# Discount rate

The discount rate is a factor applied to a projected income stream in order to discount the value of future benefits and costs to its present value  . The riskier a project is, the higher the discount rate, which will in turn reduce the future value of cash flows for the project. The discount rate of a mining project takes many risks and variables into account, including: metal price fluctuation, marketability of the commodity, location of the project, stage of development, and experience of the owner . There are different ways of determining a projects discount rate, and these methods will be briefly analyzed. Figure 1: Components of real discount rates at different stages of project development. Revenue factors include metal price, grade, recovery and throughput. 

## Need for a discount rate

The preferred methods of project evaluation are those that incorporate annual cash flow projections and recognize the time value of money, such as net present value (NPV) and the discounted cash flow rate of return (DCFROR) approaches . The mathematics required to calculate the NPV and DCFROR values is fairly straightforward, however both methods require the definition of an appropriate discount rate to establish investment criteria. This rate is used as the discount rate in the NPV method, and the minimum rate for the DCFROR. Many risk assessment techniques use discounted cash flow evaluation methods as well.

## Appropriate discount rates

Literature on discounted cash flow evaluations does not specifically deal with the selection of discount rates for mineral project evaluations . However, it should be possible to determine what an appropriate discount rate is based on industry expectations for project returns, risk factors associated with the specific mineral project, and risks related to mineral projects in general. Discount rates commonly used within the mining industry range between 5% and 15%. Higher discount rates may be used for especially high risk projects or projects in early stages of development. An example of discount rates throughout various stages of a project along with a breakdown of components are shown in Figure 1.

## Risk

The discount rate for a mineral project comprises of, either directly or indirectly, three principal components of risk:

Risk-free Interest Rate – The value of the long-term, risk-free, real interest rate. A proxy for this value is a government bond from the country of operation that has the same duration as the project life. For example, a project in Canada with a ten-year mine life would use the interest rate from a ten year government of Canada bond as their risk-free rate. .

Mineral Project Risk – Mineral project risks are risks associated with reserves, mining, processing, construction, environmental compliance, new technology, cost estimation, and the commodity being mines. Historically base metal projects have has a higher discount rate than precious metal projects as base metals are seen as being more susceptible to economic uncertainty, causing their prices to fluctuate more than precious metal prices would.

Country Risk – Country risk refers to the risks related to country-specific social, economic and political factors, these factors are expanded upon in Table 1. Country risk premiums range from 0% to 14%, this range is shown in Figure 2.

 Political Risk Government stability Political parties Constitutional risk Quality of government Foreign ownership policy (risk of nationalization) Foreign policy Government crises Taxation instability Environmental policy, environmental protectionism Transportation Climate Currency stability Foreign exchange restrictions Distribution of wealth Ethnic or religious differences withing the indigenous population Literacy rate Corruption Labour relations

## Methods for determining discount rates

It should be noted that for feasibility studies, pre-feasibility studies, preliminary economic assessments and several other instances of project evaluation, the project is assumed to be financed with 100% equity and not through other forms of financing such as debt or streaming arrangements.

### Build-up method

The build-up method consists of determining the appropriate risk-free rate to use for the project and then adding additional risk premiums to this rate to determine a cost of equity. Examples of premiums that are added to the risk-free rate are as follows:

Project Location- the location of the project can impact the riskiness of a project. If the project is located in an unstable country then this warrants a higher risk premium to be applied to the project. Examples of risk premiums for locations are shown in Figure 2.

Size Premium- the size premium is applied based off of how large a company is. The larger the company the greater the ability of the company to obtain financing and to survive economic downturns, which means the company is considered less risky than a smaller company. Example size premiums and the size of the companies that correspond to the premiums are presented as Figure 3.

Market Risk Premium- The market risk premium is the premium over the risk-free rate that could be expected if one invested in the stock market instead of the project. This premium can be estimated by identifying the appropriate index that follows the stock market of interest and calculating the long-term average market risk premium. This is done by subtracting the market return for the year in question from the risk free rate from that year and then averaging them over a period of time deemed acceptable .

### Capital asset pricing method (CAPM)

CAPM is the one of the most widely used ways to calculate the cost of equity. It is calculated using the theory that the cost of equity is related to the expected market cost of the equity, which is calculated using the beta (β) of the company’s shares and the market premium or discount applied to these shares. This is done by determining the appropriate risk-free rate (rf) and then adding the beta of the company multiplied by the market risk premium, which is the expected market return (rm) minus the risk-free rate. This formula is shown as Equation 1 with the cost of equity denoted as Ce.

### Industry survey method

This method requires similar projects, perhaps in commodity, size or country, to be examined for the discount rates they used for project evaluation. Then these discount rates are compiled to determine a discount rate which would be appropriate for project evaluation. An example of this method for a copper mine in Chile is shown below in Table 2.

 - Location Commodity Discount Rate Lundin Mining (Candelaria) Los Andes Copper (Vizcachitas) NGEX Resources (Los Helados) KGHM Polska (Sierra Gorda) Average Chile, Copiapo Province Chile, Los Andes Province Chile, Copiap Province Chile, Antofagasta Province N/A Copper, Gold, Silver Copper, Molybdenum Copper, Gold, Silver Copper, Molybdenum N/A 10% 10% 8% 8% 9%

### Weighted Average Cost of Capital (WACC)

When it is no longer assumed that a project is financed with 100% equity the WACC method should be used. WACC takes into account a company’s capital structure, how much debt and equity the company has used to finance themselves so far, and calculates an aggregated total cost of the financing so far. This calculation is done by taking the percentage of equity (Equity) multiplied by the cost of equity (Ce) plus the percentage of debt (Debt) multiplied by the cost of debt (Cd) all divided by the total amount of equity and debt raised so far. This equation is shown as Equation 2 and should provide the expected cost for the company to raise funds.