| Course | IBF-5070 Financial Modeling |
|---|---|
| Module | Module 6 |
| Paper type | Module 6 written assignment: probabilistic risk and time series equations in financial models |
| Length | About 609 words, 5 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | MBA in Finance |
| Updated | October 2026 |
Free sample paper for IBF 5070 Module 6
A 42 Percent Chance of Loss: Simulating the Cumberland Solar Project's Value
Student Name
MBA in Finance, Thomas Edison State University
IBF-5070: Financial Modeling
Mentor Name
Month Day, Year
A 42 Percent Chance of Loss: Simulating the Cumberland Solar Project's Value
Introduction
Scenarios in Module 5 showed what could happen; they did not say how likely each outcome is. Hertz (1964) proposed simulation as the answer: give each uncertain input a probability distribution, draw values for all of them together many times and record the outcome of each draw. The result is a distribution of value rather than a single number. Bodmer (2015) adds a caution: a simulation is only as good as the distributions chosen for its inputs and the relationships among them. This paper therefore explains each distribution before reporting results, and treats the three inputs as independent of one another, an assumption revisited in the conclusion.
Choosing Distributions
The generation distribution comes from the independent engineer's estimate that P90 output is 7 percent below P50, which matches a standard deviation of about 4 percent for a long-run average. The triangular construction distribution reflects contractor bids and the record of past overruns. The lognormal price distribution fits a quantity that grows by percentage changes and cannot go negative.
| Input | Distribution | Parameters | Reasoning |
|---|---|---|---|
| Generation | Normal | Mean P50, standard deviation 4% | Long-run resource uncertainty is roughly symmetric |
| Construction cost | Triangular | Low $1.12, likely $1.20, high $1.35 per watt | Overruns are more likely than savings |
| Market price after year 20 | Lognormal | Median near $55 in today's dollars, volatility 35% | Prices cannot fall below zero and have a long upper tail |
Simulation Results
The model was run 5,000 times, drawing all three inputs in each trial.
The mean is lower than the base case because the construction cost distribution is skewed toward overruns, so the average cost is above the most likely cost. Savage (2009) calls this the flaw of averages: plans built on single most likely values are wrong on average when outcomes are not symmetric. The 42 percent chance of loss is the key finding. A project with a positive base case can still be close to a coin flip.
| Result | Value, $ millions |
|---|---|
| Base-case NPV, for comparison | 3.1 |
| Mean NPV | 2.1 |
| Median NPV | 1.3 |
| 10th percentile | (6.4) |
| 90th percentile | 11.9 |
| Probability NPV is below zero | 42% |
Volatility From a Random Walk
To set the volatility of market prices, the analyst looked at history. Under a random walk, the logarithm of price changes each period by a random amount, so volatility is the standard deviation of log price changes. PJM's load-weighted average real-time price was about $27 per MWh in 2019, $22 in 2020, $40 in 2021, $80 in 2022 and $31 in 2023, according to the market monitor (Monitoring Analytics, 2024). The four annual log changes are about minus 0.23, plus 0.60, plus 0.70 and minus 0.95, with a standard deviation of about 77 percent.
That figure is far too high to apply over twenty years. Under a random walk, uncertainty grows with the square root of time, so a 77 percent annual volatility would imply a range of prices in year 21 so wide that it would be meaningless. The 2022 spike, driven by natural gas prices, reversed within a year, which is the behavior of a mean-reverting series rather than a random walk. The simulation therefore used 35 percent for the level of prices two decades out, a judgment Module 7 examines.
Conclusion
The simulation gives Cumberland a mean NPV of about $2.1 million and a 42 percent probability of losing value. These results strengthen the Module 5 recommendation to secure a higher contract price and a fixed-price construction agreement, which would narrow the distribution. The volatility calculation shows that history from a short, turbulent period must be adjusted before it drives a long-term model.
References
Bodmer, E. (2015). Corporate and project finance modeling: Theory and practice. Wiley.
Hertz, D. B. (1964). Risk analysis in capital investment. Harvard Business Review, 42(1), 95-106.
Monitoring Analytics. (2024). 2023 state of the market report for PJM. Monitoring Analytics, LLC.
Savage, S. L. (2009). The flaw of averages: Why we underestimate risk in the face of uncertainty. Wiley.
IBF 5070 Module 6 instructions, in plain terms
The fifth IBF-5070 written assignment covers probabilistic risk and time series in financial models. Expect to choose distributions for key inputs, run a Monte Carlo simulation, interpret the distribution of outcomes and calculate volatility from historical data under a random walk. Explain why each distribution fits its input, report the number of trials and the main statistics, and interpret the probability of loss. When you compute volatility, show the data and the steps, and discuss whether the result is reasonable for your model's horizon. Bodmer's chapters on probabilistic analysis guide the method. If your software lacks a simulation add-in, a data table with random draws can run a few thousand trials. Fix the random seed or save the draws, so the results can be reproduced when your mentor checks the model.
How the IBF 5070 Module 6 example is put together
The paper links back to the scenarios of Module 5 and introduces simulation with early research on risk analysis. A table sets out each distribution with parameters and reasoning. A results table reports the mean, median, percentiles and probability of loss, and the text explains why the mean falls below the base case. A volatility section computes annual volatility from five years of regional power prices under a random walk and explains why the figure is unsuitable for a twenty-year horizon. The conclusion links the results to the earlier recommendations and to the next module. The data used for volatility come from a named market monitor, which a reader can check, and the paper says exactly how the figure was computed and why it was not used unchanged. That candor about limits is part of what mentors look for.
Where the marks sit in the IBF 5070 Module 6 rubric
Mentors grade this assignment on sound choice of distributions, correct simulation and interpretation, accurate volatility calculation and critical thinking about the results. Answers that justify each distribution, and that explain why simulated and base-case values differ, show understanding. Questioning whether historical volatility suits the model's horizon demonstrates the judgment the course aims to build. Clear tables and a probability of loss tied to a decision make the analysis useful to management, and citing sources for the data adds credibility. Mentors also check that the number of trials is enough for stable results and that inputs drawn together are handled sensibly. Papers that compare simulation results with the earlier scenarios, and explain the differences, show that the student understands what each technique adds.
IBF 5070 Module 6 help from the desk
Students lose points by assigning normal distributions to everything, by reporting only the mean of the simulation or by computing volatility from price levels rather than log changes. Others apply short-term volatility to long horizons without comment. Match each distribution to the input's behavior. Report percentiles and the probability of loss. Use log changes for volatility and scale it with care. Question whether the history you used is typical of the period your model covers. Say how many trials you ran and whether results changed when you ran more. A free first sample on your own IBF-5070 Module 6 simulation is available on request.
Write yours, or have the desk draft it
This paper is an original model document written by our desk, not a submitted student paper and not an official Thomas Edison State University document. Read it for the moves, then write your own to the instructions in your classroom. If you want one built to your exact prompt and rubric, the first custom sample is free and arrives in 24 to 48 hours.
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IBF 5070 Module 6 questions, answered
Where can I find a free IBF 5070 Module 6 sample paper?
Monte Carlo results and a random walk volatility estimate for the solar project appear above.
What is Monte Carlo simulation in a financial model?
Drawing values for uncertain inputs from probability distributions many times and recording the output of each draw to build a distribution.
Why can the simulated mean differ from the base case?
Because skewed inputs, such as construction costs more likely to overrun, move the average away from the most likely value.
How is volatility calculated from a random walk?
As the standard deviation of the log changes in price over each period.
Why use a lognormal distribution for prices?
Because prices cannot fall below zero and tend to change by percentages, giving a long upper tail.