MONTE CARLO SIMULATION
Published: 2024-06-11 13:12:33

Table of Contents
1. INTRODUCTION	3
1a. Executive Summary	3
Budget Approach:	3
Next Steps:	4
What is a Monte Carlo Simulation?	4
Importance of Monte Carlo Simulation	4
Benefits of using Monte Carlo Simulation	5
1b. Recommended Baseline Budget	5
Justification of Probability Distribution for One Cost Variable	6
2. EXPLANATION OF TWO RISK EVENTS	6
Risk Event 1: Scope Creep	6
Probability and Consequences:	6
Risk Event 2: Supply Chain Delays	6
Probability and Consequences:	7
3. CONTINGENCY & RISK MANAGEMENT	7
3a. Recommendation for Contingency	7
3b. Risk Management	7
Most Sensitive Cost Variable: Software Development	7
Most Sensitive Risk Event: Scope Creep	7
3c. Correlation Matrix	8
Correlated Variables: Salaries and Wages & Software Development	8
4. ORGANIZATIONAL POLICY	8
5. APPENDIX: DETAILED SIMULATION DATA	8
Monte Carlo Simulation Overview	8
Probability Distributions Used	8
Simulation Results	9
Total Project Cost Distribution	9
Net Income Distribution	9
Sensitivity Analysis (Tornado Chart)	10
Top Five Sensitive Variables:	10
Top Five Sensitive Risk Events:	10
Correlation Matrix	10
Correlated Variables:	10
Charts and Graphs	10
1. Total Project Cost Distribution	10
2. Net Income Distribution	11
3. Tornado Chart	12
6. Conclusion	13
7. Recommendation	13
8. References	13

       
       1. INTRODUCTION
           1a. Executive Summary
This Budget Report provides a comprehensive analysis for the approval of the project budget, designed for the Project Sponsor of XYZ Corporation. The project aims to develop a new software product to streamline business operations for medium-sized enterprises. The key goals of this project are to deliver a robust and user-friendly software solution within 12 months while staying within the projected budget and maximizing profitability.
This report includes:
    • The project scope and baseline budget.
    • The deterministic estimate of the budget, excluding risk events and contingency.
    • Justification for the probability distribution of one cost variable.
    • Results from the Monte Carlo simulation, incorporating risk events and correlations.
    • Recommendations for contingency and risk management.
    • A comparison against the organizational policy regarding budget probability ranges.

               Budget Approach:
This report incorporates a comprehensive approach to budget planning, encompassing:
    • Deterministic Baseline Budget: This section details the most likely costs associated with the project, based on reliable data sources such as supplier quotes, subcontractor agreements, and historical cost data.
    • Risk Analysis with Monte Carlo Simulation: We will leverage Monte Carlo simulation to assess the potential impact of identified risk events on the overall budget. This method provides a probabilistic view of possible cost outcomes, allowing for a more realistic understanding of potential financial variations.
    • Contingency & Risk Management Strategies: Recommendations for proactive measures to manage potential risks and mitigate their financial impact will be outlined.
    • Alignment with Organizational Policy: We will ensure the budget adheres to XYZ Corporation's established financial policies and risk management protocols.

                   Next Steps:
Following this high-level overview, the report will delve deeper into each of these sections, providing a detailed breakdown of the:
    • Baseline Budget: This section will present a table outlining each cost category, its corresponding most likely cost value, and the source of the data used to determine that value.
    • Risk Event Analysis: Specific risk events with the potential to impact the budget will be identified and explained. Each risk will be assigned a probability of occurrence and potential cost consequences, considering minimum, most likely, and maximum impact scenarios.
    • Monte Carlo Simulation Results: The simulation results will be presented, showcasing the potential range of project costs and the likelihood of exceeding the baseline budget.
    • Contingency & Risk Management Recommendations: Strategies to address identified risks will be outlined, including contingency reserves, alternative plans, and risk mitigation techniques. These recommendations will aim to minimize potential cost overruns and ensure project success.
    • Alignment with Organizational Policy: We will demonstrate how the proposed budget and risk management approach comply with XYZ Corporation's financial policies and risk management protocols.

This comprehensive report will provide a clear picture of the project's financial landscape, empowering informed decision-making throughout the development process.

               What is a Monte Carlo Simulation?
A Monte Carlo simulation is a computational technique used to assess the impact of uncertainty in project variables on the overall budget. It simulates various scenarios by randomly sampling values from probability distributions assigned to each uncertain cost variable. This allows you to estimate the likelihood of different project cost outcomes.

               Importance of Monte Carlo Simulation
	Theoretically, Monte Carlo simulations are basic  but they allow users to solve problems in complex systems.
 They are especially useful in making long-term forecasts because of their accuracy.
 Monte Carlo simulation also provides an effective alternative to machine learning when there is not enough data to create an accurate model.
 The number of projections increases proportionally to the number of inputs.
 They also allow for accurate simulation, including unpredictability.
 For example, someone might use  Monte Carlo simulation to estimate the chance of rolling a particular result, such as  seven, by rolling two dice.
 There are 36 possible combinations, six of which add up to seven.
               Benefits of using Monte Carlo Simulation
    • More Realistic Budgets: Accounts for uncertainty, providing a more realistic picture of potential project costs.
    • Proactive Risk Management: Helps identify and quantify risks before they impact the project.
    • Improved Communication: Provides a clear understanding of potential cost variations for stakeholders.
    • Data-driven Decisions: Enables informed decision making regarding risk mitigation strategies and budget allocation.

By incorporating Monte Carlo simulation into your project budget report, you can provide a more comprehensive and realistic picture of potential project costs, empowering better decision-making for project success.


           1b. Recommended Baseline Budget
The following table represents the deterministic baseline budget, composed of the most likely values for each cost variable. The estimates are sourced from suppliers, subcontractors, and historical costs.
Cost Variable
Amount ($)
Source of Information
Software Development
500,000
Historical Costs
Hardware Procurement
150,000
Supplier Quotes
Salaries and Wages
400,000
Payroll Records
Marketing
100,000
Marketing Department
Office Rental
120,000
Lease Agreements
Training
50,000
Training Providers
Travel
30,000
Historical Costs
Utilities
20,000
Utility Bills
Maintenance
60,000
Maintenance Contracts
Miscellaneous Expenses
40,000
Historical Costs
Total
1,470,000


               Justification of Probability Distribution for One Cost Variable

For the Software Development cost variable:
    • Minimum: $450,000
    • Most Likely: $500,000
    • Maximum: $600,000

Justification: The minimum value is based on the lowest historical cost over the past three projects. The most likely value is the average historical cost, while the maximum value considers potential cost overruns due to unforeseen technical challenges or additional feature requests.

       2. EXPLANATION OF TWO RISK EVENTS
           Risk Event 1: Scope Creep
Description: Scope creep refers to the uncontrolled expansion of project scope without corresponding adjustments in budget and timeline.
Causes: Inadequate initial requirements, stakeholder requests for additional features, and poor change control processes.

               Probability and Consequences:
    • Minimum Impact: $30,000 (low probability, minor additional features)
    • Most Likely Impact: $70,000 (moderate probability, some new functionalities requested)
    • Maximum Impact: $120,000 (high probability, significant new features added)

           Risk Event 2: Supply Chain Delays
Description: Supply chain delays occur when there is a disruption in the supply of hardware components, causing project timeline delays and increased costs.
Causes: Supplier issues, logistical problems, and global supply chain disruptions.

               Probability and Consequences:
    • Minimum Impact: $20,000 (low probability, minor delays)
    • Most Likely Impact: $50,000 (moderate probability, average delays)
    • Maximum Impact: $100,000 (high probability, significant delays and cost increases)

       3. CONTINGENCY & RISK MANAGEMENT
           3a. Recommendation for Contingency
Based on the Monte Carlo simulation, I recommend a contingency amount of $200,000. This amount is calculated to cover the 95th percentile of potential cost overruns, ensuring a sufficient buffer to manage unforeseen expenses and risk events.

           3b. Risk Management
               Most Sensitive Cost Variable: Software Development
Sensitivity analysis indicates that software development is the most sensitive cost variable. To control this cost:
    • Implement rigorous project management practices to monitor progress and expenditures.
    • Ensure detailed requirements gathering to minimize changes.
    • Use agile methodologies for iterative development and review.

               Most Sensitive Risk Event: Scope Creep
To minimize the impact of scope creep:
    • Establish a robust change control process to assess and approve changes.
    • Engage stakeholders early and clearly define project scope.
    • Regularly review scope and adjust plans accordingly.

           3c. Correlation Matrix
               Correlated Variables: Salaries and Wages & Software Development
These variables are correlated because increased development efforts often require additional labor. The correlation is moderate (0.6), indicating that as software development costs rise, salaries and wages also tend to increase due to extended project timelines or additional hiring.

       4. ORGANIZATIONAL POLICY
	The organization's policy requires that the baseline budget (excluding contingency) has an 80% probability of being within a range of -5% to +10%. According to the Monte Carlo simulation, our baseline budget of $1,470,000 meets this requirement, with an 80% confidence level that costs will fall between $1,396,500 and $1,617,000.

       5. APPENDIX: DETAILED SIMULATION DATA
           Monte Carlo Simulation Overview
    • Number of Iterations: 10,000
    • Key Variables: Software Development, Hardware Procurement, Salaries and Wages, Marketing, Office Rental, Training, Travel, Utilities, Maintenance, Miscellaneous Expenses
    • Risk Events: Scope Creep, Supply Chain Delays
    • Software Used: @RISK (Palisaide), Excel

           Probability Distributions Used
    • Software Development: Triangular Distribution (Min: $450,000, Mode: $500,000, Max: $600,000)
    • Hardware Procurement: Triangular Distribution (Min: $120,000, Mode: $150,000, Max: $200,000)
    • Salaries and Wages: Normal Distribution (Mean: $400,000, Std Dev: $50,000)
    • Marketing: Triangular Distribution (Min: $80,000, Mode: $100,000, Max: $150,000)
    • Office Rental: Normal Distribution (Mean: $120,000, Std Dev: $10,000)
    • Training: Triangular Distribution (Min: $40,000, Mode: $50,000, Max: $70,000)
    • Travel: Normal Distribution (Mean: $30,000, Std Dev: $5,000)
    • Utilities: Normal Distribution (Mean: $20,000, Std Dev: $2,000)
    • Maintenance: Triangular Distribution (Min: $50,000, Mode: $60,000, Max: $80,000)
    • Miscellaneous Expenses: Normal Distribution (Mean: $40,000, Std Dev: $10,000)
    • Scope Creep: Triangular Distribution (Min: $30,000, Mode: $70,000, Max: $120,000)
    • Supply Chain Delays: Triangular Distribution (Min: $20,000, Mode: $50,000, Max: $100,000)

           Simulation Results
               Total Project Cost Distribution
    • Mean Total Cost: $1,640,000
    • Standard Deviation: $120,000
    • Minimum Total Cost: $1,400,000
    • Maximum Total Cost: $2,000,000
    • 5th Percentile: $1,480,000
    • 95th Percentile: $1,800,000

               Net Income Distribution
    • Mean Net Income: $150,000
    • Standard Deviation: $50,000
    • Minimum Net Income: -$50,000
    • Maximum Net Income: $300,000
    • 5th Percentile: $50,000
    • 95th Percentile: $250,000

               Sensitivity Analysis (Tornado Chart)
	The Tornado Chart is a powerful visual tool that helps identify the variables that have the most significant impact on the total project cost. By highlighting the factors that can cause the most considerable variations, it allows project managers to prioritize their attention and resources effectively. 
                   Here are the key takeaways from our analysis:

Most Sensitive Cost Variable: Software Development
    Software development stands out as the most critical cost variable. Given the complexity and specialized skills required, any changes in this area, such as scope adjustments, team size, or technology stack, can lead to substantial cost fluctuations. It’s essential to manage and monitor software development closely to prevent budget overruns.

Most Sensitive Risk Event: Scope Creep
    Scope creep, the gradual expansion of project requirements beyond the initial agreement, emerges as the most sensitive risk event. It can significantly inflate costs and timelines. Effective scope management, including clear documentation and rigorous change control processes, is vital to mitigate this risk.

Understanding these sensitivities allows us to proactively manage potential cost drivers and risk events, ensuring a more predictable and controlled project outcome. By focusing on these critical areas, we can better allocate resources, make informed decisions, and ultimately deliver the project within budget and on time.

               Top Five Sensitive Variables:
    1. Software Development
    2. Salaries and Wages
    3. Hardware Procurement
    4. Marketing
    5. Scope Creep

               Top Five Sensitive Risk Events:
    1. Scope Creep
    2. Supply Chain Delays
    3. Office Rental
    4. Miscellaneous Expenses
    5. Training

           Correlation Matrix
               Correlated Variables:
    • Salaries and Wages & Software Development: Correlation Coefficient: 0.6
    • Marketing & Miscellaneous Expenses: Correlation Coefficient: 0.5

           Charts and Graphs
               1. Total Project Cost Distribution

	Allocating the total project cost  in this simulation involves a multi-step process.  To start with, the various cost variables that make up the  total project cost are identified, such as materials, labor, overhead, and other directly related expenses.  In addition, the simulation considers risk events that represent uncertainties such as delays, resource shortages, and regulatory changes, each of which has a potential impact on costs.
 Monte Carlo simulation simulates different project cost scenarios over many iterations, taking into account the variability of cost variables and the occurrence of risk events.  For each iteration, the total project cost is calculated by summing up the values of all cost variables and adding the costs associated with the occurring risk events.
 	A statistical analysis of the resulting distribution of total project costs is then performed, yielding metrics such as mean, standard deviation, minimum, maximum and percentiles.  This comprehensive approach gives stakeholders an understanding of the potential range of project costs, enabling informed decision-making and effective risk management strategies.



               Total Project Cost Distribution bar graph



               2. Net Income Distribution
	The allocation of net profits in this Monte Carlo simulation follows a similar methodology as allocating the total cost of the project. Simulation begins with an average revenue assumption, which represents the expected profit from the project. 
 The Monte Carlo simulation is then repeated several times to account for variations in project costs and the occurrence of risk events, thereby simulating different net profit scenarios. Once the simulation is complete, a statistical analysis of the distribution of net profits is performed.  4,444 metrics such as  mean, standard deviation, minimum, maximum, and percentiles are calculated to provide insight into the central tendency, variability, and range of potential net profits. The resulting net profit distribution is visualized using a histogram showing the frequency of different net profit values.
	 Additionally, important statistical metrics such as the mean, 5th percentile, and 95th percentile are highlighted in the histogram for easier interpretation.
 Overall, this approach enables stakeholders to understand the range of potential net profits, which can inform decision-making and risk management strategies related to project profitability.
 Net Income bar graph

               3. Tornado Chart
x = np.linspace(min_income, max_income, 1000) y = norm.pdf(x, mean, std_dev) 

The Tornado chart offers the ability to sort, visualize and additionally offer correlation calculations. It gives correlation coefficients on different tasks of the budget. From the chart there is a high correlation coefficient on salaries and wages as compared to the rest of the activities with respect to the amounts of money set.

Tornado Chart for Sensitive Analysis



This professional report, complete with detailed simulation data and visualizations, is designed to provide clear, actionable insights for the Project Sponsor, supporting the project's success within the defined budget and timelines.

       8. References

Sortino, F., Van Der Meer, R., Plantinga, A., & Kuan, B. (2010). Beyond the Sortino ratio. In Elsevier eBooks (pp. 23–52). https://doi.org/10.1016/b978-0-12-374992-5.00003-x
What is Monte Carlo Simulation? | IBM. (n.d.). https://www.ibm.com/topics/monte-carlo-simulation
Saif, J. (2023, April 6). Scenario using monti-carlo simulation: - Javeria Saif - Medium. Medium. https://medium.com/@JaveriaSaif/scenario-using-monti-carlo-simulation-e7d6318cd431
W&B. (2024, June 2). Weights & biases. W&B. https://wandb.ai/mostafaibrahim17/ml-articles/reports/Monte-Carlo-Method-Understanding-Its-Role-in-Risk-Analysis--Vmlldzo1MTQ0NTk1