| Course | BU 396 Managing Project Risks |
|---|---|
| Unit | Unit 4 |
| Paper type | Quantitative risk analysis |
| Length | About 910 words, 6 pages |
| Format | APA 7 student paper |
| School | Herzing University |
| Program | BS in Project Management |
| Updated | September 2026 |
Free sample paper for BU 396 Unit 4
A One-in-Three Chance of Losing Nothing and a One-in-Ten Chance of Losing $104,000: A Quantitative Risk Analysis for a Composite Riverfront Festival
Student Name
Business, Herzing University
BU 396: Managing Project Risks
Instructor Name
March 4, 2026
A One-in-Three Chance of Losing Nothing and a One-in-Ten Chance of Losing $104,000: A Quantitative Risk Analysis for a Composite Riverfront Festival
What Was Modeled
This analysis puts numbers on the five risks carried forward from the qualitative scoring for the Riverfest, the made-up August event this course follows. They were chosen because each could cost the organizing Partnership a large sum if it occurred: severe storms forcing the park to be cleared (R01), the headliner canceling (R08), a verbal sponsor withdrawing (R13), more than five vendors canceling (R09) and a generator failure (R12). Safety risks, such as heat illness and crowd disorder, were not modeled in dollars; their treatment is a matter of prevention and response planning, and putting a price on injury would misstate what the Partnership is trying to protect. The purpose is to estimate the range of financial losses these five risks could produce together and to derive a contingency amount from that range.
Inputs
For each risk the model needs a probability of occurring and a range of cost if it does, expressed as an optimistic, most likely and pessimistic value. The table lists the inputs and where each came from. All figures belong to the composite case.
The ranges were collected in a short session with the finance manager and the events director, who were asked first for the pessimistic value, then the optimistic one and only then the most likely. Asking for the extremes first is a common way to reduce anchoring, the tendency to fix on the first number mentioned and adjust too little from it.
| Risk | Probability | Optimistic | Most likely | Pessimistic | Source and confidence |
|---|---|---|---|---|---|
| R01 Storms clear the park | 20% | $40,000 | $85,000 | $150,000 | Partnership's past event records and refund policy; low confidence on the pessimistic value |
| R08 Headliner cancels | 8% | $15,000 | $30,000 | $60,000 | Booking agent's quotes for replacement acts; medium confidence |
| R13 Sponsor withdraws | 35% | $10,000 | $25,000 | $45,000 | Values of the three verbal sponsorships; medium confidence |
| R09 Vendor cancellations | 25% | $3,000 | $6,000 | $12,000 | Vendor fee schedule; high confidence |
| R12 Generator failure | 10% | $5,000 | $12,000 | $25,000 | Rental company's replacement terms and one lost stage evening; medium confidence |
Method
The analysis used a Monte Carlo simulation, written in Python, with 10,000 iterations. In each iteration, each risk either occurred or did not according to its probability; if it occurred, its cost was drawn from a triangular distribution defined by the three values. The costs of the risks that occurred were added to give that iteration's total loss. After 10,000 iterations, the totals form a distribution showing how often different losses would occur. The triangular shape was chosen because it needs only the three estimates the team could supply and gives more weight to the most likely value than a uniform distribution would. The risks were treated as independent, an assumption discussed below. Kerzner (2017) and the Project Management Institute (2019) both describe simulation as the standard way to combine several uncertain risks, since adding expected values alone hides the chance of several bad outcomes arriving together.
As a check, the expected value of each risk was also calculated as its probability times the average of its three values. The five expected values sum to about $33,600, close to the simulation's mean of $33,200, which confirms that the simulation is behaving sensibly.
Output
The simulated losses are spread widely. In about 32 percent of iterations, none of the five risks occurred, and the loss was zero. The median loss, the 50th percentile, was about $19,300. The mean was about $33,200, pulled above the median by occasional large losses. At the 80th percentile, losses reached about $62,300; at the 90th, about $104,300; and at the 95th, about $125,900. The largest single loss in 10,000 iterations was about $200,000, when storms and a sponsor withdrawal occurred together with other risks.
The long upper tail is almost entirely driven by R01. Storms are the only risk whose cost can exceed $100,000, and every iteration above the 90th percentile includes a storm.
For the board, the practical reading is that in a typical year the five risks will cost somewhere around $20,000, that there is a real chance of a year with no losses at all and that roughly one year in ten could bring losses above $100,000, almost always because of a storm.
| Measure | Total loss from the five risks |
|---|---|
| Chance of no loss | About 32% |
| Median (P50) | About $19,300 |
| Mean | About $33,200 |
| 80th percentile (P80) | About $62,300 |
| 90th percentile (P90) | About $104,300 |
| 95th percentile (P95) | About $125,900 |
Deriving a Contingency
A contingency sized at the mean, about $33,000, would cover the average outcome but leave the Partnership short in roughly one year in four. Sized at the 80th percentile, about $62,000, it would cover four outcomes in five. The analysis recommends holding a contingency at the 80th percentile level, about $62,000, or 15 percent of the $410,000 budget, unless a response in Unit 5 changes the shape of the tail. Because storms drive almost all of the upper tail, a response that caps the cost of a storm, such as insurance, would lower the 80th percentile far more than any response to the other four risks.
Caveats
Four caveats limit how far this result can be trusted. First, the inputs are judgments; the pessimistic cost of a storm in particular rests on few past events and could be too low or too high. Second, the risks were treated as independent, but some are linked: a stormy forecast could prompt a sponsor to reconsider or vendors to cancel, which would make bad outcomes cluster more than the model assumes and fatten the tail. Third, the triangular distribution cuts off at the pessimistic value, so it cannot represent a loss worse than the team imagined. Hubbard (2020) warns that models built on expert ranges tend to be overconfident, and Flyvbjerg (2006) found that project forecasts systematically understate the chance of large overruns. Fourth, the model covers only five risks; the others, including safety risks, are managed but not priced here. The contingency should therefore be treated as a planning figure, revisited when the responses in Unit 5 are chosen. The Cedar Bend Riverfest and every input are composites created for this course.
References
Flyvbjerg, B. (2006). From Nobel Prize to project management: Getting risks right. Project Management Journal, 37(3), 5-15. https://doi.org/10.1177/875697280603700302
Hubbard, D. W. (2020). The failure of risk management: Why it's broken and how to fix it (2nd ed.). Wiley.
Kerzner, H. (2017). Project management: A systems approach to planning, scheduling, and controlling (12th ed.). Wiley.
Project Management Institute. (2019). The standard for risk management in portfolios, programs, and projects. Project Management Institute.
What the BU 396 Unit 4 instructions ask for
The Unit 4 assignment asks students to analyze their highest-priority risks quantitatively. Most versions want the risks carried forward named, input estimates provided with their sources, a stated method such as expected monetary value, a decision tree or a simulation, results reported as a range with confidence levels and a contingency amount derived from the results. Many rubrics also ask for the limitations of the analysis. Instructors care more about transparency of inputs and honest interpretation than about sophisticated software. A spreadsheet simulation or a simple script is usually enough. Expect a few pages with an inputs table and an output table, citing sources on quantitative risk analysis in APA 7, and explain in plain terms what the percentiles mean for the sponsor.
How the BU 396 Unit 4 example is put together
The sample begins by naming the five risks modeled and explaining why safety risks were not priced. An inputs table lists each risk's probability and optimistic, most likely and pessimistic costs with a source and confidence note, and a paragraph explains how the ranges were collected to limit anchoring. The method section describes the Monte Carlo simulation, the triangular distributions and the independence assumption, then checks the result against summed expected values. The output section reports the chance of no loss, the median, mean and upper percentiles in a table and explains that storms drive the tail. The contingency section compares sizing at the mean and at the 80th percentile, and the caveats section lists four limitations.
BU 396 Unit 4 rubric: what full points look like
The rubric for quantitative analysis generally weighs the inputs, the method, the interpretation of results and the contingency recommendation, along with limitations. Inputs earn full points when each estimate has a stated source and confidence rather than appearing from nowhere. The method is judged by a clear description a reader could reproduce, including assumptions such as independence and the distribution shape. Interpretation scores highest when results are reported as a range with percentiles and the drivers of the tail are identified, as the sample does. The contingency recommendation rewards a figure derived from the results with a stated confidence level. Honest caveats about inputs and assumptions earn additional credit, and a check of the model against a simpler calculation shows care.
Common BU 396 Unit 4 mistakes, and how to avoid them
A frequent Unit 4 mistake is reporting a single number, such as expected value, as if it described the whole risk. Another is using inputs with no stated source, which makes the result impossible to judge. Students often assume risks are independent without saying so, even when some clearly move together. Some papers set contingency at the mean, which leaves the project short about half the time. Others present simulation output without explaining what the percentiles mean for the project. Finally, identify what drives the result; knowing that one risk causes most of the tail tells the sponsor where a response would do the most good and sets up the response unit.
Get a BU 396 Unit 4 example written to your instructions
Send the Unit 4 instructions and the BU 396 rubric from your classroom, plus the shortlist and any tool your section requires. We write a custom example that tables its inputs with provenance, names the method, reports a range at a stated confidence, ranks the inputs by influence and marks every value as case material. First custom sample free, returned in 24 to 48 hours.
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BU 396 Unit 4 questions, answered
Do I need software to run a simulation?
Only where the instructions require a particular tool. Many sections accept a spreadsheet model with a modest number of runs, and some want the arithmetic done by hand on a small set of entries. Whichever you use, report the setup so the result can be rebuilt: the shape assumed for each input, how many runs, and what the output actually represents.
Where should the three point estimates come from?
From reasoning you can show, and it should be visible reasoning rather than a confident number. A comparable piece of work, a lead time you can argue from, the span between the fastest and the slowest anybody managed something similar. Label all of it as an estimate for the constructed project, because a figure presented as market truth is the error this unit attracts.
How much contingency should the analysis recommend?
That belongs to the model rather than to a rule of thumb, and the paper is graded on showing the link between them. Take what your distribution gives at the confidence the case sponsor asks for, then say what funding the middle of the range would mean and what the higher figure buys. An amount stated without its confidence reads as firm when it is not.
Where can I find a free BU 396 Unit 4 sample paper?
The finished BU 396 Unit 4 analysis, inputs through contingency, can be read above at no charge. For the same analysis for your own shortlist, send the prompt with your risk estimates, and a free custom quantitative analysis will be worked out, generally inside two days.
Do I need software for the BU 396 Unit 4 simulation?
Not special software. The sample's simulation was written in a short Python script, and a spreadsheet with random number functions can do the same. What matters is stating the inputs, the distribution, the number of iterations and how you checked the result.