Industry: Mining and Natural Resources
Product: ModelRisk
Application: Mine planning

The $52M strip-ratio decision

A 12-year copper-gold open-pit project in the southern Andes faced a binary mine-design call: a low-strip pit (waste:ore = 2.1, mine life 11.4 yr, NPV deterministic $312M) or a high-strip pit (waste:ore = 3.8, mine life 14.8 yr, NPV deterministic $364M). The deterministic answer said "take the bigger pit." The Monte Carlo rerun told a different story, and the two NPV distributions below show it at a glance: the high-strip option had P10 NPV = -$56M against the low-strip P10 NPV of $110M — a difference of $166M of downside risk, against a $52M difference in deterministic expected value.


The mine planning team chose the low-strip option. Its distribution is tighter and almost entirely positive; the high-strip distribution is wider, with a fat left tail crossing zero and an upside concentrated in a right tail no one could reliably realise. Mine-planning decisions are sequential, capital-heavy, and exposed to commodity-price tails that mean-reverting industrial-metals dynamics make worse rather than better — deterministic LOM schedules are the wrong tool for choosing between two pits.

The block-model uncertainty that drives everything else

The deposit has 7.2 million SGS-realised blocks at 15 m × 15 m × 10 m, with mean head grade 0.48% Cu and 0.31 g/t Au. Block-level grade is right-skewed LogNormal with σ_log = 0.38 per 60 m × 60 m bench panel. The probabilistic mine plan inherits this directly: each Monte Carlo iteration draws one of 80 conditional realisations from the SGS engine, so the production schedule reacts to genuine grade variability — not the false-precision smoothed mean.

Three more probabilistic priors layer on top of the geology:

• Copper price: mean-reverting LogNormal around $8,400/t with 4.2-year half-life and σ = 0.28 — not GBM, which would let the long-run price drift without bound.
• Gold price: mean-reverting around $1,950/oz, half-life 3.8 yr.
• AISC (mining + processing + G&A): LogNormal across cost-stack components, baseline $1,180/oz AuEq.

Crucially, copper and gold prices are linked by a Gaussian copula with ρ = 0.42 — when copper softens, gold typically firms (safe-haven dynamic), which damps the joint NPV downside relative to an independence assumption by about $24M at P10.

Where Geometric Brownian Motion goes wrong for industrial metals

The standard textbook approach to commodity-price modelling — Geometric Brownian Motion — is right for a few classes of asset but wrong for industrial metals. Copper, nickel and iron ore are mean-reverting on a 3-to-5-year cycle because high prices induce supply response (mothballed mines reactivate, scrap recycling increases) and low prices cull marginal supply. Modelling copper as GBM allows the long-run price to drift to either $4,000/t or $20,000/t with equal probability over 12 years — neither is realistic. The Ornstein-Uhlenbeck process on log-price keeps the long-run distribution centred on the cost-curve equilibrium.

NPV distribution: low-strip vs. high-strip

Running 50,000 trials per pit option gave:

The high-strip pit has the higher mean — but also has 13% probability of returning negative NPV, against the low-strip pit's 3%. The high-strip's upside is concentrated in a right tail where realised copper sits above $9,500/t for most of the LOM; that tail finances roughly half the deterministic NPV advantage.

Why Monte Carlo, not a point estimate

The deterministic answer ranked the pits $364M vs. $312M and recommended high-strip. The probabilistic answer ranked them $341M mean vs. $298M mean but added: high-strip has 13% chance of loss vs. low-strip's 3%, and the $43M expected-value advantage is concentrated in a price tail. For a balance sheet that cannot survive a 13%-probability $56M write-down, the right decision is the lower-mean option.

Tornado: what's actually moving the NPV


Copper price dominates with ±$74M of NPV impact. Block-model grade uncertainty is second. Mining cost ($/t mined, which the high-strip option amplifies) is third — the same input that drives strip ratio drives strip-ratio risk. Gold price ranks fourth in spite of being the second commodity, because the copper-gold copula partly hedges its standalone effect.

What the model changed

• Low-strip pit selected over high-strip — $43M of expected value left on the table to avoid 10 percentage points of probability of loss.
• Forward-sales hedge sized to cover P10 copper exposure (32% of LOM production), reducing P10 NPV downside by another $36M.
• Mine plan optimised for "value at P10" rather than NPV mean — shifted three of the early-LOM bench schedules to higher-grade, higher-confidence blocks, lifting the P10 by $18M for zero mean cost.
• Capital phasing delayed $58M of plant-expansion capex into year 4, gated on first-three-years actual head grade vs. forecast P50 — a real-option formulation only the probabilistic model could support.

ModelRisk functionality used

• Mean-reverting LogNormal (Ornstein-Uhlenbeck on log-price) for both copper and gold, replacing GBM and producing a long-run price distribution centred on the cost-curve equilibrium.
• Gaussian copula linking copper-gold prices with ρ = 0.42, capturing the safe-haven hedge and damping joint P10 NPV by $24M.
• 80 SGS block-model realisations feeding the production schedule, so head-grade variability is real rather than smoothed.
• Real-option capex-gating module computing the value of delaying $58M of plant expansion until year 4 head-grade data is in — a probabilistic-only construct worth $14M of mean NPV.
• P10-optimised mine schedule versus mean-optimised, demonstrating that the "best" early bench sequence depends on which moment of the NPV distribution the project is being designed for.

The right pit is rarely the one with the highest mean NPV; it is the one whose distribution your balance sheet can survive.