18-Geol-B8 Resource Economics & Valuation · May 2016
Question 1 of 6: Net Smelter Return Royalty Purchase — Value and Minimum Acceptable Rate
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — May 2016 — 04-Geol-B8, Resource Economics and Valuation. Three-hour, open-book exam; any non-communicating calculator permitted. Six questions are printed; the exam's own cover notes state that only the first four questions in the answer book are marked, and each of the six is of equal value (25 marks) — all six are answered here as a complete study resource. Most questions require mathematical solutions, and clarity and organization of the steps involved are explicitly graded.
Reference texts: Torries, Evaluating Mineral Projects: Applications and Misconceptions (SME, 1998) — discounted cash flow valuation of mine projects, net smelter return economics, royalty valuation, and cut-off grade theory; Rudenno, The Mining Valuation Handbook, 4th ed. (Wrightbooks, 2012) — comparable-transaction and appraised-value (Kilburn) methods, copper-equivalent grade, and resource/reserve-stage valuation; EGBC Geoscience Professional Practice Guidelines for assumption-disclosure conventions on open-book calculations.
Question 1: Net Smelter Return Royalty Purchase — Value and Minimum Acceptable Rate (25 marks)
Given. The deposit, processing and marketing terms for the operation underlying the royalty, and the price/terms of the royalty itself, are as below. The net smelter value (NSV) of the copper concentrate is defined by the exam's own variables: $M$ = concentrate grade, $D$ = unit deduction, $P$ = copper price, $r$ = refining charge, $T$ = treatment charge, $C$ = gold credit.
Item
Value
Recoverable reserves
20.0 million tonnes
Annual mining/milling capacity
2.0 million tonnes/yr
Head grades
2.5% Cu, 1.0 g/t Au
Processing recoveries
Cu 90%, Au 75%
Metal prices
Cu USD 3,679/tonne, Au USD 15/gram
Copper concentrate grade $M$
30% Cu
Unit deduction $D$
2.0%
Refining charge $r$
USD 200/tonne Cu
Treatment charge $T$
USD 100/tonne of concentrate
Gold credit terms
pay for 93.3% of gold in concentrate, less 1 g/t
Cost of capital
8%
Royalty offered / price
3% NSR for USD 20 million
Operator's annual tax payments
USD 15 million (belongs to the mine operator, not the royalty holder)
Find. Whether the USD 20 million purchase of the 3% NSR royalty is justified, and the minimum royalty rate GeoRoyalties should accept for that same USD 20 million.
Approach. Build the net smelter value per tonne of concentrate from the mill's own mass balance (concentrate yield and gold grade in concentrate), apply that per-tonne-of-ore over the fixed annual capacity to get the project's total annual NSR, take 3% of it as the royalty cash flow, discount that 10-year annuity at the 8% cost of capital, and compare the resulting present value against the USD 20 million asking price; the same annuity relationship, solved in reverse, gives the minimum acceptable royalty rate.
Mine life and concentrate mass balance. Mine life $=20.0/2.0=10$ years. Copper reporting to concentrate is $2.5\%\times90\%=2.25\%$ Cu by mass of ore; at a 30% Cu concentrate grade the concentrate yield is
$$y_{\text{conc}}=\frac{0.025\times0.90}{0.30}=\boxed{0.0750\ \text{t concentrate/t ore}}\quad(13.33\ \text{t ore per t concentrate}).$$
Gold grade reporting to concentrate. Gold recovered per tonne of ore is $1.0\times0.75=0.75$ g/t; spread over the 13.33 t of ore that makes one tonne of concentrate,
$$\text{Au}_{\text{conc}}=0.75\times13.33=\boxed{10.0\ \text{g Au/t concentrate}}.$$
Net smelter value per tonne of concentrate. The paper's printed NSV formula is reconstructed from its stated variable list as $\text{NSV}=\dfrac{M-D}{100}(P-r)-T+C$ — the payable copper fraction times its net (price less refining) value, less the flat treatment charge, plus the gold credit. With $M-D=30-2=28\%$:
$$\text{NSV}_{\text{Cu}}=\frac{28}{100}\times(3679-200)=0.28\times3479=\$974.12/\text{t conc},\qquad \text{after treatment: }974.12-100=\$874.12/\text{t conc}.$$
The gold credit pays 93.3% of (10.0 − 1.0) = 8.397 g/t at USD 15/g:
$$C_{\text{Au}}=0.933\times(10.0-1.0)\times15=8.397\times15=\$125.96/\text{t conc}.$$
$$\text{NSV}=874.12+125.96=\boxed{\$1000.08/\text{t concentrate}}.$$
Annual net smelter return of the whole project. Converting to a per-tonne-of-ore basis via the concentrate yield, then scaling to the 2.0 Mt/yr capacity:
$$\text{NSV}_{\text{ore}}=1000.08\times0.0750=\$75.01/\text{t ore},\qquad \text{Annual NSR}=75.01\times2{,}000{,}000=\boxed{\$150.01\ \text{million/yr}}.$$
The operator's own USD 15 million/yr tax payment plays no part in this — an NSR royalty is a fixed percentage of gross smelter revenue, paid ahead of (and unaffected by) the operator's cost structure, financing or tax position.
Value of the 3% royalty and the purchase decision. The royalty cash flow is $0.03\times150.01=\$4.500$ million/yr for the 10-year mine life. At the 8% cost of capital the 10-year annuity factor is $\dfrac{1-(1.08)^{-10}}{0.08}=6.7101$, so
$$PV_{\text{royalty}}=4.500\times6.7101=\boxed{\$30.20\ \text{million}}.$$
Since USD 30.20 million exceeds the USD 20 million asking price (NPV = +USD 10.20 million), GeoRoyalties should purchase the royalty interest.
Minimum acceptable royalty rate. Setting the present value of the royalty stream equal to the USD 20 million price and solving for the rate:
$$r_{\min}=\frac{20}{150.01\times6.7101}=\frac{20}{1006.6}=\boxed{1.99\%}.$$
Any royalty rate at or above 1.99% returns at least USD 20 million in present value at an 8% discount rate; the 3% rate on offer comfortably clears this threshold.
Check: the operator's USD 15 million/yr tax payment is supplied data not needed to value the royalty — a royalty is a claim on gross smelter revenue, computed independently of the operator's tax, financing or capital structure. It is flagged here rather than silently omitted so a reader does not read its absence as an oversight. The gold-credit line “pay for 93.3% of gold in copper concentrate less one gram” is read as 93.3% of (gold grade − 1 g/t); the alternative reading (93.3% of the gold grade, then less 1 g) gives a credit of USD 124.95/t instead of USD 125.96/t, which moves the royalty PV by only about 0.1% and changes neither conclusion.
