The Formulas Wall
Earned Value — Variances & Indices
SV = EV − PV
+ ahead · − behind
CV = EV − AC
+ under · − over
SPI = EV ÷ PV
>1 ahead
CPI = EV ÷ AC
>1 under budget
CV% = CV ÷ EV
SV% = SV ÷ PV
Earned Value — Forecasting
EAC = BAC ÷ CPI
current trend (default)
EAC = AC + (BAC − EV)
variance was one-off
EAC = AC + (BAC−EV) ÷ (CPI×SPI)
cost & schedule
EAC = AC + bottom-up ETC
re-estimate
ETC = EAC − AC
VAC = BAC − EAC
TCPI = (BAC−EV) ÷ (BAC−AC)
to hit BAC
TCPI = (BAC−EV) ÷ (EAC−AC)
to hit EAC
Estimating
PERT (Eₑ) = (O + 4M + P) ÷ 6
beta / weighted
σ = (P − O) ÷ 6
std deviation
Variance = ((P − O) ÷ 6)²
Triangular = (O + M + P) ÷ 3
Ranges: ±1σ ≈ 68% · ±2σ ≈ 95% · ±3σ ≈ 99.7% of outcomes.
Schedule / Critical-Path Network
Total Float = LS − ES = LF − EF
Free Float = ESₙₑₓₜ − EF − 1
Forward: EF = ES + Dur − 1
Backward: LS = LF − Dur + 1
Critical path = longest path = zero total float. (Drop the −1 / +1 if you count from day 0.)
Communication & Risk
Channels = n(n − 1) ÷ 2
EMV = Σ (Probability × Impact)
− threat · + opportunity
Finance (decision)
- NPV — higher is better; already discounted.
- IRR — higher is better.
- ROI = (gain − cost) ÷ cost; higher better.
- Payback — shorter is better.
- BCR = benefits ÷ costs; > 1 good.
Contract (bonus)
PTA = ((Ceiling − Target Price) ÷ buyer share) + Target Cost
Point of total assumption — above it, the seller bears all extra cost (incentive contracts).
Sign-Reading & Golden Rules
- EV first in every EVM formula.
- Variance = subtract; index = divide.
- Positive variance & index > 1 = good.
- Cost ↔ AC; Schedule ↔ PV.
- EV = % complete × BAC.
- ETC = EAC − AC; VAC = BAC − EAC.
- TCPI > CPI ⇒ recovery is hard.
- Float 0 ⇒ on the critical path.
Most-Tested
- CPI / SPI interpretation & EAC = BAC/CPI.
- PERT (O+4M+P)/6 and σ = (P−O)/6.
- Channels n(n−1)/2.
- Total float = LS − ES.
- EMV for decision trees.