Mine Economics

Mines are huge investments with long payback. Learn capital and operating costs, cash flow, discounting, Net Present Value (NPV), Internal Rate of Return (IRR), payback period, sensitivity analysis and how price, grade and costs drive project value.

A new copper mine can cost $1–5 billion before it earns a dollar. Engineers must show that future cash flows justify this capital. Because money received later is worth less than money today, cash flows are discounted — producing the NPV used to rank projects.

An analogy

Discounting is like the reverse of a savings account: $100 promised in ten years is worth only what you'd need to deposit today to grow into $100.

Costs and revenue

Capital cost (capex): pre-stripping, shafts, plant, infrastructure, equipment. Operating cost (opex): mining, processing, G&A per tonne. Revenue = metal recovered × price − treatment, refining and transport charges. Royalties and taxes reduce cash flow.

NPV, IRR and payback

NPV > 0 means the project earns more than the discount rate (typically 5–10 % real for mining). IRR is the rate at which NPV = 0 — compare with the hurdle rate. Payback is the time to recover capital (simple but ignores later cash).

Sensitivity analysis

Spider and tornado charts show NPV change for ±10–30 % in price, grade, recovery, opex and capex. Revenue drivers (price, grade, recovery) usually dominate, followed by opex, then capex.

Risk and uncertainty

Monte Carlo simulation of price and geology gives a distribution of NPV and probability of loss. Real options value flexibility (expansions, deferral). Hill of value studies test combinations of cut-off grade and production rate to find the most robust plan.

Formulas

• Net present value: NPV = −I₀ + Σ CF_t / (1 + r)^t
• Level annuity: PV = CF × [1 − (1 + r)^(−n)] / r
• IRR: NPV(r = IRR) = 0
• Cash flow: CF = Revenue − Opex − Tax − Sustaining capex

Worked example: NPV and IRR

Given: Capex $500M; Cash flow $120M/yr for 8 years; Discount rate 8 %

Find: NPV, IRR and payback.

• Annuity factor = (1 − 1.08⁻⁸)/0.08 = 5.747
• NPV = 120 × 5.747 − 500 = $190M
• IRR (NPV = 0) ≈ 17.3 %; payback = 500/120 = 4.2 yr

Answer: NPV $190M, IRR 17.3 %, payback 4.2 years

Worked example: Price sensitivity

Given: Revenue $400M/yr, opex $280M/yr (CF $120M)

Find: NPV if price drops 10 %.

• Revenue $360M → CF $80M
• NPV = 80 × 5.747 − 500 = −$40M

Answer: A 10 % price fall destroys the project — high operating leverage

Common mistakes

• Wrong: Using payback alone to rank projects. — Right: Payback ignores later cash — use NPV and IRR.
• Wrong: Mixing nominal cash flows with real discount rates. — Right: Be consistent: real with real, nominal with nominal.

Applications

• Investment decisions: Boards approve projects on NPV/IRR at feasibility.
• Mine planning: Schedules optimised to bring high-value ore forward.
• M&A valuation: Companies buy and sell mines on discounted cash flow.

Key takeaways

• NPV = −I₀ + Σ CF/(1 + r)^t.
• IRR: rate where NPV = 0.
• Revenue drivers dominate sensitivity.
• Use risk analysis for robust decisions.

Going further

• Monte Carlo valuation: Probability distributions of NPV from price and grade risk.
• Hill of value: 3D surface of NPV vs cut-off and throughput.
• After-tax modelling: Depreciation, royalties and tax holidays change value.