Industry: Mining and Natural Resources Product: ModelRisk Application: Mine-Plan Sequencing under Geological and Price Uncertainty
The deterministic LOM model handed two answers across the metallurgist's desk. Plan A — a 20-year uniform extraction at 12 Mt/yr blended head grade — returned an NPV of about $390M. Plan B — a phased plan, 5 years of high-grade (top-quartile) ore at 6 Mt/yr, then expand to 12 Mt/yr for 18 more years — returned roughly $370M. The two strategies sat within deterministic noise of each other and the decision drifted for a year. ModelRisk reframed the same question: not which plan has the higher mean, but which plan owns the better left tail and the earlier cash-flow profile that the project finance covenant actually rewards.
A 200-million-tonne copper-gold-molybdenum deposit at 0.65% Cu was put through the same simulation under both extraction sequences. The two plans land almost on top of each other in mean NPV ($436M uniform, $431M phased), but the shape of the distribution — where the left tail sits — is where the decision actually lives:
Both plans draw from the same orebody, but they sample it differently. The uniform plan averages everything; the phased plan front-loads the top-25% grade zone at roughly 1.4× the deposit mean (~0.91% Cu) for five years before reverting to the diluted remainder (~0.57% Cu).
The two plans land roughly on top of each other in mean NPV, but the distributions tell a different story. Phased shows a tighter, more concentrated distribution. The uniform plan has a longer left tail driven by the combination of full upfront capex, longer permitting, and an extra ~2 years before first cash. Both plans carry a substantial chance of a negative-NPV outcome at the wide price and grade uncertainty modelled — roughly 41% for uniform against 37% for phased — but the phased plan's shorter left tail (P10 of −$901M versus uniform's −$1,170M) is the difference that the project-finance covenant actually prices.
The same picture as cumulative probability:
Below roughly $580M of NPV the phased CDF lies above the uniform CDF — phased is the downside-protected choice across the entire lower half of the outcome range. Above that crossover the two curves swap, because the bigger Plant 1 in the uniform plan can monetise an upside copper-price scenario more aggressively, giving uniform the heavier right tail (P90 of $2,246M versus phased's $1,898M). The phased plan is the downside-protected choice; the uniform plan is the upside-leveraged choice. The choice depends on where the project finance covenant lives, not where the mid-case lands.
Copper price and ore grade dominate, as always — these are the two LME-and-drilling inputs the project effectively bets on. Recovery ranks third, just ahead of unit OPEX and capex. Permit delay appears sixth — the phased plan's smaller starter plant carries a much shorter delay distribution, which is one mechanism by which it earns the tighter NPV curve. Tonnage is the smallest driver here because LogNormal σ on tonnage is the smallest, and tonnage interacts only weakly with the early-life cash flows that discount most heavily.
Sweeping the assumed copper price from $5,500/t to $12,000/t under both plans:
At Cu prices below roughly $8,500/t the phased plan wins on mean NPV — its early cash flow at top-quartile grade carries the project through the bear scenario before the long-tail risk of running Phase 2 at $6,500/t copper. Above that crossover the uniform plan pulls ahead on the mean, because the full plant monetises the upside more efficiently; at $12,000/t copper the uniform mean of $1,890M beats the phased $1,759M. The two strategies are close on a trial-by-trial basis — the probability that the phased plan beats the uniform plan drifts down only gently with copper price, from about 59% at $5,500/t to 48% at $12,000/t, crossing 50/50 near the $9,000–10,000/t band. The mean lines diverge more than the win-probability does, because phased trades a thinner left tail for a thinner right tail. The project economist now states the recommendation conditional on the assumed price deck, not as a single answer.
A mine plan is not "the LOM schedule" — it is the conditional NPV distribution given a sequence of decisions that the geology and the market together police. Monte Carlo simulation in ModelRisk is what makes the comparison between two plans honest: same future, same draws, two strategies, and a left tail you can actually defend in front of the people writing the cheques.