Project performance at a glance

01.1 — Earned value core & forecasting

CV · SV · CPI · SPI · EAC · ETC · VAC · TCPI

Enter the four base measures below and every earned-value metric updates live. The performance metrics describe project health today; the forecasting metrics project that health forward to completion. All monetary figures share whatever currency you enter.

Full analysis

CV  = EV − AC        SV  = EV − PV
CPI = EV ÷ AC        SPI = EV ÷ PV
EAC = BAC ÷ CPI      ETC = EAC − AC
VAC = BAC − EAC
TCPI = (BAC − EV) ÷ (BAC − AC)

Parameters

BAC — Budget at Completion

The total approved budget for all project work. The baseline everything else is measured against.

e.g. 100000

PV — Planned Value

The budgeted cost of the work that was scheduled to be done by now (also called BCWS).

e.g. 50000

EV — Earned Value

The budgeted cost of the work actually completed so far: % complete × BAC (also called BCWP).

e.g. 45000

AC — Actual Cost

What the completed work really cost, regardless of what was budgeted (also called ACWP).

e.g. 60000

EAC — management forecast (optional)

A forecast you have committed to, if it differs from BAC ÷ CPI. Only TCPI — to hit EAC uses it; leave blank to read that line against the calculated EAC.

e.g. 125000

Results

Performance today

Cost Variance (CV)

Budget health in currency: value earned minus money spent.

Schedule Variance (SV)

Schedule health expressed in currency: work done minus work planned.

Cost Performance Index (CPI)

Cost efficiency: value earned per unit of money spent.

Schedule Performance Index (SPI)

Schedule efficiency: rate of progress versus the plan.

Cost–Schedule Index (CSI)

CPI × SPI — a single overall-health number; hard to recover once it drops far below 1.

% Complete

Share of the total scope actually finished: EV ÷ BAC.

% Spent

Share of the total budget already consumed: AC ÷ BAC.

Forecasting completion

EAC — typical variance

BAC ÷ CPI. Forecast final cost assuming today’s cost efficiency continues — the default assumption.

EAC — atypical variance

AC + (BAC − EV). Use when the variance was a one-off and the remaining work will go to plan.

EAC — cost & schedule

AC + (BAC − EV) ÷ (CPI × SPI). Use when schedule pressure is also driving cost (e.g. a hard deadline).

ETC — Estimate to Complete

EAC − AC (using the typical-variance EAC). Money still needed to finish the remaining work.

VAC — Variance at Completion

BAC − EAC (using the typical-variance EAC, BAC ÷ CPI). The over- or under-run expected on the day the project finishes.

TCPI — to hit BAC

(BAC − EV) ÷ (BAC − AC). The cost efficiency you must sustain on all remaining work to still land on the original budget.

TCPI — to hit EAC

(BAC − EV) ÷ (EAC − AC). The efficiency needed to hit a revised forecast instead of the original budget. Against the calculated EAC of BAC ÷ CPI this reduces to CPI itself, so it only becomes an independent test once you enter a management forecast above.

Charts

Cost position

What was planned, what was earned, what it cost — against the budget line.

CPI–SPI quadrant

Cost efficiency against schedule efficiency, crossed at 1.00.

TCPI required efficiency

The cost performance the remaining work must sustain to still hit BAC.

01.2 — Earned Schedule

ES · SV(t) · SPI(t) · IEAC(t)

SPI can look healthy late in a project because PV is running out. Earned Schedule puts EV back on the time axis. This card assumes LINEAR PV — the useful, explicit approximation for a four-input reading. Treat IEAC(t) as a trend, not a committed finish date.

Full analysis

ES = PD × (EV ÷ BAC)
SV(t) = ES − AT
SPI(t) = ES ÷ AT
IEAC(t) = PD ÷ SPI(t)

Parameters

BAC — Budget at Completion

Total approved budget for the complete scope. Currency; must be greater than 0.

e.g. 200000

PD — Planned duration

Baseline duration from start to planned finish. Periods; use a positive value.

e.g. 12

AT — Actual time

Time elapsed at the status date. Periods; must be greater than 0 for SPI(t).

e.g. 8

EV — Earned Value

Budgeted value of the work actually complete. Same currency as BAC; zero is valid.

e.g. 120000

Results

Earned time

Earned Schedule (ES)

The baseline time equivalent of the EV entered.

Schedule Variance (SV(t))

The time difference at the status date. Negative means late.

Schedule Performance Index (SPI(t))

Time efficiency, with 1.00 as the plan line.

Forecasting completion

Independent Estimate at Completion (IEAC(t))

A duration forecast under the same efficiency and linear-PV assumption; it is not a promise and it is not a calendar finish date.

How to use it

1. Enter BAC and PD from the approved baseline, then enter EV and AT from the same status date.
2. Read SV(t) for the time gap and SPI(t) for the direction and efficiency of travel. Check that the linear-PV assumption is reasonable for this project.
3. Use IEAC(t) as a trend to test recovery options; reconcile it to the time-phased schedule before committing to a finish date.

Charts

Earned time position

The time the completed work earned against actual time and plan.

SPI(t) time efficiency

Earned schedule per period of actual time, crossed at 1.00.

01.3 — Time forecasting (SPI-based)

Planned duration ÷ SPI

Cost gets EAC; schedule gets this. Dividing the planned duration by the schedule performance index projects when the project will actually finish if the current pace continues. It is an approximation — SPI drifts back toward 1.0 late in a project as planned value tops out, so trust it early and mid-project and re-check often.

Forecast duration = Planned duration ÷ SPI
SPI = EV ÷ PV

Parameters

Planned duration

The baseline total duration, in any time unit — the forecast comes back in the same unit.

e.g. 12

EV — Earned Value

Budgeted cost of the work actually completed to date.

e.g. 45000

PV — Planned Value

Budgeted cost of the work scheduled to be done by now.

e.g. 50000

Results

SPI

Pace versus plan — the engine of the forecast.

Forecast duration

Expected total duration if the current pace holds.

Projected slip

Forecast minus plan — the schedule overrun taking shape.

Charts

Planned vs forecast duration

Where the project lands if today’s pace holds — not a certainty, a trend.

02.1 — Burn rate & runway

Spend pace · runway · budget used

Divide what you have spent by how long you have been spending it and you get the burn rate — the project’s cash velocity. Runway converts the remaining budget into time at that pace. Use any period unit (months, sprints); the runway comes back in the same unit.

Burn rate = Spent ÷ Periods elapsed
Runway = (Budget − Spent) ÷ Burn rate

Parameters

Total budget

Approved funds for the whole project.

e.g. 120000

Spent to date

Actual cost so far — same as AC in earned value.

e.g. 45000

Periods elapsed

How many months / sprints of spending produced that cost.

e.g. 3

Planned periods remaining (optional)

How much longer the plan says the work will take — to test whether the money outlives the work.

e.g. 6

Results

Burn rate

Average spend per period — the pace at which the budget is being consumed.

Budget remaining

Funds left before the budget is exhausted.

Runway (periods)

How many more periods the remaining budget lasts at the current burn rate.

% of budget used

Share of total funds already consumed.

Charts

Runway vs plan

Whether the remaining money outlasts the remaining work.

03.1 — Three-point estimate (PERT)

Triangular · Beta · σ · confidence ranges

Instead of a single guess, you estimate three scenarios and blend them. The PERT (beta) formula weights the most-likely case 4× because real outcomes cluster around it; the standard deviation then converts your optimism–pessimism spread into confidence ranges you can commit to. Works for durations and for costs alike. The 68 / 95 / 99.7% figures below are properties of the normal curve, while a single activity follows a skewed beta — read them as a good working approximation for one activity, and as genuinely accurate for the sum of several, which is where the roll-up below sends them.

Full analysis

Triangular = (O + M + P) ÷ 3
PERT (beta) = (O + 4M + P) ÷ 6
σ = (P − O) ÷ 6        Variance = σ²

Parameters

O — Optimistic

Best-case estimate: everything goes right. Roughly the 1-in-100 lucky outcome.

e.g. 4

M — Most Likely

The realistic estimate you would give under normal conditions.

e.g. 6

P — Pessimistic

Worst-case estimate: known risks materialise. Roughly the 1-in-100 unlucky outcome.

e.g. 12

Results

Triangular average

Simple mean of the three points — use when you have no reason to trust M more.

PERT (beta) estimate

Weighted mean, 4× on Most Likely — the standard exam and planning answer.

Standard deviation (σ)

How spread out the outcome could be. A wide O–P gap means low confidence.

Variance (σ²)

σ squared. Variances (not σ) are what you add up along a path to get path-level uncertainty.

68% confidence (±1σ)

Roughly two times in three, the real result lands inside this range.

95% confidence (±2σ)

The range usually quoted when someone asks for a commitment.

99.7% confidence (±3σ)

Near-certainty bounds — use for hard external deadlines.

Charts

Three-point distribution

The shape of the estimate, the PERT expected value, and the 68% band around it.

03.2 — Path uncertainty roll-up

σ(path) = √(Σ σ²)

Uncertainties don’t add — variances do. To get the uncertainty of a whole path (or project), square each activity’s σ, add them, and take the square root. The roll-up is always smaller than the simple sum of σ’s, which is why padding every task individually is wrong: the math already diversifies the risk. That diversification assumes the activities are INDEPENDENT. Correlated risks — one team, one supplier, one weather window — break the assumption, and the true path σ is then larger than this. It also covers a single path, not the merge bias where parallel paths converge.

σ(path) = √(σ₁² + σ₂² + … + σₙ²)

Parameters

Activity σ values (comma-separated)

The standard deviation of each activity on the path, from the three-point calculator above.

e.g. 1.33, 0.5, 2

Results

Path σ

The combined uncertainty of the whole chain — use it for path-level confidence ranges.

Naive sum of σ’s

What you would get by simply adding the uncertainties — shown for contrast.

Charts

Roll-up vs naive sum

Why adding standard deviations overstates a path’s real uncertainty.

03.3 — Learning curve

T(n) = T₁ × n^(log rate ÷ log 2)

Every doubling of repetitions cuts the per-unit time by a fixed percentage: on an 80% curve, unit 2 takes 80% of unit 1’s time, unit 4 takes 80% of unit 2’s, and so on. Use it to estimate repetitive work — floors of a building, server migrations, test cycles — instead of multiplying the first unit’s time by the count. This is the unit (Crawford) model.

Time for unit n = T₁ × n^(log(rate ÷ 100) ÷ log 2)
rate is the learning rate as entered, in percent: 80 means 0.8

Parameters

T₁ — first unit time (or cost)

How long the first repetition took — the anchor of the curve.

e.g. 100

Learning rate (%)

Per-doubling retention: 80 means each doubling takes 80% of the previous. Typical: 70–90%; 100 = no learning.

e.g. 80

Unit number (n)

Which repetition you want the estimate for.

e.g. 4

Results

Time for unit n

Predicted effort for that repetition.

Improvement vs unit 1

How much faster unit n is than the first attempt.

Charts

Learning curve

Per-unit time against a flat no-learning baseline, with the selected unit marked.

04.1 — Float (slack)

Total float · free float · critical path test

Total float is how long an activity can slip without delaying the project finish. Free float is how long it can slip without delaying its immediate successor. Zero total float means the activity is on the critical path. Enter the dates from your forward/backward pass — either day numbers or durations, as long as they are consistent (this calculator uses the continuous convention where EF = ES + duration).

Full analysis

Total Float = LS − ES = LF − EF
Free Float = ES(successor) − EF

Parameters

ES — Early Start

The soonest the activity can start, from the forward pass.

e.g. 5

EF — Early Finish

The soonest it can finish: ES + duration.

e.g. 9

LS — Late Start

The latest it can start without delaying the project, from the backward pass.

e.g. 8

LF — Late Finish

The latest it can finish without delaying the project.

e.g. 12

Successor ES (optional)

Early start of the next activity — only needed for free float.

e.g. 11

Results

Total float

Slip allowance before the project end date moves: LS − ES.

Cross-check (LF − EF)

Should equal LS − ES; a mismatch means a pass was computed inconsistently.

Free float

Slip allowance before the next activity is disturbed: successor ES − EF.

Charts

Early vs late window

How much room the activity has before it becomes critical.

05.1 — Crash cost slope

(Crash cost − Normal cost) ÷ time saved

Most activities can be sped up — more people, overtime, premium suppliers — but only so far and at a price. The cost slope is the price of each time unit saved. To compress rationally: crash only critical-path activities, cheapest slope first, and stop when the slope costs more than the deadline is worth. Run this once per candidate activity and compare.

Cost slope = (Crash cost − Normal cost) ÷ (Normal duration − Crash duration)

Parameters

Normal cost

Cost of the activity at its normal, efficient pace.

e.g. 10000

Crash cost

Cost at the fastest possible pace — overtime, extra staff, expediting fees included.

e.g. 16000

Normal duration

Duration at the normal pace (any time unit).

e.g. 10

Crash duration

The shortest duration physically achievable — beyond it, money buys nothing.

e.g. 8

Results

Cost slope

Extra cost per time unit saved on this activity.

Maximum time saved

The most this activity can be shortened: normal minus crash duration.

Full crash premium

Total extra cost of buying all the available time.

Charts

Normal vs crash

The cost slope drawn as a line — its gradient is the price of each time unit saved.

06.1 — Full-time equivalents (FTE)

Effort ÷ capacity

FTE converts a pile of estimated effort into how many full-time people the work actually needs within a given window. One FTE is one person fully allocated. Use productive hours per period, not contract hours — meetings, support and admin eat 15–30% before project work starts.

FTE = Effort hours ÷ (Productive hours per period × Periods)

Parameters

Total effort (hours)

Estimated person-hours of work to deliver in the window.

e.g. 2080

Productive hours / person / period

Hours one person can really spend on this work each period — e.g. 130 of a 160-hour month after overhead.

e.g. 130

Periods in the window

How many periods (months, sprints) the work is spread across.

e.g. 4

Results

FTE required

Full-time people the work demands over the window.

Headcount (rounded up)

Whole people to staff if nobody can split across projects cleanly.

06.2 — Utilization

Allocated ÷ available

The share of a person’s available time already committed. Sustained utilization near 100% removes all slack: queues form, small surprises cascade, and cycle times explode (the queueing math behind this lives in Lean & Flow). Plan people like you plan servers — with headroom.

Utilization % = Allocated hours ÷ Available hours × 100

Parameters

Allocated hours

Hours of committed work in the period across all assignments.

e.g. 150

Available hours

Hours the person actually has in the period.

e.g. 160

Results

Utilization

Commitment level for the period.

Uncommitted hours

Hours left for the work nobody predicted.

Charts

Commitment level

Where utilization sits against the point delays start to amplify.

06.3 — Loaded labor cost

Rate × (1 + overhead)

A person’s cost to the project is never just their pay rate. The loaded (burdened) rate adds employer overhead — benefits, payroll taxes, equipment, facilities, licences — typically 25–50% on top. Budgets built on bare rates systematically understate cost and get discovered at the worst possible time.

Loaded cost = Hours × Rate × (1 + Overhead %)

Parameters

Effort (hours)

Person-hours of work being costed.

e.g. 400

Base rate (per hour)

The bare pay or contract rate before burden.

e.g. 60

Overhead / burden (%)

Employer add-ons as a percentage of the base rate — ask finance; 25–50% is typical for employees.

e.g. 35

Results

Base cost

Hours × bare rate — the number that looks deceptively affordable.

Loaded cost

The true cost to the organisation, burden included.

Loaded hourly rate

The per-hour figure to use in every estimate.

07.1 — Communication channels

n(n−1) ÷ 2

Every pair of people on a project is a potential communication path that can carry — or garble — information. This count is used to justify communication plans, meeting structures and why large stakeholder groups need formal channels. Count everyone who communicates about the project, including yourself and the sponsor.

Channels = n × (n − 1) ÷ 2

Parameters

n — People now

Current number of people communicating on the project (team + stakeholders + you).

e.g. 10

People after change (optional)

Headcount after adding or removing members — to see how many channels the change creates.

e.g. 15

Results

Channels now

One-to-one paths that currently exist.

Channels after change

Paths at the new headcount.

Channels added

New paths the headcount change creates — the hidden coordination cost.

Charts

Channel growth

Why one more person on a large team costs more coordination than on a small one.

08.1 — Expected Monetary Value (EMV)

Probability × impact

EMV is the probability-weighted value of an uncertain event — what the risk is “worth” on average if you could run the project many times. Enter threats with a negative impact and opportunities with a positive one. Summing the EMV of every identified risk gives the contingency reserve; EMV is also the math behind decision-tree analysis.

Full analysis

EMV = Probability × Impact

Parameters

Probability (%)

Likelihood the risk event actually occurs, from qualitative analysis or data. 0–100.

e.g. 30

Impact

Full monetary consequence if it occurs. Negative for threats (costs), positive for opportunities (gains).

e.g. -50000

Results

Expected Monetary Value

The amount to carry in the contingency reserve for this single risk.

Impact if it happens

Reminder: EMV is an average — if the event fires you feel the full impact, not the EMV.

Charts

EMV against full exposure

The average outcome versus what actually happens if the event fires.

08.2 — Qualitative risk score

Probability × impact, on a 1–5 scale

Before risks are worth quantifying in money, they are ranked qualitatively: rate probability and impact on an agreed 1–5 scale and multiply. The product places each risk in the probability–impact matrix and decides how much attention it gets. The scales are ordinal — a 4 is not “twice” a 2 — so use the score to rank, not to budget.

Full analysis

Risk score = Probability (1–5) × Impact (1–5)

Parameters

Probability rating (1–5)

1 = rare, 3 = possible, 5 = almost certain — per your organisation’s definitions.

e.g. 4

Impact rating (1–5)

1 = negligible, 3 = moderate, 5 = severe effect on objectives.

e.g. 3

Results

Risk score

Position in the 25-cell probability–impact matrix.

Charts

Probability–impact matrix

Where this risk sits in the standard 5×5 grid.

08.3 — Contingency reserve roll-up

Σ EMV across the risk register

Sum the expected monetary value of every identified risk and you get the contingency reserve — the funded buffer for known-unknowns, owned by the project manager. Enter matching lists: one probability and one impact per risk, threats negative, opportunities positive. (Unknown-unknowns are covered separately by management reserve, which sits outside the baseline.)

Contingency reserve = − Σ (Probabilityᵢ × Impactᵢ)

Parameters

Probabilities % (comma-separated)

Likelihood of each risk, in register order — e.g. 30, 10, 50.

e.g. 30, 10, 50

Impacts (same order)

Monetary consequence of each risk: threats negative, opportunities positive.

e.g. -50000, -20000, 10000

Results

Net EMV of the register

Probability-weighted sum of all risks — usually negative when threats dominate.

Suggested contingency reserve

The buffer to add to the cost baseline (zero if net EMV is positive).

Charts

Register contribution

Which risks drive the reserve — each risk’s own EMV, side by side.

09.1 — Decision tree — compare two options

EMV = −cost + p·payoff(success) + (1−p)·payoff(failure)

Each option is a branch: pay its cost, then chance decides between a success payoff and a failure payoff. The branch with the higher expected monetary value wins — on average. Classic uses: build vs buy, prototype vs commit, upgrade vs replace. Remember EMV is a long-run average; for one-shot, bet-the-company decisions, weigh the worst case too.

Full analysis

EMV(option) = − Cost
             + P(success) × Payoff(success)
             + (1 − P) × Payoff(failure)

Parameters

Option A — cost

Upfront cost of choosing branch A.

e.g. 40000

Option A — P(success) %

Probability branch A succeeds.

e.g. 60

Option A — payoff if success

Value delivered when A succeeds.

e.g. 100000

Option A — payoff if failure

Value (often 0, sometimes negative) when A fails.

e.g. 0

Option B — cost

Upfront cost of choosing branch B.

e.g. 10000

Option B — P(success) %

Probability branch B succeeds.

e.g. 30

Option B — payoff if success

Value delivered when B succeeds.

e.g. 60000

Option B — payoff if failure

Value when B fails.

e.g. 0

Results

EMV — Option A

Expected value of branch A after its cost.

EMV — Option B

Expected value of branch B after its cost.

Better option

The branch with the higher expected value, and by how much.

Charts

Expected value comparison

Which branch wins on average, and how wide a bet each one is.

10.1 — DPMO & sigma level

Defects per million opportunities

DPMO normalizes defect counts by how many chances there were to fail, so processes of different complexity can be compared fairly. The sigma level restates DPMO on the Six Sigma scale (with the conventional 1.5σ shift): 3σ ≈ 66,800 defects per million, 4σ ≈ 6,210, 6σ ≈ 3.4.

DPMO = Defects × 1,000,000 ÷ (Units × Opportunities per unit)
Sigma level ≈ 0.8406 + √(29.37 − 2.221 × ln DPMO)

Parameters

Defects found

Total defects observed in the sample.

e.g. 25

Units inspected

How many items, transactions or deliverables were checked.

e.g. 1000

Opportunities per unit

Distinct ways each unit could be defective — fields on a form, joints on an assembly.

e.g. 4

Results

DPMO

Defects expected per million opportunities at this rate.

Process yield

Share of opportunities that pass defect-free.

Sigma level

The process capability on the Six Sigma scale, 1.5σ shift included.

Charts

Sigma level

Process performance on the Six Sigma scale.

10.2 — Control limits (±3σ)

UCL · LCL · warning zone

A control chart flags when a process leaves its normal noise band. The limits sit three standard deviations either side of the historical mean: a point outside them — or seven consecutive points on one side of the mean (the rule of seven) — signals the process is out of control and needs investigation, not tampering.

UCL = Mean + 3σ        LCL = Mean − 3σ

Parameters

Process mean

The long-run average of the measurement, from historical data.

e.g. 50

Process σ

Standard deviation of the measurement under normal conditions.

e.g. 2

Results

Upper control limit

Mean + 3σ — the ceiling of normal variation.

Lower control limit

Mean − 3σ — the floor of normal variation.

Warning zone (±2σ)

Inner band where points are legal but worth watching.

Charts

Control band

The mean, the ±2σ warning zone, and the ±3σ control limits on one axis.

10.3 — Process capability (Cp / Cpk)

Can the process meet the spec?

Control limits describe what the process does; specification limits describe what the customer needs. Capability indices compare the two. Cp asks whether the spec window is wide enough for the process spread (ignoring centering); Cpk penalises a process that drifts off-centre. The common acceptance bar is Cpk ≥ 1.33.

Full analysis

Cp  = (USL − LSL) ÷ 6σ
Cpk = min(USL − Mean, Mean − LSL) ÷ 3σ

Parameters

USL — upper spec limit

The highest value the customer or requirement accepts.

e.g. 10

LSL — lower spec limit

The lowest acceptable value.

e.g. 4

Process mean

Where the process actually centres, from measurement data.

e.g. 6

Process σ

Standard deviation of the process output.

e.g. 0.5

Results

Cp — potential capability

Spec width versus process spread, assuming perfect centering.

Cpk — actual capability

Capability including how far off-centre the process runs.

Charts

Spec window vs process spread

Whether the ±3σ process spread fits inside the customer’s spec limits, and how centred it is.

10.4 — Cost of Quality (CoQ)

Conformance vs failure spend

Everything quality costs, split into money spent on purpose and money lost to failure. Conformance costs are investments: prevention (training, standards, design reviews) and appraisal (testing, inspections, audits). Non-conformance costs are the bill for defects: internal failures (rework, scrap) and external ones (warranty, support, reputation). Mature organisations deliberately shift spend from the failure side to the prevention side.

Conformance = Prevention + Appraisal
Non-conformance = Internal failures + External failures
CoQ = Conformance + Non-conformance

Parameters

Prevention costs

Spent stopping defects from happening: training, standards, quality planning.

e.g. 20000

Appraisal costs

Spent finding defects early: testing, inspection, audits.

e.g. 30000

Internal failure costs

Defects caught before the customer: rework, scrap, retesting.

e.g. 40000

External failure costs

Defects that reached the customer: warranty, incident response, lost business.

e.g. 25000

Results

Cost of conformance

The deliberate investment in quality.

Cost of non-conformance

The price of failure, internal and external.

Total cost of quality

Everything quality costs, both sides combined.

Failure share of CoQ

What portion of quality spend is failure rather than investment.

Charts

Conformance vs failure spend

Where quality money goes — investment against the cost of failure.

11.1 — Return on Investment (ROI)

(Benefit − Cost) ÷ Cost

The simplest project-selection measure: how much you get back per unit invested, ignoring timing. Good for quick comparisons; misleading for long projects because it ignores when the money arrives — use NPV for that.

Full analysis

ROI % = (Benefit − Cost) ÷ Cost × 100

Parameters

Total cost

Everything invested in the project: build, licences, labour, run costs over the horizon you are measuring.

e.g. 200000

Total benefit

Total value returned over the same horizon: revenue, savings, avoided costs.

e.g. 260000

Results

ROI

Percentage return over the whole horizon (not per year).

Net benefit

Absolute value created: benefit minus cost.

11.2 — NPV · IRR · Payback

Discounted cash-flow appraisal

The rigorous way to value a project: every future cash flow is discounted back to today because money later is worth less than money now. NPV is the value created in today’s money; IRR is the discount rate at which the project merely breaks even; payback tells you how long capital is at risk. When choosing between projects, pick the higher NPV.

Full analysis

NPV = −Investment + Σ  CFₜ ÷ (1 + r)ᵗ
IRR: the r where NPV = 0
Payback: periods until cumulative cash flow ≥ 0

Parameters

Discount rate (%)

Cost of capital or required return per period — the hurdle the project must beat.

e.g. 10

Initial investment

Cash out at period 0, entered as a positive number.

e.g. 1000

Cash flows (comma-separated)

Net cash in (or out, negative) for each following period, in order: period 1, 2, 3…

e.g. 500, 500, 500

Results

Net Present Value

Value created in today’s money after paying back capital and the required return.

Internal Rate of Return

The project’s intrinsic return per period. Compare it to the discount rate. Reliable only for conventional flows — one outlay followed by inflows. If the signs change more than once, IRR can have several answers or none, and NPV is the measure to trust.

Benefit–Cost Ratio

Present value of the future net cash flows per unit invested — net, so a negative period nets off rather than counting as a benefit. Above 1 means benefits outweigh costs.

Payback period

Periods until the undiscounted cash recovers the investment — a measure of capital risk, not profitability.

Charts

Cumulative cash flow

Discounted against undiscounted — where the project actually breaks even.

11.3 — Present & Future Value

FV = PV(1 + r)ⁿ

The time-value-of-money primitive behind NPV. Future value answers “what will this be worth after n periods of compounding?”; present value answers the reverse: “what is a promised future amount worth today?”. Both outputs are computed from the single amount you enter.

FV = Amount × (1 + r)ⁿ
PV = Amount ÷ (1 + r)ⁿ

Parameters

Amount

The sum of money to move through time.

e.g. 10000

Rate per period (%)

Interest or discount rate for each compounding period.

e.g. 8

Periods (n)

Number of compounding periods — years if the rate is annual.

e.g. 5

Results

Future value

What the amount grows to if invested today at the given rate.

Present value

What a payment of that amount, received n periods from now, is worth today.

Doubling time (Rule of 72)

72 ÷ rate: the mental-math shortcut for how many periods money takes to double.

11.4 — Break-even point

Fixed costs ÷ contribution margin

How many units (or billable hours, or subscriptions) you must sell before the venture stops losing money. The denominator — price minus variable cost — is the contribution margin: what each unit contributes toward covering fixed costs.

Break-even units = Fixed costs ÷ (Price − Variable cost per unit)

Parameters

Fixed costs

Costs that exist regardless of volume: rent, salaries, licences, the project build itself.

e.g. 50000

Price per unit

Revenue received for each unit sold.

e.g. 25

Variable cost per unit

Cost incurred for each additional unit: materials, transaction fees, support.

e.g. 15

Results

Break-even units

Volume at which total revenue equals total cost.

Break-even revenue

The revenue level at that volume.

Contribution margin / unit

Price − variable cost: what each sale contributes to fixed costs.

Charts

Revenue vs cost

Where the revenue line crosses total cost.

11.5 — Straight-line depreciation

(Cost − Salvage) ÷ Useful life

Spreads an asset’s cost evenly across its useful life — the depreciation method assumed in PMP exam questions and the simplest for business cases that must account for capital assets.

Annual depreciation = (Cost − Salvage value) ÷ Useful life

Parameters

Purchase cost

What the asset costs to acquire and put into service.

e.g. 120000

Salvage value

Expected resale or scrap value at the end of its useful life.

e.g. 20000

Useful life (years)

How many years the asset will be productive.

e.g. 5

Results

Depreciation per year

The expense recognised each year of the asset’s life.

Depreciation rate

Share of the depreciable base expensed each year: 1 ÷ life.

11.6 — Weighted scoring model

Σ (weight × score)

The standard way to compare options against several criteria at once: weight each criterion by importance, score the option against each, and sum weight × score. Run it once per option and compare the totals. Its real value is political — the weights force stakeholders to argue about priorities before the decision, not after it.

Weighted score = Σ (weightᵢ × scoreᵢ) ÷ Σ weightᵢ

Parameters

Criteria weights (comma-separated)

Importance of each criterion, any scale — e.g. strategic fit 5, cost 3, risk 2.

e.g. 5, 3, 2

Option scores (same order)

How this option rates on each criterion, on your scoring scale (say 1–10), in the same order as the weights.

e.g. 8, 6, 9

Results

Weighted score

The option’s weighted average on your scoring scale — directly comparable across options.

Raw weighted total

The unnormalized Σ weight × score, as many textbooks present it.

Charts

Weighted contribution

Each criterion’s share of the total score — the weights, made visible.

12.1 — Point of Total Assumption (PTA)

Where the seller starts paying for overruns

In a Fixed-Price-Incentive-Fee contract, cost overruns are shared according to the buyer/seller ratio only up to the ceiling price. The PTA is the actual-cost level at which the buyer’s share of the overrun has consumed the room up to the ceiling; beyond it, every additional dollar of cost comes out of the seller’s fee. Sellers manage hard to stay below it.

PTA = (Ceiling price − Target price) ÷ Buyer share + Target cost

Parameters

Ceiling price

The maximum the buyer will ever pay, regardless of cost.

e.g. 180000

Target price

Target cost + target fee: what both parties expect the buyer to pay.

e.g. 165000

Target cost

The cost both parties negotiated as the expected outcome.

e.g. 150000

Buyer share (%)

Buyer’s portion of the share ratio. An “80/20 split” means the buyer covers 80% of overruns — enter 80.

e.g. 80

Results

Point of Total Assumption

The actual cost at which the seller assumes all further overrun.

Overrun absorbed before PTA

How much the cost can overrun target before the PTA is reached.

Charts

Shared-risk band

Target cost, the point of total assumption, and the ceiling on one cost axis.

12.2 — FPIF final fee & price

Settling an incentive contract

When the work is done, the incentive formula converts the cost outcome into the seller’s final fee: the seller keeps its share of any saving and gives up its share of any overrun. If a ceiling price is set, the buyer never pays more than it.

Final fee = Target fee + (Target cost − Actual cost) × Seller share
If the ceiling binds: Final fee = Ceiling price − Actual cost
Final price = min(Actual cost + Final fee, Ceiling price)

Parameters

Target cost

Negotiated expected cost of the work.

e.g. 150000

Target fee

Profit the seller earns if actual cost exactly equals target cost.

e.g. 15000

Actual cost

What the work really cost the seller.

e.g. 140000

Seller share (%)

Seller’s portion of the ratio. In an 80/20 split, enter 20.

e.g. 20

Ceiling price (optional)

Contract maximum — caps what the buyer pays.

e.g. 180000

Results

Final fee

Seller’s profit after applying the incentive share. Once the ceiling binds, the fee erodes dollar for dollar with the overrun and can go negative.

Final price (buyer pays)

Actual cost plus final fee, capped at the ceiling if one is set.

Charts

Final price vs actual cost

The slope changes at the PTA and flattens at the ceiling — that bend is where seller risk changes.

12.3 — CPIF final fee & price

Cost-plus with a bounded incentive

In a Cost-Plus-Incentive-Fee contract the buyer reimburses all allowable costs, but the seller’s fee moves with performance: it grows when the seller beats the target cost and shrinks on overruns, always clamped between a negotiated minimum and maximum fee. Unlike FPIF there is no ceiling price — cost risk stays mostly with the buyer, which is why CPIF suits work too uncertain to fix-price.

Fee = Target fee + (Target cost − Actual cost) × Seller share
Final fee = clamp(Fee, Min fee, Max fee)
Final price = Actual cost + Final fee

Parameters

Target cost

Negotiated expected cost of the work.

e.g. 100000

Target fee

Fee the seller earns if cost lands exactly on target.

e.g. 10000

Actual cost

What the work really cost — fully reimbursed by the buyer.

e.g. 90000

Seller share (%)

Seller’s portion of the share ratio. In an 80/20 split, enter 20.

e.g. 20

Minimum fee (optional)

Fee floor — the least the seller can earn however badly cost overruns.

e.g. 4000

Maximum fee (optional)

Fee ceiling — the most the seller can earn however well it performs.

e.g. 15000

Results

Final fee

Incentive-adjusted fee, clamped to the min/max band if provided.

Final price (buyer pays)

Reimbursed actual cost plus the final fee — no ceiling in CPIF.

Charts

Seller fee vs actual cost

The fee moves with performance, then clamps flat at the negotiated floor and ceiling.

13.1 — Velocity & release forecast

Backlog ÷ velocity

Velocity is the average number of story points a team completes per sprint, measured from finished sprints only (yesterday’s weather). Dividing the remaining backlog by velocity gives the most honest forecast available: how many sprints of work remain at the current, demonstrated pace.

Full analysis

Velocity = Points completed ÷ Sprints completed
Sprints remaining = ⌈ Remaining backlog ÷ Velocity ⌉

Parameters

Points completed

Total story points fully done (meeting the Definition of Done) across the measured sprints.

e.g. 120

Sprints completed

Number of finished sprints those points came from — use at least 3 for a stable average.

e.g. 4

Remaining backlog (points)

Estimated points left in the release or project scope.

e.g. 200

Sprint length (weeks, optional)

Length of one sprint — converts the forecast into calendar time.

e.g. 2

Results

Velocity

Demonstrated delivery rate in points per sprint.

Sprints remaining

Whole sprints needed to clear the backlog at current velocity.

Calendar time remaining

Sprints remaining × sprint length.

Charts

Backlog burndown forecast

The remaining backlog burning down at the team’s demonstrated velocity.

13.2 — Sprint capacity

People × days × hours × focus

Capacity planning in hours, for sprint-level task commitment. Start from raw availability, then apply a focus factor — the share of the day genuinely available for sprint work after ceremonies, support duty, e-mail and context switching. Teams that skip the focus factor systematically over-commit. Use capacity for task hours; use velocity (above) for story points — they answer different questions.

Capacity = Members × Days × Hours per day × Focus factor

Parameters

Team members

People doing sprint work — count partial allocations as fractions (0.5 for half-time).

e.g. 5

Working days in sprint

Sprint length minus holidays and planned leave.

e.g. 9

Hours per day

Nominal working hours per person per day.

e.g. 8

Focus factor (%)

Share of the day truly available for sprint work — 60–70% is realistic for most teams.

e.g. 65

Results

Raw hours

Theoretical availability before reality intervenes.

Plannable capacity (hours)

What the team can actually commit to after the focus factor.

Charts

Raw vs plannable capacity

The focus factor is the gap — committing to raw hours is how sprints fail.

13.3 — Say/do ratio

Delivered ÷ committed

The simplest measure of forecast reliability: of what the team committed to at sprint planning, how much was actually delivered? Track it over several sprints. A team that consistently delivers what it says — even if it says less — is worth more to planning than a fast team nobody can predict.

Say/do % = Points delivered ÷ Points committed × 100

Parameters

Points committed

Story points the team signed up for at sprint planning.

e.g. 34

Points delivered

Points fully done (per the Definition of Done) by sprint end.

e.g. 29

Results

Say/do ratio

Forecast reliability for this sprint.

Commitment gap (points)

Delivered minus committed — negative means work rolled over.

Charts

Forecast reliability

Where the say/do ratio sits against the reliable band.

14.1 — Little’s Law & flow efficiency

Cycle time = WIP ÷ throughput

Given any two of work-in-progress, throughput and cycle time, Little’s Law fixes the third. It is the mathematical case for WIP limits: with throughput unchanged, every extra item you start adds directly to how long everything takes. Flow efficiency then reveals how much of that cycle time is actual work versus waiting in queues.

Cycle time = WIP ÷ Throughput
Flow efficiency % = Active work time ÷ Cycle time × 100

Parameters

WIP — work in progress

Items currently started and unfinished on the board.

e.g. 12

Throughput (items / period)

Items finished per period — pick days or weeks and stay consistent.

e.g. 3

Active work per item (optional)

Hands-on time an item actually receives, in the same period units — for flow efficiency.

e.g. 0.5

Results

Average cycle time

How long a newly started item takes to finish, in your chosen periods.

Flow efficiency

Share of the cycle time that is real work rather than waiting.

Charts

WIP vs cycle time

The linear relationship behind WIP limits — at fixed throughput, cycle time tracks WIP directly.