Break Even And Internal Cut-Off

Breakeven cut-off grades and Internal cut-off grades are defined as follows:

Breakeven cut-off grade is defined as the grade where revenue generated will exactly pay all costs and give 0 profit. Internal cut-off grade is defined as the grade where revenue generated will pay for all processing costs only. Material between the lower internal cut-off grade and the higher breakeven cut-off gradewill pay for all processing costs and part of the mining cost. The idea behind the internal cut-off grade is that if you must mine block X to uncover higher grade ore block Y below and block X has enough metal to pay for its processing costs and part of its mining cost (say 60%), than you are better off sending block X to the processing plant rather than the waste dump. The Lerch Grossman pitoptimization program makes sure that the deeper block Y has a sufficient profit to pay for the other 40% of the mining cost of block X in this example.

Following are detailed numerical examples of breakeven cutoff grade and internal cutoff grade calculations for both mill ore and leach ore.

Example 1: Leach ore

Mining cost = $0.75/tonne
Leaching cost = $0.10/tonne
SXEW cost =$0.16/lb cu
Selling costs = $0.04/lb cu
Recovery = 25%
Cu price = $0.85/lb cu

1. Breakeven cut-off grade is grade where revenue generated will exactly pay all costs and give 0 profit. Since SXEW costs and Selling costs are in units of $/lb we include these costs in the revenue calculation by subtracting them from the copper price. Calculate breakeven cut-off grade with the following formulas:Profit/tonne = Revenue/tonne – Cost/tonne
0 = Revenue/tonne – Cost/tonne
Revenue/tonne = (Cu Price – SXEW cost – selling cost) * lbs cu/tonne * recovery
Cost/tonne ore = mining cost + leaching cost
Substitute numbers and solve for lbs cu/tonne:
0 = ((0.85 – 0.16 – 0.04) * lbs cu/tonne * .25) – (0.75 + 0.10)
lbs cu/tonne = 5.23
Convert 5.23 lbs cu/tonne to % cu:
(5.23/2204.6) * 100= 0.237% cu = breakeven cut-off grade for leach

2. Internal cut-off grade is grade where revenue generated will exactly pay processing costs only. Since SXEW costs and Selling costs are in units of $/lb we include these costs in the revenue calculation by subtracting them from the copper price. Calculate internal cut-off grade with the same formulas but leave mining cost out this time:Profit/tonne = Revenue/tonne – Cost/tonne
0 = Revenue/tonne – Cost/tonne
Revenue/tonne = (Cu Price – SXEW cost – selling cost) * lbs cu/tonne * recovery
Cost/tonne ore = leaching cost
Substitute numbers and solve for lbs cu/tonne:
0 = ((0.85 – 0.16 – 0.04) * lbs cu/tonne * .25) –0.10
lbs cu/tonne ore = 0.615
Convert 0.615 lbs cu/tonne to % cu:
(0.615/2204.6) * 100 = 0.028% cu =internal cut-off grade for leach

The internal cut-off grade is very low because of the low costs for leaching/SXEW operation.
For material between the internal cut-off grade and the breakeven cut-off grade you will lose less money sending the tonne to a leach dump rather than sending the tonne to a waste dump. For material above the breakeven cut-off you will begin to make a profit from leaching.This is illustrated in the table below which compares values/tonne for a set of copper grades:

%Cu grade .27 .25 .237 .2 .15 .1 .05 .028 .02
$ Value going to Leach 0.11 0.05 0.0 -0.13 -0.31 -0.49 -0.67 -0.75 -0.78
$ Value going to Waste
(= mining cost) -0.75 -0.75 -0.75 -0.75 -0.75 -0.75 -0.75 -0.75 -0.75

Example 2: Mill Ore
Mining cost = $0.75/tonne
Milling cost = $2.60/tonneSmelting cost = $0.14/lb cu
Refining costs = $0.03/lb cu
Cu Transportation and selling costs = $0.02/lb cu
Cu Recovery = 85%
Cu price = $0.85/lb cu

Moly processing costs = $0.05/tonne
Moly treatment costs = $0.38/lb Mo
Moly Transportation and selling costs = $0.03/lb Mo
Moly recovery = 35%
Moly Price = $3.50/lb mo

Mill ore has two revenue generating metals, copper and moly. The...