Expenditures that are related to time rather than to tonnage or production require careful thought, but there is a clear rule that allows you to decide which should be included:
Any expenditure that would stop if mining stopped must be included in one of the costs input to Four-D, and conversely, any expenditure that would not stop if mining stopped must be excluded.
The reasoning behind this is that, when the optimizer adds a block to the pit outline, it may effectively extend the life of the mine. If it does, the extra costs that would occur as a result of this extended life must be paid for. Otherwise the optimizer will add blocks to the pit that reduce rather than increase its real value.
Since the optimizer can only take note of costs expressed through the block values, it is necessary to share these time-related costs between the blocks in some way. How they should be shared depends on whether production is limited by mining, by processing or by the market. Usually it is limited by processing, and, in this case, only the mining of an ore block extends the life of the mine. The ore block values should therefore include an allowance for time costs. This is done by adding an appropriate amount to the processing cost per tonne. If production is limited by mining, as in some heap leach operations, every block that is mined extends the life of the mine, so that time costs should be added to the mining cost. A market limit means that time costs should be added to the selling cost. In each case, the amount added is the time costs per year divided by the throughput limit per year.
During analysis, as distinct from optimization, it is possible to handle time costs explicitly.
The reference block
Four-D assumes that all costs that you give it are calculated for a particular block in the model. This block, called the “reference block“, is usually at the surface, but it can be anywhere you nominate. The concept of a reference block is very important in Four-D.
Waste mining and processing costs should be worked out for the reference block even if there is no appropriate material in that block. That is, the reference block may consist entirely of barren material, but you should still work out the processing cost as though the material to be processed was in that block.
Four-D deals with any variation of these costs, such as the increase of mining cost with depth, by the use of “cost adjustment factors”. There can be adjustment factors for waste mining cost and for processing cost for each block in the model. There can be a second adjustment for waste mining cost that depends on rock type.
Extra ore mining costs
Because different equipment may be used, it is not uncommon for the cost per tonne of mining ore to be greater than the cost per tonne of mining waste. For Four-D purposes, this extra cost should be added to the processing cost.
For example, if the costs of mining and processing ore are $1.54 and $7.37 respectively, and the cost of mining waste is $0.82, then, for Four-D purposes, we use a processing cost of $8.09 (=1.54 + 7.37-0.82).
Remember that it is important to calculate these figures initially as though mining were taking place at the reference block, even if there is no mineralized material in the reference block. If the costs are different in other parts of the model, then the differences should be handled by including positional mining and/or processing cost adjustment factors in the model.
Once you have calculated the various costs then, for optimization purposes, they are input to Four-D as ratios rather than as currency amounts. In effect, the cost of mining undefined waste at the reference block is used as the unit of currency and other costs are expressed in such units.
Thus processing cost is entered as the cost of processing a tonne of material divided by the cost of mining a tonne of undefined waste at the reference block. Rehabilitation cost and selling cost are handled in the same way.
During analysis, after the optimization, you enter the cost of mining undefined waste at the reference block, and the ratios are then used to calculate the processing, rehabilitation and selling costs from this.
Some examples of the handling of various costs may be helpful and these are discussed below.
Consider a processing mill that costs $10m to build and commission.
If the mine were to be shut down, for whatever reason, on day 2 of operations, the mill would have a certain salvage value, say $6m. In this case $4m has gone for ever. It is an “up-front” or “sunk” cost that must be subtracted from any optimized value of the pit itself, or entered during analysis as an initial capital expenditure. It is not a cost for optimization purposes.
We can deal with the remaining $6m in one of two ways.
If we assume that there will be an on-going program of maintenance and capital replacement that will keep the salvage value of the mill close to $6m in today’s dollars, then the $6m is theoretically recoverable when the mine is closed, and so is not a cost. However the maintenance and periodic capital replacement expenses are costs for these purposes, because they would stop if mining stopped. They should be averaged and treated as a time cost.
Alternatively, we can assume that only essential maintenance will be done, and that the salvage value of the mill will progressively decline. In this case the expected rate of this decline should be treated as a time cost. Note that the rate of decline is not necessarily the same as the depreciation rate that is used by accountants. In most cases the depreciation rate is set by taxation considerations, and may reduce the book value to zero when the salvage value is clearly not zero.
We discuss the interest on the salvage value below.
If the expected life of the mine is shorter than the operating life of a truck, then truck purchases can be treated in the same way as the cost of the mill.
If the life of the mine is much longer than the life of a truck, then trucks will have to be purchased progressively to maintain the fleet, and such purchases will stop if mining is stopped. Consequently the cost of purchasing trucks should be averaged out over the life of the mine and treated as a time cost.
Unless the life of the mine is expected to be very long, some compromise between the above two approaches is usually required.
Contract mining companies must take these factors into account when quoting for a job, and it is sometimes useful to think as they do when you are working out the costs for your own fleet. You should include everything that they do, except for their allowance for profit.
On-site administration costs will usually stop if mining is stopped. They must therefore be treated as a time cost.
Head office administration costs may, or may not, stop if mining stops at this particular mine, and thus may, or may not, be included.
Bank loans for initial costs
Repayment (principal and interest) of a bank loan taken out to cover initial set-up costs will have to continue whether mining continues or not. It should therefore not be included in the costs used when calculating block values.
Of course, these repayments will have to come from the cash flow of the mine. If the mine is not going to produce enough cash flow to cover them, the project should not proceed. You should not introduce these repayments as costs in an attempt to “improve” the optimization. The result will be quite the opposite. You will get a smaller pit with a smaller total cash flow.
Although the bank loan repayments themselves are not included, some of the items that the loan was used to pay for may be included, as is explained further below.
Bank loans for recoverable costs
If you borrow money from the bank for day-to-day working capital or for items, such as the $6m discussed in the mill example above, then you can reasonably expect to repay the loan if mining stops. Consequently the interest paid on such a loan is a cost that stops if mining stops. It should therefore be treated as a time cost. Note that Four-D works throughout in today’s currency, so the interest rate used should not include an allowance for inflation.
Grade control costs
It is often necessary to do grade control work on waste as well as ore. In this case, grade control costs apply to waste costs too. If only some of the waste is grade controlled, then the correct way to handle it is to load the cost of those particular waste blocks. However many users make an estimate of the tonnes of such waste per tonne of ore, and load the cost of mining ore.
Support – cable bolts
If the permitted pit wall slope is to be increased by the use of cable bolts, the cost per tonne is related to pit size, which has to be estimated. Then a cost per square metre of wall can be transformed into a cost per tonne of waste. This is an iterative estimate, but fortunately costs per tonne are usually low.
These examples do not cover all possible costs, but should indicate how to treat most costs.