PMI Formulae
Content
Time Management
Precedence Diagram: Activity on Node
Forward Pass: Find early start and finish based on Project Start date.
Early Finish = Early Start + Duration
Early Start = Max or Last of all (previous early finishes)
(Reason: That is earliest time you can start activity after all previous activities it is dependent on are over)
Backward Pass: Find Late start and finish based on Project End date.
Late Start = Late Finish - Duration
Late Finish = Min of all (Late Starts of previous activities in backward pass)
(Reason: That is latest time you can finish activity without affecting latest start of all further activities)
Float = Late Finish - Early Finish
Float = Late Start - Early Start
(Meaning: Duration by an activity can be delayed without affecting end date of project)
Free Float = Early Start (j) - Early Finish (i)
= Early Start of activity - Early Finish of previous activity
(Meaning: Duration by an activity can be delayed without affecting early start of subsequent activity)
Weighted value = (Optimistic + 4 X Most likely + Pessimistic)/4
Arrow Diagram Method: Activity on arrow
Forward Pass: Earliest Time of event
Backward Pass: Latest Time of event
Float = Latest Time of event - Earliest Time of event
Cost Management
Earned value analysis
Schedule Variance = EV- PV
SPI = EV/PV
Cost Variance = EV- AC
CPI = EV/AC
Negative variance is slippage. Positive is we are doing better than planned.
Performance Index <1 is slippage. More than 1 means we are doing better than planned.
EAC: Estimate At Completion
ETC: Estimate To complete. Expenditure from this point onwards to complete project.
EAC = BAC/CPI = AC + (BAC-EV)/CPI
Typical problems. Likely to continue. Assume the
project execution is same after the present point with respect to the till date execution
EAC = AC + (BAC-EV) Atypical problems. Now onward things will be as planned earlier
EAC = AC + ETC
Basis of estimation was not correct. Fresh re-estimation of remaining work.
Duration to complete Project = Planned Duration/SPI
Depreciation:
Cost of machine 1200. Life 4 Years, Scrap Value 200.
Depreciable cost = Cost of asset - Salvage value = 1200-200=1000
Linear
Depreciation Each year = (Cost - residual value)/Life = (1200-200)/4 = 250
Accelerated :
Sum of remaining life = 4 + 3 + 2 + 1= 10
First Year= 1000*4/10= 400
Second Year: 1000 * 3/10= 300
Third Year = 1000* 2/10= 200
Fourth Year = 1000*1/10.= 100
Double Declining Balance
12.5% of 1000 = 125
25% of 1000-1000X12.5% = 25 % of 875
50% of remaining
100 % of remaining
Value is incoming so it is better to be positive and more.
Cost is expenditure and should be minimum.
Capitalized cost = Initial cost + Annual cost/Rate
Capitalized Value = Annual return/Rate
eg. Rate of capital is 10%
Initial cost is 1000 and annual cost is 10, Annual return is 150.
Capitalized cost = 1000 + 10/0.1 = 1100.
Capitalized Value = 150/0.1 = 1500
Project Selection method
Present Value, Net resent Value
IRR
Payback period
Benifit Cost Ratio
Pay Back period: Simplistic.
Pay Back period = Net Investment / Average Annual Cash flow.
Investment 1500
Cash Flow Year1 : 800
Cash Flow Year2 : 650
Cash Flow Year3 : 750
Pay Back Period = 1500 /(800 + 650 + 750) = 2.1 Years
ROI = Average Annual Profit/Investment
Investment 1000, Annual yield is 100. then ROI = 100/1000 = 10%
Interest = Principal X Rate X Time = P * R *T
Future Value of Money = Present Value X (1 + n(rate))
Compound Interest
Future Value = Present Value X ( 1 + rate)n
Net Present Value (NPV) = Sum of original Investment + Current Value of future cash flow.
Internal Rate of return = when Present value of cash flow equals initial investment
IRR is discount rate when NPV =0.
IRR The rate (of interest) when project revenues and project costs are equal.
Higher IRR is preferred.
Risk Management
Simple Probability
Probability: Chance of selecting one card of pack 1/52
Chance of alternative outcome = 1- outcome.
e.g probability of Diamond card is 1/4 probability on non diamond card is 1-1/4 = 3/4
Chance of two event occurring P1 and P2 is P1*P2.
Chance of occurring either P1 or P2is P1 + P2
Statistics
Mean: Sum(values)/N
Mode: Most likely event, Max( Values)
Median (50% vales are higher 50% values are Lower). If values are arranged in ascending order the center
value is median.
Variance and Standard deviation is spread around central value.
variance = (Standard Deviation)2 = (Sigma)2 for Gaussian distribution
For three point estimate
mean value = (Optimistic + 4 X Most likely + Pessimistic)/4
Std Dev = (Pessimistic - Optimistic)/6
Variance = (Standard Deviation)2
To find project mean and deviation
Add mean value of critical path. Add Variances. Find square root of this variance as deviation of critical
path. You cannot add deviations directly.
e.g. if A,B,C for critical path
Task
Opti.
Most like.
A
O
M
B
C
Pess.
P
Pert (Mean)
(O + 4M + P)/4
Std Dev
(P - O)/6
Variance
((P - O)/6)2
Completion duration = (A-Mean + B-Mean + C-Mean) +- (Square Root(A- Var + B- Var + C- Var))
Expected Value of risk
Expected Value = Impact1*P1 + Impact2*P2 + Impact3*P3 ...
Positive Impact or expected values are gains and negative are losses.
Decision Tree.
Expected Value of Decision = P1 * P2 * P3.. * Benefit of Decision
Standard/Normal/Gaussian distribution
+_(1 Sigma) = 68.26==68.3
+_(2 Sigma) = 95.46==95.5
+_(3 Sigma) = 99.73==99.7
+_(6 Sigma) = ???
Precedence Diagram: Activity on Node
Forward Pass: Find early start and finish based on Project Start date.
Early Finish = Early Start + Duration
Early Start = Max or Last of all (previous early finishes)
(Reason: That is earliest time you can start activity after all previous activities it is dependent on are over)
Backward Pass: Find Late start and finish based on Project End date.
Late Start = Late Finish - Duration
Late Finish = Min of all (Late Starts of previous activities in backward pass)
(Reason: That is latest time you can finish activity without affecting latest start of all further activities)
Float = Late Finish - Early Finish
Float = Late Start - Early Start
(Meaning: Duration by an activity can be delayed without affecting end date of project)
Free Float = Early Start (j) - Early Finish (i)
= Early Start of activity - Early Finish of previous activity
(Meaning: Duration by an activity can be delayed without affecting early start of subsequent activity)
Weighted value = (Optimistic + 4 X Most likely + Pessimistic)/4
Arrow Diagram Method: Activity on arrow
Forward Pass: Earliest Time of event
Backward Pass: Latest Time of event
Float = Latest Time of event - Earliest Time of event
Cost Management
Earned value analysis
Schedule Variance = EV- PV
SPI = EV/PV
Cost Variance = EV- AC
CPI = EV/AC
Negative variance is slippage. Positive is we are doing better than planned.
Performance Index <1 is slippage. More than 1 means we are doing better than planned.
EAC: Estimate At Completion
ETC: Estimate To complete. Expenditure from this point onwards to complete project.
EAC = BAC/CPI = AC + (BAC-EV)/CPI
Typical problems. Likely to continue. Assume the
project execution is same after the present point with respect to the till date execution
EAC = AC + (BAC-EV) Atypical problems. Now onward things will be as planned earlier
EAC = AC + ETC
Basis of estimation was not correct. Fresh re-estimation of remaining work.
Duration to complete Project = Planned Duration/SPI
Depreciation:
Cost of machine 1200. Life 4 Years, Scrap Value 200.
Depreciable cost = Cost of asset - Salvage value = 1200-200=1000
Linear
Depreciation Each year = (Cost - residual value)/Life = (1200-200)/4 = 250
Accelerated :
Sum of remaining life = 4 + 3 + 2 + 1= 10
First Year= 1000*4/10= 400
Second Year: 1000 * 3/10= 300
Third Year = 1000* 2/10= 200
Fourth Year = 1000*1/10.= 100
Double Declining Balance
12.5% of 1000 = 125
25% of 1000-1000X12.5% = 25 % of 875
50% of remaining
100 % of remaining
Value is incoming so it is better to be positive and more.
Cost is expenditure and should be minimum.
Capitalized cost = Initial cost + Annual cost/Rate
Capitalized Value = Annual return/Rate
eg. Rate of capital is 10%
Initial cost is 1000 and annual cost is 10, Annual return is 150.
Capitalized cost = 1000 + 10/0.1 = 1100.
Capitalized Value = 150/0.1 = 1500
Project Selection method
Present Value, Net resent Value
IRR
Payback period
Benifit Cost Ratio
Pay Back period: Simplistic.
Pay Back period = Net Investment / Average Annual Cash flow.
Investment 1500
Cash Flow Year1 : 800
Cash Flow Year2 : 650
Cash Flow Year3 : 750
Pay Back Period = 1500 /(800 + 650 + 750) = 2.1 Years
ROI = Average Annual Profit/Investment
Investment 1000, Annual yield is 100. then ROI = 100/1000 = 10%
Interest = Principal X Rate X Time = P * R *T
Future Value of Money = Present Value X (1 + n(rate))
Compound Interest
Future Value = Present Value X ( 1 + rate)n
Net Present Value (NPV) = Sum of original Investment + Current Value of future cash flow.
Internal Rate of return = when Present value of cash flow equals initial investment
IRR is discount rate when NPV =0.
IRR The rate (of interest) when project revenues and project costs are equal.
Higher IRR is preferred.
Risk Management
Simple Probability
Probability: Chance of selecting one card of pack 1/52
Chance of alternative outcome = 1- outcome.
e.g probability of Diamond card is 1/4 probability on non diamond card is 1-1/4 = 3/4
Chance of two event occurring P1 and P2 is P1*P2.
Chance of occurring either P1 or P2is P1 + P2
Statistics
Mean: Sum(values)/N
Mode: Most likely event, Max( Values)
Median (50% vales are higher 50% values are Lower). If values are arranged in ascending order the center
value is median.
Variance and Standard deviation is spread around central value.
variance = (Standard Deviation)2 = (Sigma)2 for Gaussian distribution
For three point estimate
mean value = (Optimistic + 4 X Most likely + Pessimistic)/4
Std Dev = (Pessimistic - Optimistic)/6
Variance = (Standard Deviation)2
To find project mean and deviation
Add mean value of critical path. Add Variances. Find square root of this variance as deviation of critical
path. You cannot add deviations directly.
e.g. if A,B,C for critical path
Task
Opti.
Most like.
A
O
M
B
C
Pess.
P
Pert (Mean)
(O + 4M + P)/4
Std Dev
(P - O)/6
Variance
((P - O)/6)2
Completion duration = (A-Mean + B-Mean + C-Mean) +- (Square Root(A- Var + B- Var + C- Var))
Expected Value of risk
Expected Value = Impact1*P1 + Impact2*P2 + Impact3*P3 ...
Positive Impact or expected values are gains and negative are losses.
Decision Tree.
Expected Value of Decision = P1 * P2 * P3.. * Benefit of Decision
Standard/Normal/Gaussian distribution
+_(1 Sigma) = 68.26==68.3
+_(2 Sigma) = 95.46==95.5
+_(3 Sigma) = 99.73==99.7
+_(6 Sigma) = ???
