- Beatriz Faria

# The Monte Carlo technnique as a boost for NPV Simulations in mining projects

Many mining companies utilize the Net Present Value (NPV) methodology to estimate the value of a project and its profitability.

**How does it work?**

NPV calculation is made by measuring the projected cash flow for the project over a period of time and calculating the present value of this cash flow based on the present economy's interest rate.

**What is the problem with it?**

The calculations are made on following the current interest rate to presume static assumptions. This approach, with so, does not consider variability (fluctuations of the exchange rate, the interest rate, or the performance of the upgraded industrial process (used to calculate the increased throughput or savings), which is a big part of the real life progress and influences the financial outcome largely.

This is where simulation can add value by giving the ability to estimate a more realistic financial outcome of the project.

**The Monte Carlo Simulation**

Monte Carlo simulation is a mathematical technique that allows accounting for risk in quantitative analysis and decision making. It samples from the random distributions of the variables and calculates the NPV repeatedly, obtaining at least 10.000 NPV scenarios with a wide range of input values combinations. Using simulation to sample values from a distribution instead of constant assumptions allows capturing the distribution of possible NPVs. With that information in hand, decision makers have more power to evaluate the chances of being profitable or not. They can also evaluate their chances to be above or below a specific threshold.

In mining, risk analysis using Monte Carlo simulation is used to analyze the effects that orebody variability has on the circuit performance and the probabilities they will occur, i.e. the likelihood of achieving design throughput or not. This methodology is an alternative way of applying geometallurgy and multi-scenario simulation in the design of a circuit featuring AG/SAG mills. The method relies in using statistics to analyze geometallurgical and mining data to model the variability of specific energy requirements of SAB (SAG and ball mill) and SABC (SAG and ball mill with-pebble crushing) circuits for mill design purposes. Ultimately, the application of this method can be used to evaluate and minimize design risks.

**How does that relate to us?**

As mentioned above throughput is the main variable to determine financial outcome of a mining project, and that throughput is mostly determined by the ore hardness, its grindability and the time it takes to process it. Unfortunately, the industry knows nothing about hardness if compared to grade intel. For each hardness test made for a mining project feasibility study, at least 1000 grade tests are conducted, but guess which one determines the throughput (TPD)?

So why don’t the mining industry test more for hardness? The main problem for many mine companies with high volume testing is the cost involved in conventional rock breakage tests, as they are laborious, time consuming, large samples handling and shipping, therefore expensive.

With that in mind, Geopyora became a pioneer in the rock breakage characterization testing sector by implementing a technology that allows mining companies to test a large number of samples at a low cost using the same discrete samples used for geochemical assays.

With this kind of hardness knowledge its not only possible to narrow down NPV probabilities to more realistic scenarios but also use that information to optimize ore processing on operating projects.

We can also know which areas on mine sites that are faster to process in the sense of obtaining more resources in less time. Optimizing the drill and blast schedule to produce more resources in the early stages generates more income on its initial months and, by that, increases the NPV.