERT Standard Deviation (All Activities)
You may be required to calculate the duration of multiple activities and give their standard deviation. This is done by taking the square root of the total variance.
|√sum((Pessimistic – Optimistic) / 6)^2 (Add up the variances of all the activities and then take the square root.)||The result is one standard deviation (or variance) from the mean of the given series of activities|
Determines how long an activity lasts. There are two formulas both will give the same result
|Duration = EF – ES + 1 Duration = LF – LS + 1||Number of days this activity lasts|
Determines how many days you can delay an activity without delaying the early start of the next activity. On most sample PMP exam questions, the network diagrams are too small to show activities where free float and total float are different. In most sample questions they will be the same.
|Free Float = Earliest ES of Following Activities – ES of Present Activity – Duration of Present Activity||Number of days this activity can be delayed without delaying the early start of the next activity.
Note: If the present activity has more than one following activities, then use the Earliest ES of any of the following activities
Determines how many days you can delay an activity without delaying the project. There are two formulas both will give the same result
|Total Float = LS – ES Total Float = LF – EF||Number of days this activity can be delayed without delaying the project|
|Early Finish (EF)
Determine when an activity will finish at the earliest
|EF = (ES + duration) – 1||Day on which this activity can finish earliest|
|Early Start (ES)
Determine when an activity can start at the earliest
|ES = (EF of predecessor) + 1||Day on which this activity can start earliest|
|Late Finish (LF)
Determine when an activity should finish at the latest
|LF = (LS of successor) – 1||Day on which this activity can finish latest.|
|Late Start (LS)
Determine when an activity should start at the latest
|LS = (LF – duration) + 1||Day on which this activity can start latest|
|Present Value (PV)
Receiving money in the present (today) has a different value than receiving money in the future (in three years). This formula calculates how much. (Also described as value today of future cash flows.) PV in this case should not be confused with the Planned Value (PV)
|PV = FV / (1+r)^n||The result is the amount of money you need to invest today (PV) for n years at r % interest in order to end up with the target sum (FV). The higher the PV the better.|
|Future Value (FV)
Receiving money in the future (in three years) has a different value than receiving money in the present (today). This formula calculates how much. (Also described as the discounted value of a future cash flow.)
|FV = PV * (1+r)^n||The result is the amount of money you will end up with (FV) if you invest a sum of money (PV) for n years at r % interest.|
|Net Present Value (NPV)
Method for financial evaluation of long-term projects. (Also described as Present value of cash inflow / benefits minus present value of cash outflow / costs.)
|Formula not required for exam.||Positive NPV is good. Negative NPV is bad. The project with the higher NPV is the “better” project.|
|Return on Investment (ROI)
Ratio of money gained or lost on an investment relative to the amount of money invested. The amount of money gained or lost is often referred to as interest, profit/loss, gain/loss, or net income/loss.
|Formula not required for Exam||The project with the higher ROI is better and should be selected.|
|Internal Rate of Return (IRR)
Interest rate at which the present value of the cash flows equals the initial investment. More precise and more conservative than NPV.
|The project with the higher IRR is better and should be selected.|
Rough tool to estimate the time it takes to recover the initial investment by adding up the future cash inflows until they are equal to the initial investment. (Or in plain English: The time it takes until you make a profit.)
|Add up the projected cash inflow minus expenses until you reach the initial investment||The project with the shorter payback period is better and should be selected.|
|Benefit Cost Ratio (BCR)
Ratio that describes the cost versus benefits of a project.
|Benefit / Cost||BCR < 1 is bad. BCR > 1 is good. The project with the bigger BCR is the “better” one|
|Cost Benefit Ratio (CBR)
Ratio that describes the benefits versus cost of a project. This is simply the reverse of the Benefit Cost Ratio
|Cost / Benefit||CBR > 1 is bad. CBR < 1 is good. The project with the lower CBR is the “better” one.|
Opportunity cost is the cost incurred by choosing one option over an alternative one. Thus, opportunity cost is the cost of pursuing one choice instead of another.
|Opportunity Cost = The value of the project not chosen.||For the PMP exam the opportunity cost is usually a monetary value: Project B was selected over project A, therefore the opportunity cost is the unrealized profit of project A. Note that NO calculation is required.|
The number of communication channels on a team.
|n * (n-1) / 2||Total number of communication channels among n people of a group|
|n-1||Number of communication channels that one member of the team has with everyone else on the team. I.e. you have to make this many phone calls to call everyone else|
|Expected Monetary Value (EMV (Expected Monetary Value))
Gain or loss that will result when an event occurs. Takes probability into account. For instance: If it rains we will loose $200. There is a 25% chance that it will rain, therefore the EMV is: 0.25 * $200 = $50
|Probability * Impact in currency||A monetary value that represents the expected gain or loss of an event should it come to be|
|Point of Total Assumption (PTA)
The point of total assumption (PTA) is a price determined by a fixed price plus incentive fee contract (FPIF) above which the seller pays the cost overrun. In addition, once the costs on an FPIF contract reach PTA, the maximum amount the buyer will pay is the ceiling price
|PTA = ((Ceiling Price – Target Price) / Buyer’s Share Ratio) + Target Cost||The result is a monetary value. When reached then the seller covers all of the cost risk beyond.|
A method that depreciates the same amount (or percent) each year by dividing the asset’s cost by the number of years it is expected to be in service. The simplest of the depreciation methods.
|Depreciation Expense = Asset Cost / Useful Life
Depreciation Expense = (Asset Cost – Scrap Value) / Useful Life
Depreciation Rate = 100% / Useful Life
|The result is either the Depreciation Expense (the yearly depreciation amount: $200) or the Depreciation Rate (the yearly depreciation percentage: 5%). If a Scrap Value is given then this can also be factored in by subtracting it|
|Double Declining Balance
Most common depreciation method that provides for a higher depreciation charge in the first year of an asset’s life and gradually decreasing charges in subsequent years. It does this by depreciating twice the straight-line depreciation rate from an assets book value at the beginning of the year.
|Depreciation Rate = 2 * (100% / Useful Life)
Depreciation Expense = Depreciation Rate * Book Value at Beginning of Year
Book Value = Book Value at beginning of year – Depreciation Expense
|The Depreciation Rate stays the same over the years, but the Depreciation Expense gets smaller each year because it is calculated from a smaller book value each year.|
|Sum-of-Years’ Digits Method
Sum-of-Years’ Digits is a depreciation method that results in a more accelerated write-off than straight line, but less than declining-balance method. Under this method annual depreciation is determined by multiplying the Depreciable Cost by a schedule of fraction based on the useful life of the asset.
|Sum of the digits = Useful Life + (Useful Life – 1) + (Useful Life – 2) + etc.
Depreciation rate = fraction of years left and sum of the digits (i.e. 4/15th)
|Both depreciation rate and depreciation fraction get smaller over time.
Example: Sum of the digits: If the useful life is 5, then it is 5 + 4 + 3 + 2 + 1 =15 Depreciation rate: 5/15th for the 1st year, 4/15th for the 2nd year, 3/15th for the 3rd year, 2/15th for the 4th year, and 1/15th for the 5th year
|Average = Mean
In mathematics, an average refers to a measure of the “middle” of a data set. The most common method is the arithmetic mean. That is why the “Average” is sometimes also and simply called the “Mean”.
|The sum of all the members of the list divided by the number of items in the list.
Average of 2, 4, 6 = (2 + 4 + 6) / 3 = 4
|The result is a number representing the arithmetic mean|
The middle value that separates the higher half from the lower half of the data set.
|Arrange the values from lowest value to highest value and pick the middle one. Example: 4 is the median in 2, 4, 6
If there is an even number of values,
calculate the mean of the two middle values. Example: 5 is the median in 2, 4, 6, 8 because 4 + 6 / 2 = 5
|The result is a number representing the median.|
The most frequent value in a given data set.
|Find the value in a data set that occurs most often. Example: 2 is the mode of 1, 2, 2, 3||The result is a number representing the mode|
II – PMP Important Values
|1 sigma||68.26%||Also: 1 standard deviation|
|2 sigma||95.46%||Also: 2 standard deviation|
|3 sigma||99.73||Also: 3 standard deviation|
|6 sigma||99.99%||Also: 6 standard deviation|
|Control Limits||Usually 3 standard deviations above and below the mean||Control limits reflect the expected variation in the data|
|Control Specifications||Not fixed but defined by the customer||Must be looser than the control limits. Represents the customer’s requirements.|
|Rough Order of Magnitude estimate||-25% to +75% (PMBOK® Guide)
|Preliminary estimate||-15% to + 50%|
|Budget estimate||-10% to +25%|
|Definitive estimate||-5% to +10%|
|Float on the critical path||0 days|
|Pareto Diagram||80/20||For instance: 80% of your problems are due to 20% of the causes|
|Time a PM spends communicating||90%||According to Harold Kerzner|
|Crashing a project||Crash the tasks with the least expensive crash cost first||Only crash activities on the critical path|
|Value of the inventory in a Just in Time (JIT) environment||0% (or very close to 0%.)|
|Sunk Cost||A cost that has been incurred and cannot be reversed.||Sunk cost is never a factor when making project decisions.|
|In the USA the number -100 is the same as (100). Both indicate “minus one hundred”|