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.
Given. Deposit and project economics as below; the USD 30 million acquisition cost is paid USD 15 million at the end of year 1 and USD 15 million at the end of year 2, and is added to the preproduction capital base for tax (depreciation) purposes.
Item
Value
Deposit size
10 million tonnes
Annual ore capacity
2 million tonnes/yr
Average ore grade
2% Cu
Processing recovery
90.1%
Net smelter return
75.0%
Copper price
USD 5,000/tonne Cu
Operating costs
USD 35.00/tonne of ore
Preproduction capital (excl. acquisition)
USD 100 million, spread evenly over years 1–2
Acquisition cost
USD 30 million, USD 15M at end of yr 1 and USD 15M at end of yr 2
Depreciation
20%/yr of total capital, beginning in the first year of production
Taxation
40% of taxable income
Required rate of return
15%
Find. Whether the deposit acquisition is justified at a 15% required rate of return.
Approach. Lay out the project timeline — two development years (1–2) carrying the acquisition instalments and the preproduction capital, followed by five production years (3–7, since 10 Mt ÷ 2 Mt/yr = 5 years) — then build one representative after-tax production-year cash flow (revenue less operating costs less tax, with straight-line depreciation on the full USD 130 million capital base as a non-cash tax shield added back), and discount every cash flow to time zero at the 15% hurdle rate.
Project timeline and depreciable capital base. Development spans years 1–2 (each carrying USD 15M of the acquisition plus USD 50M of the USD 100M preproduction capital, i.e. USD 65M/yr); production spans years 3–7 (5 years, from 10 Mt ÷ 2 Mt/yr). Because the acquisition is explicitly treated as extra preproduction capital for tax purposes, the depreciable base is the full
$$\text{Capital}=100+30=\boxed{\$130\ \text{million}},\qquad \text{Depreciation}=0.20\times130=\boxed{\$26.0\ \text{million/yr (years 3\textendash7)}}.$$
Annual production-year revenue and operating cost. Payable copper is $2.0\times0.02\times0.901\times0.75=27{,}030$ tonnes/yr, so
$$\text{Revenue}=27{,}030\times5000=\boxed{\$135.15\ \text{million/yr}},\qquad \text{Operating cost}=2.0\times35.00=\$70.00\ \text{million/yr}.$$
After-tax cash flow, years 3–7. With EBITDA $=135.15-70.00=\$65.15$M and depreciation of USD 26.0M as a non-cash tax shield:
$$\text{Taxable income}=65.15-26.0=\$39.15\text{M},\qquad \text{Tax}=0.40\times39.15=\$15.66\text{M},\qquad \text{Net income}=39.15-15.66=\$23.49\text{M}.$$
Adding depreciation back (it is not a cash outflow):
$$\text{ATCF}=23.49+26.0=\boxed{\$49.49\ \text{million/yr, years 3\textendash7}}.$$
Present value of the development-year outflows. Each of years 1 and 2 carries USD 65.0M (USD 15M acquisition instalment + USD 50M preproduction capital):
$$PV_{\text{dev}}=-\frac{65.0}{1.15}-\frac{65.0}{1.15^{2}}=-56.52-49.15=\boxed{-\$105.67\ \text{million}}.$$
Present value of the production-year cash flows. The 5-year, USD 49.49M/yr annuity (years 3–7) has a 15% annuity factor of $\dfrac{1-(1.15)^{-5}}{0.15}=3.3522$, valued as of the end of year 2 and then discounted back two more years to time zero:
$$PV_{\text{prod}}=\frac{49.49\times3.3522}{1.15^{2}}=\frac{165.90}{1.3225}=\boxed{\$125.44\ \text{million}}.$$
Net present value and decision.
$$NPV=125.44-105.67=\boxed{+\$19.77\ \text{million}}.$$
Since the NPV is positive at the 15% required rate of return, the acquisition of the deposit is recommended.
Cash-flow timeline: two years of development outflows (acquisition instalments + preproduction capital) followed by five years of after-tax production inflows.
