Question 3 of 19: Net Present Value of a Mineral Property

Question 1.3: Net Present Value of a Mineral Property (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

1.3.1 — Definition. Net Present Value is the sum of all a project's future after-tax cash flows, each discounted back to the present at the investor's minimum acceptable (hurdle) rate, less the initial capital outlay — it converts a stream of cash occurring at different times into one single, directly comparable present-day dollar figure. A positive NPV means the project returns more than the hurdle rate demands (value-creating); a negative NPV means it returns less (value-destroying), even if it is nominally profitable on an undiscounted basis.

Given. Initial investment $I_0=\$100\text{M}$; project life $n=10$ yr; salvage value $S=\$20\text{M}$ (received at end of year 10); annual revenue $R=\$40\text{M}$/yr; annual operating cost $C=\$22\text{M}$/yr; discount rate $i=12\%$; compound interest factor $\text{CIF}=(1+i)^n=3.106$; present worth (annuity) factor $\text{PWF}=\dfrac{1-(1+i)^{-n}}{i}=5.650$.

Find. The project NPV (1.3.2), and the investment conclusion it supports (1.3.3).

Approach. Discount the constant annual net operating cash flow as an ordinary annuity using the given PWF, discount the single lump-sum salvage receipt at year 10 using the given CIF (as a present-worth-of-a-single-payment factor, $1/\text{CIF}$), and net both against the initial outlay.

1. Annual net operating cash flow. $$CF_{\text{net}} = R - C = 40 - 22 = \$18\text{M/yr}$$
2. Present value of the 10-year annuity of net cash flow. $$PV_{\text{annuity}} = CF_{\text{net}}\times \text{PWF} = 18 \times 5.650 = \$101.700\text{M}$$
3. Present value of the year-10 salvage receipt. $$PV_{\text{salvage}} = \frac{S}{\text{CIF}} = \frac{20}{3.106} = \$6.439\text{M}$$
4. Net Present Value. $$NPV = -I_0 + PV_{\text{annuity}} + PV_{\text{salvage}} = -100 + 101.700 + 6.439$$ $$\boxed{NPV \approx \$8.14\text{M}}$$

1.3.3 — Conclusion. The NPV is positive ($\approx\$8.14$M), so at a 12% hurdle rate the project is expected to return more value than the minimum the investor requires and should proceed on financial grounds — but the margin is thin relative to the $100M capital at risk (an NPV only ~8% of initial investment), so the decision is sensitive to even modest downside variation in metal price, grade or operating cost; a sensitivity/risk analysis on those inputs, not the single base-case figure alone, should inform the final investment decision.

1.3.4 — Adjustment for mining-specific risk. Mining NPVs should generally be treated more conservatively (effectively lowered, or equivalently evaluated at a higher risk-adjusted discount rate) than a typical industrial venture, because mine cash-flow timelines are unusually long (multi-year permitting and construction before any revenue, followed by a decade-plus production life) and carry compounding geological, permitting, commodity-price and political-risk uncertainty that a manufacturing or services NPV does not — the further out and less certain a cash flow, the more a prudent discount rate should penalize it, so mining projects commonly use a higher hurdle rate (or explicit risk discounts on reserve categories) than the headline "12%" figure alone would suggest.