Cut-off grades. Everyone gets hung up about cut-off grades, as if they’re voodoo. The basic text is Lane’s Economic Definition of Ore (1968) but it’s a tough read. By way of simple explanation:
The first thing that needs to be understood is what is the limiting factor of the mine. Is it mine limited, mill limited or market limited?
- An open pit can mine as much dirt as you like, but the mill has a capacity of 1.5Mtpa, so it’s mill limited.
- An underground mine can fit 1Mtpa up the decline to feed a 1.5Mtpa mill. It’s mine limited.
- A crappy iron ore junior could sell 8Mtpa of 58% high-phos fines in 2012, but now can’t sell a cracker. It’s market limited.
Mill limited is generally the case. Market limited is difficult to analyse and I won’t go into it here. Nor will I go into the mathematics, but, when analysing cut-off grades, fixed costs are added to the limiting factor.
So, for the open cut, the mill operating cost is, say, $25/t plus $8/t fixed costs (rule of thumb – each department in a mine costs at least $1Mpa: geology, mining, maintenance, admin, survey, safety & enviro etc.). This may have the effect of reducing the amount of ore available but also reduces the variable mining cost, which, counterintuitively, may also expand the pit to find more ore to pay for the fixed costs. It depends on the operation.
Cut-off grades introduce opportunity cost. Each tonne of ore fed into a mill in a mill-limited or mined in a mine-limited operation potentially displaces a tonne of higher-grade material that could produce higher margins at the same operating cost.
This is why ore loss and dilution are so important (rule of thumb – 5% for each in a well managed, bog-standard pit, mostly much higher underground). If you feed in a tonne of mullock, it costs you $33, for no return.
Having understood the limiting factor, there are usually then three cut-off grades applied to the operation:
- Incremental cut-off grade: mill operating cost/(grade x recovery x metal price). Mathematically, the mining cost in open pits cancels out and is irrelevant – if ya don’t mine, ya don’t got no ore.
This is used to determine how much of the Mineral Resource may be economic. The best strategy is to stockpile low-grade ore or marginal ore for later processing if higher grade material is available and the dirt doesn’t deteriorate with time, reducing recoveries through (usually) oxidation of sulphides. It is better to fill the mill with this material to carry fixed costs when the project is mine limited or temporarily mine limited for some reason (eg the wet season).
- Operating cut-off grade: (mill operating cost + mine operating cost + site overheads)/(grade x recovery x metal price). This is used in mine planning for monthly, quarterly, annual plans, whatever.
- Full cut-off grade: (mill operating cost + mine operating cost + site overheads + opportunity cost)/(grade x recovery x metal price). This is used to maximise the margins early on in the life of the mine to maximise NPV and repay capital.
The opportunity cost is where most people become confused. An opportunity cost is defined as “the cost of taking a particular course of action as opposed to another option”. Lane mathematically relates opportunity cost in mining projects to a project’s present value and discount rate, simultaneously calculating cut-offs for mining, processing and marketing to result in an optimal cut-off. Again, the mathematics is involved. This can be done on a spreadsheet, but there are a number of commercial software algorithms that do this.
From these cut-offs, the engineer can derive a schedule and cash-flow model.
It’s important to consider that cut-off grades are boundary values. Three simple rules:
- Don’t process anything that makes less money
- Fill the mill to ensure fixed costs are covered. How many projects are there that have large legacy mills with large fixed costs but not enough ore at hand to fill the mill? Campaign milling is not ideal.
- Fill the mill with the material that makes the most money first.
The actual cut-offs applied are an output and not an input.
At the end of the mine’s life, when the Resource has been mined and the mill paid off and the Directors are backslapping and high-fiving, the stockpiled marginal ore can be fed through the mill, hopefully producing sufficient revenue to pay for rehab and closure costs.
Time dependent, folks. The Competent Person for Reserves MUST take a reasonable view on future commodity prices and exchange rates. For example, if you see a cobalt “Reserve” that uses a cobalt price significantly greater than the consensus future price at the time of reporting (and there’s plenty of places you can get this from), then run or start shorting.
A lot of this stuff can be automated by various software packages, which takes the labour out of it and is better at performing complex iterations and examining constraints. But it is important that the resultant schedule be carefully examined by a competent engineer and modified to smooth production. A lumpy schedule causes variable demands on equipment, which leads to operational problems.
In short, no meaningful schedule, no Ore Reserve. The engineer must demonstrate that the ore is physically accessible during the life of the operation. An annualised summary just doesn’t cut it.