# Monte Carlo simulation

**Introduction**

Mining companies require significant funding to begin a project, and to obtain this financing, they must often turn to debt markets. Due to the substantial investment, it is essential that mining projects be evaluated in terms of economic viability. Mine management involves improving existing mine processes to reduce overall costs and maximize the Net Present Value (NPV) of a project. The purpose of any mine management team is to create value from a project to increase wealth for shareholders who have taken risk in investing their money into a project. In order to substantiate the economic evaluation of a project, they must determine the outcomes of risks taken in their mine planning^{[1]}.

**Risk**

There are numerous risks that mining company’s encounter that could have an effect on a project’s long-term economic viability. Such risks faced by the mining and metals industry are outlined in a report by Ernst and Young. These risks include productivity improvement, capital dilemmas, social license to operate, resource nationalism, capital projects, price and currency volatility, infrastructure access, sharing the benefits, balancing talent needs, and access to water and energy^{[2]}. Due to the uncertainty and variability of these risks, it is important for project planners to extensively utilize risk analysis techniques. Risk analysis allows planners to determine all the possible outcomes of a decision regarding finance, costs, forecasting models, and project management as well as the risks associated with each. This allows for better decision making^{[3]}.

**History**

Stanislaw Ulam created the Monte Carlo method in the late 1940s on the basis of determining the probability of winning a solitaire game. He began trying to solve the solitaire problem using combinational calculations which lead him to consider how problems regarding neutron diffusion might be represented as a succession of random operations. The Monte Carlow simulation is any technique of statistical data sampling used to approximate solutions to quantitative problems. Ulam, with the help of John von Neumann and Nicholas Metropolis, recognized the potential for the recently invented computer to automate sampling. He was eventually able to develop computer software algorithms and transform non-random problems into random forms that would facilitate their solution from statistical sampling. This work has changed the way statistical sampling is viewed to a formal methodology that is able to be used in a wide variety of problems. The methodology was named Monte Carlo after the casinos in Monte Carlo^{[4]}.

**Monte Carlo Assessment**

The Monte Carlo simulation is a mathematical simulation that allows for planners to account for risk in a quantitative way (Palisade Corporation, 2015). Monte Carlo simulation is a term that describes a computer simulation that uses random numbers generated by a program^{[5]}. Unlike a sensitivity analysis which involves changing the input variables one at a time, the Monte Carlo process involves changing two or more key input variables at the same time^{[6]}.

For the Monte Carlo simulation, fixed variables are replaced with random variables that create random variability in the model. The model is then recalculated numerous times, in which the random variable changes each cycle. The results from the model are analyzed and statistics from the information are derived^{[3]}.

Changing multiple input variables creates a much more accurate prediction of project risks rather than changing a single variable. Although, the challenge involved with changing multiple variables is the extremely large number of possible variable combinations and the different amounts of variation in each. Therefore, Monte Carlo analyses are performed on custom computers in order to accommodate the large number of possible iterations ^{[6]}.

**References**

- ↑ Lemelin, B. (2009). Mine Project Evaluation: A real Options Approach with Least-Squares Monte Carlo Simulations. Quebec City: University of Laval.
- ↑ Ernst and Young. (2015). Business Risks Facing Mining and Metals. Toronto: Ernst and Young.
- ↑
^{3.0}^{3.1}RiskAmp. (2014). What is Monte Carlo Simulation. RiskAmp. - ↑ Holten, G. A. (2015). The Monte Carlo Method. Retrieved from Value-at-Risk: Theory and Practice: http://value-at-risk.net/the-monte-carlo-method/.
- ↑ Heuberger, R. (2005). Risk Analysis in the Mining Industry.
- ↑
^{6.0}^{6.1}Mining Man. (n.d.). Mining Financial Basics #7 - Monte Carlo Simulation. Retrieved March 2, 2015, from Mining Man: http://www.miningman.com/Blog/May-2010/Monte-Carlo-Simulation-Analysis-Financial-Basics-7.