## Pages

### Mining Companies: Net Present Value Calculation

The Net Present Value (NPV) is one of the most important numbers that a company will release during an economic study (details here). However, a NPV is based off a particular commodity price, and investors are not always presented with the NPV of a project at a range of commodity prices. For example, if the gold price is \$1,500/oz when an economic study is created, but quickly falls to \$1,000/oz, you need to be able to re-calculate the NPV for this lower gold price. This tutorial will look at the general method of calculating a pre-tax NPV. The processes used in real economic scoping studies are far more rigorous in terms of forecasting steps one through six and eight; this tutorial looks at the overall process rather than at each component in turn.

An Imaginary Example: GoldMoon Resources

First I will run through an imaginary example of how a NPV is calculated. The method is standard across the industry, albeit I will use a simplified version to ensure that it is easier to follow. GoldMoon is a gold exploration company located in the UK; GoldMoon has 100% of the project so all revenues are due to GoldMoon solely.

Step 1: Determine the Life of Mine (LOM) for the Resource
- Let's say that the LOM is 5 years. Let's also say that GoldMoon has a geologically extractable gold reserve of 150,000 ounces, of which 142,000 are commercially extractable

Step 2: Forecast the quantity of gold ounces produced in each year

- Let's say the 142,000 of commercially extractable gold ounce inventory is produced in the following order: 20,000 gold ounces in Year 1, then 30,000 (Y2), 32,000 (Y3), 35,000 (Y4) & 25,000 (Y5)

Step 3: Estimate the Commodity Price to use
- Let's say that we will be cautious and take a \$1,000/oz gold price and use this across the entire NPV projection. (You can always back-adjust this later on)

Step 4: Calculate Total Revenues for each year
- Take the gold ounces produced each year and multiply it by the \$1,000 gold price we have assumed. That generates the following revenues for each year

Step 5: Forecast Operating Costs for each year
- Either use a set of numbers from an existing economic study or estimate a sensible gross margin for each year. For example, a 60% gross margin on revenues on \$30,000,000 would suggest operating costs of \$12,000,000. For the table below we have just multiplied each total revenue figure by the operating costs of 40% (which is just 100% - 60% gross margin).

Step 6: Forecast Capital Expenditure (CAPEX) and Contingency for each year
- There are two primarily types of capital expenditure; initial and sustaining. These are numbers that are often provided by the company. Here you also should factor in contingency costs, potentially on a flat rate across the five years or weighted if there is high initial capital expenditure

Step 7: Calculate Free Cash Flow
- For each year you need to calculate the free cash flow. Take the Total Revenues and subtract both Operating Costs and Total CAPEX

Step 8: Decide upon a Discount Rate
- This should reflect the stage of the project in terms of maturity. For projects where the resources are only inferred or indicated, and for scoping studies, it is wise to apply a 7.5% discount rate (or potentially 10%). If the project is more developed in terms of resource base or economic studies, then a 5% discount rate can be applied. For the purpose of this example I will use a 7.5% discount rate, which is equivalent to 0.075

Step 9: Calculate the Net Present Value
- Now we have all the numbers required, we can calculate the Net Present Value of the project using a \$1,000/oz gold price. The formula to use is as follows where FCF = Free Cash Flow and DR = Discount Rate

Substituting in the values calculated in Step 7, the equation changes as below

Plugging these numbers into a calculator and adding them together, retrieves a Net Present Value, at a 7.5% discount rate, of \$43.24 million. That tells us that the discounted cash flows of GoldMoon's gold project totals \$43.24m in today's money at the Pre-tax level using a \$1,000/oz gold price. It is simple to adjust for a higher or lower gold price; simply recalculate the revenues line and plug these figures back into the process.

Using this Pre-tax NPV at a 7.5% discount, you can now start to compare the discount to the pre-tax NPV of other projects. If GoldMoon is trading at a market cap whereby the discount between the NPV and market cap is 70%, but all other peers are trading at a 50% discount to their 7.5% NPV, then you can start to make the case for GoldMoon being undervalued. However, the NPV is only one aspect of an economic study and as per this tutorial, you should consider all aspects of a company's mining project.