Capstone: integrated planning and calculation strategy for the exam

This final lesson brings the course together in two ways. First, it revisits Project Compass at a single status date and shows how scope, schedule and cost information combine into one picture for decision-making, including the agile measures used for the app. Second, it gives a structured approach to the calculation and situational questions on scope, schedule and cost that appear on the PMP exam: which formulas to know, how to read a question, common traps and how to check an answer quickly. Quality, risk, procurement and change control, which complete the Process domain, follow in PMP-131.

Project Compass at month 6

At the end of month 6, the project manager prepares an integrated status review for the board. The fit-out has reached the HVAC upgrade; the app team has completed six sprints; overall earned value is available from the control accounts. Each part tells part of the story.

# Capstone check: one status date, three views of Project Compass
import math
# 1. Fit-out schedule: PERT on the critical path (working days)
crit = [(12, 15, 21), (15, 20, 35), (8, 10, 14), (16, 20, 30), (12, 15, 21),
        (8, 10, 13), (6, 8, 11), (2, 2, 2)]
mean = sum((o + 4 * m + p) / 6 for o, m, p in crit)
sd = math.sqrt(sum(((p - o) / 6) ** 2 for o, m, p in crit))
z = (110 - mean) / sd
prob = 0.5 * (1 + math.erf(z / math.sqrt(2)))
print(f"Fit-out: mean {mean:.1f} days, SD {sd:.2f}; P(within 110 days) = {prob:.0%}")

# 2. Mobile app release: burn-up forecast
done, scope, velocity, growth = 128, 262, 21.3, 7.0
print(f"App: {scope - done} points left; {math.ceil((scope - done) / (velocity - growth))} sprints with growth, "
      f"{math.ceil((scope - done) / velocity)} if scope is frozen")

# 3. Whole project: earned value ($000)
BAC, PV, EV, AC = 2400, 1440, 1290, 1400
CPI, SPI = EV / AC, EV / PV
print(f"EVM: CPI {CPI:.3f}, SPI {SPI:.3f}, EAC {BAC / CPI:,.0f}, "
      f"ETC {BAC / CPI - AC:,.0f}, TCPI(BAC) {(BAC - EV) / (BAC - AC):.3f}")
reserve_left = 120 - 40                  # management reserve minus approved draws
print(f"Overrun at BAC/CPI: {BAC / CPI - BAC:,.0f} vs management reserve left {reserve_left}")

Fit-out: mean 104.3 days, SD 4.84; P(within 110 days) = 88%
App: 134 points left; 10 sprints with growth, 7 if scope is frozen
EVM: CPI 0.921, SPI 0.896, EAC 2,605, ETC 1,205, TCPI(BAC) 1.110
Overrun at BAC/CPI: 205 vs management reserve left 80

The three views agree in direction but add different information. The fit-out PERT calculation for the critical path alone suggests an 88 % chance of finishing the network within 110 working days; the Monte Carlo simulation from lesson 8, which captures merge bias, puts it nearer 61 %. The app has 134 points left; at current velocity and scope growth it needs about 10 more sprints, but the product owner can bring that down to 7 by freezing release 1 scope. Overall earned value shows a CPI of 0.92 and SPI of 0.90, with an EAC of about $2.6 million against a BAC of $2.4 million. The projected overrun of about $205,000 exceeds the $80,000 of management reserve remaining after an earlier approved draw, although some contingency reserve also remains.

The project manager's recommendations integrate scope, schedule and cost. Freeze release 1 app scope and move room booking to release 2, which protects the opening date. Rent a third encoding station for tagging, which costs about $6,000 but removes the equipment constraint found in lesson 6. Value engineer the remaining finishes. Ask the board either to approve a revised budget with a TCPI target the team can meet, or to accept defined scope reductions. Each recommendation is presented with its impact on the baselines, and any approved change goes through change control and updates the relevant baselines and forecasts.

Integration: how a change ripples

Planning outputs are linked, so a change in one area affects others. Suppose the board approves a second community room after all. The scope statement and WBS gain a work package; requirements and the traceability matrix gain entries; new activities enter the network, possibly on the critical path; durations and resources are estimated; cost estimates rise; the cost baseline and funding requirements change; and the EVM baseline is updated so that future performance is measured against the new plan. Change control exists to make this ripple deliberate and visible. PMP-131 covers the integrated change control process in detail.

Formulas to know

The exam expects you to know these formulas without a reference sheet. Write them down from memory during your study until you can reproduce them reliably.

Beyond formulas, know the rules of thumb: forward pass takes the largest predecessor EF, backward pass the smallest successor LS; crash the cheapest critical activity first; leveling may extend the schedule, smoothing does not; contingency is in the cost baseline, management reserve is not; BAC excludes management reserve; and negative variances or indices below 1 are unfavorable.

A method for calculation questions

Calculation questions are usually short, but under time pressure it is easy to misread them. A consistent method helps.

• Read the last sentence first, so you know what is being asked: SPI, EAC, float, probability.
• Identify the data given and write it down: BAC, PV, EV, AC; or O, M, P; or network durations.
• Check the assumption: does the question say performance will continue, the variance was one-off, or the date is fixed?
• Choose the formula and calculate, keeping enough decimal places until the end.
• Sanity-check: is the answer in the right direction? If CPI is below 1, EAC should exceed BAC. If an activity is critical, its float should be zero.
• Look at the options: if two are close, recheck the formula variant (triangular versus PERT, TCPI on BAC versus EAC).

Situational questions on scope, schedule and cost

Many questions on these topics are situational rather than numerical. They describe a problem and ask what the project manager should do next. Patterns from this course include:

Underlying these patterns are a few principles the exam rewards. Analyze before acting. Use the agreed processes, such as change control and the risk management plan, rather than acting unilaterally. Involve the right decision-maker. Be honest about variances and forecasts. Prefer options that address root causes over those that hide symptoms. And tailor the approach: an answer that applies heavy predictive process to a small adaptive team, or no process to a regulated construction project, is usually wrong.

Agile measures for scope, schedule and cost

Hybrid projects report adaptive work with its own measures, which the exam expects you to read. A burndown chart shows remaining work against time, sloping down toward zero; a burn-up chart shows completed work rising toward a total scope line, which makes scope changes visible. Velocity is completed points per iteration. A cumulative flow diagram shows how many items are in each state (to do, in progress, done) over time; widening bands in progress signal a bottleneck. Cost per iteration or per point links agile progress to budget, and a simple agile EVM can treat each iteration's planned points as planned value. PMP-140 covers these in detail; for this course, be able to forecast a finish from velocity and scope growth, and recognize what a widening gap on a burn-up chart means.

Final checklist for planning

Before you baseline a plan on a real project, or answer a planning question on the exam, check the following. Are requirements clear, prioritized and traced? Does the scope statement list deliverables, acceptance criteria and exclusions? Does the WBS include 100 % of the work, including project management? Are activities linked with sound logic and no open ends? Are durations based on documented estimates with ranges? Has the critical path been identified and checked against resource limits? Has schedule risk been considered, and is the committed date at an agreed confidence level? Do cost estimates cover all resources, with escalation and contingency? Is the cost baseline time-phased and reconciled with funding? Are reserves explicit and controlled by the right people? Is there a way to measure progress objectively, such as earned value for predictive work and burn charts for adaptive work?

A plan that passes these checks will still change, because projects are uncertain. But it gives the team a sound basis to coordinate, the sponsor a fair basis to hold the project to account, and the project manager an early warning when reality departs from the plan.