24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-Mmp-A4 Mine Valuation and Mineral Resource Estimation, 2013-Dec. 3 hours duration; one handwritten 8.5×11 in reference sheet permitted (not an open-book exam); only approved Sharp or Casio calculators allowed. Question 1 is compulsory (40 marks, parts 1.1–1.7); candidates then select FOUR of the six optional Questions 2–7 (15 marks each) to complete the paper.
Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging estimators, compositing and support); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (NPV/cut-off grade methodology, cost estimating, financing structures); Torries, Evaluating Mineral Projects: Applications and Misconceptions (SME) (mine valuation, cost of capital, inflation treatment); Gentry & O'Neil, Mine Investment Analysis (net smelter return, smelter/refining contract terms); SME Mining Engineering Handbook, 3rd ed. (mineral economics, capital and operating cost estimating).
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.
Given.
| Year | Revenue ($M) | Op. Cost ($M) | Tax ($M) |
|---|---|---|---|
| 1 | 1.10 | 0.41 | 0.159 |
| 2 | 0.90 | 0.39 | 0.162 |
| 3 | 1.00 | 0.40 | 0.166 |
| 4 | 1.20 | 0.42 | 0.168 |
| 5 | 0.80 | 0.20 | 0.092 |
Purchase cost = $\$0.70$M (Year 0); salvage value = $\$0.10$M (Year 5); cost of capital r = 8%.
Find. After-tax cash flow each year, and the asset's NPV.
Approach. Compute each year's after-tax cash flow as Revenue − Operating Cost − Tax (adding salvage to Year 5), discount each at 8% using DF=1/(1.08)t, and sum the present values less the initial purchase cost.
| Year | After-tax CF ($M) | DF @ 8% | PV ($M) |
|---|---|---|---|
| 0 | −0.700 | 1.0000 | −0.700 |
| 1 | 0.531 | 0.9259 | 0.4917 |
| 2 | 0.348 | 0.8573 | 0.2984 |
| 3 | 0.434 | 0.7938 | 0.3445 |
| 4 | 0.612 | 0.7350 | 0.4498 |
| 5 | 0.608 | 0.6806 | 0.4138 |
| NPV | $\$1.298$M | ||
6.2 NPV, cost of capital, ROR and DCF-ROR in decision making. The 8% cost of capital represents the minimum acceptable return the company's capital providers require for the risk taken; discounting the project's cash flows at that rate and finding a POSITIVE NPV (as here, +$\$1.298$M) means the asset is expected to create value above and beyond that required return, and is the primary basis for an accept decision. Rate of Return (ROR), in its simple/accounting form, typically compares average annual profit to the initial investment and ignores both the time value of money and the actual timing pattern of cash flows – it is a quick screening measure only. Discounted Cash-Flow Rate of Return (DCF-ROR), also called the Internal Rate of Return (IRR), is the discount rate at which the project's NPV equals zero, and properly accounts for the time value of money and the full timing profile of cash flows, giving a single percentage that can be compared directly against the 8% cost-of-capital hurdle (IRR > 8% ⇒ accept, consistent with the positive NPV found above). NPV is generally preferred as the PRIMARY ranking criterion, especially when comparing mutually exclusive projects of different scale or cash-flow timing, because it expresses value in dollars (directly additive across a portfolio) and does not suffer from IRR's potential multiple-root or non-standard-reinvestment-rate issues; DCF-ROR/IRR remains a useful secondary check, showing the margin of safety between the project's own return and the cost of capital.
