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In this section, the mathematical tools are developed to calculate the value of a tonne of ore sent to a mill, processed and concentrated, and sold to a smelter. This section introduces the concept of the net smelter return (NSR). It discusses the main components of the equations to calculate NSR, indicating the sources of information for each as a function of the design stage. The concept of the NSR factor is presented, along with its uses, applications and limitations.
A complete example of the calculations for a polymetallic ore is worked through and discussed.
An excel file also is also provided so that the reader can review the equations in detail.
Contents
Net smelter return
The net smelter return (NSR) refers to the revenues expected from the mill feed, taking into consideration mill recoveries, transport costs of the concentrate to the smelter, treatment and refining charges, and other deductions at the smelter.
Components of the calculations
While a few other factors are sometimes mentioned in the literature and in practice, the list presented here captures 98% of the net smelter return value. Not all items listed are applicable to each metal concentrate; for this reason, the reader will have to review the references provided at the end of this section to see where each item applies.
The main factors required for the calculations are:
 Recovery factor of the metal at the mill  to know what proportion of the metal sent to the mill is actually sold.
 Concentrate grade  to establish how much metal is contained in a tonne of concentrate.
 Transport cost  from the gate at the mine site to the smelter. Associated costs are charged for loading and representation at port facilities.
 Payable metals  to establish the base quantity of metal that the smelter will use to determine payment. Some deductions are fixed, while others are based on a sliding scale as a function of the grade of the metal in the concentrate.
 Treatment charges  to determine the cost of processing one tonne of concentrate at the smelter.
 Penalties  the extra cost of processing deleterious elements present in the concentrate.
 Price participation  a proportional escalator cost to capture large metal price variations during the contract period.
 Refining charges  to determine the cost of refining the metal recovered at the smelter.
At the scoping level, most information can be estimated from spot prices discussed in press releases. At the Prefeasibility study level, smelter availability may become an issue and discussions must be held with a few smelters. Detailed contracts terms are not necessarily determined through these discussions, but better estimates can be made. Contracts must be discussed with specific smelters at the feasibility level. Table 1 presents the best information sources for calculating components at each of these three stages of mine design.
Table 1: Sources of information at the different stages of the design process
Net smelter return  Scoping  Prefeasibility  Feasibility 

Treatment charges  Spot prices  Discussions with smelters  Negotiated contract 
Refining charges  Spot prices  Discussions with smelters  Negotiated contract 
Penalties and other deductions  Estimated from experience  Discussions with smelter  Negotiated contract 
Transport costs  Spot prices  Discussions with transporter  Negotiated contract 
Net smelter return factors
The NSR factors refer to the value a unit of metal grade ($ per gram of gold, $ per % nickel). These factors can be used in a variety of situations:
 Estimate rapidly the value of every block in the resources and reserves models by multiplying the grades by the factors. The blocks can easily be sorted as required.
 Estimate the value of a mining sector for an economical study.
 Calculate the revenues of mine plans.
 Calculate the value of broken mineralization in the mine to decide whether to send it to the mill or to waste.
 Perform quick metal price sensitivity studies.
There are many advantages to this approach:
 Polymetallic ores grades are rapidly converted to dollars per tonne.
 The value of reserves can be quickly compared to the applicable costs to determine their viability; cutoff grades become cutoff NSRs.
 At the design stage, spreadsheets can be used to quickly identify economical reserve blocks.
 During the extraction of a sector, its value can be quickly estimated by comparing the reconciled grades to the design.
 The effect of commodity price fluctuations can be evaluated quickly.
The method does have some limitations:
 This approach tends to smooth out the statistical distribution of the block values. This will happen if the metal recovery at the mill is proportional to the feed grade. This way, lower grade blocks are overvalued and higher grade blocks are undervalued.
 This approach is valid only within the operating parameters of the mill.
Example:
Let’s assume that chalcopyrite and sphalerite produced in the mine are sent to a mill with copper and zinc flotation circuits, and that the copper concentrate is sold to two smelters and that the zinc concentrate is sold to a zinc smelter. The detailed calculations can be found in the Excel file NSR calculations.xlsx.
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Figure 1: The milling process
In this example, the mill feed is 275,000 tonnes grading 2.32% Cu, 2.55 g/t Au, and 5.69% Zn. This mill feed can represent three months’ or a year’s production from the mine, or is the grade of a sector on which an economical study is conducted. Either way, the NSR factors calculated for this feed can be applied to every individual reserve blocks or stopes to calculate their value.
As shown in Table 2, copper and gold are recovered in the copper concentrate and zinc and minor gold are recovered in the zinc concentrate. The copper concentrate grades 21% and the zinc con grades 53%. Values marked in yellow are given and others are calculated.
Table 2: Metallurgical balance
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Table 3 details the steps to calculate the value of the copper and gold in the copper concentrate sold to smelter A. In the case of copper:
 A fixed deduction of 1.1 units (22.05 lbs * 1.1) is charged.
 The treatment charge is equal to $75 per tonne of concentrate. Transport, with loading and representation, cost $39 per tonne.
 The refining charges are equal to $0.075 per pound of payable copper.
As for gold:
 The metal deduction is equal to 2.5 grams. This deduction can be based on a sliding scale set as a function of the concentrate gold grade.
 No treatment or transport costs are applied. This is a judgment call on the part of the user to decide if the costs apply or not and in which proportions they do. In the example, it is assumed that this is the amount of gold present (or absent) in the ore and concentrate will have no influence on the treatment and transport costs of the copper concentrate and that therefore the gold should not have to pay for that portion of costs.
 Refining charges are equal to $6 per payable ounce of gold.
As a result, the copper and gold net smelter returns for copper concentrate sold to Smelter A are equal to $511 and $515 per tonne of concentrate, or $48.01 and $48.37 per tonne of ore. When these numbers are divided by the mill feed grade, the copper and gold NSR factors are equal to $20.69 per % Cu and $18.97 per gram of gold.
Table 3: Estimation of the value of metals in the copper concentrate sold to smelter A
The exercise is repeated for copper concentrate sold to smelter B and zinc concentrate sold to smelter C, and the results are combined in Table 4.
Table 4: Compilation of NSR returns
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These factors can be used to estimate the value of reserve blocks, stopes, daily production, or the average value of the mill feed, as shown in Table 5.
Table 5. Net Smelter Return of mill feed
References
Goldie, R. A. (1992). Net smelter return models and their use in the exploration, evaluation and exploitation of polymetallic deposits. Ore Deposit Models V. II, Geoscience Canada Reprint Series 6, (pp. 6375). This reference gives clear information on the components included in the equations for many metal concentrates.
Goldie, R. J. (1996). The dollar: An economic geologist's most important unit of measurement. CIM Bulletin , 89 (997), pp. 3941.
Lafleur, P.J. (1988, November ). Statistical Geology. The Northern Mining Magazine, 2529. This reference gives an example of an NSR factor calculation for a polymetallic ore.