Crude 5%/50% Interpolated IRR Estimate: 24-MMP-A4 Mine Valuation and Mineral Resource Estimation, December 2018, Q23

Question 23 of 29: Crude 5%/50% Interpolated IRR Estimate

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

EGBC National Exam — Mining and Mineral Processing Engineering, 09-MMP-A4 Mine Valuation and Mineral Resource Estimation, 2018-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 1.1–1.8); candidates then select THREE of the five optional Questions 2–6 (20 marks each) to complete the paper.

Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging, anisotropy); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV/IRR and cut-off grade methodology); Gentry & O'Neil, Mine Investment Analysis (smelter/refining contract terms, net smelter return, taxation and risk); Guilbert & Park, The Geology of Ore Deposits, and Evans, Ore Geology and Industrial Minerals (VMS/SEDEX and porphyry deposit models); SME Mining Engineering Handbook, 3rd ed. (mineral exploration/evaluation stages, ore reserve classification); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).

Question 6.2: Crude 5%/50% Interpolated IRR Estimate (2 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.

Given.

Alternative	NPV @ 5%	NPV @ 50%
6A	+USD 29.7M	−USD 23.9M
6B	+USD 49.1M	−USD 30.1M

Approach. Linear interpolation across the full 45-point trial range: $IRR \approx 5\% + \dfrac{NPV_{5\%}}{NPV_{5\%}-NPV_{50\%}}\times45\%$.

Alternative 6A. $$IRR_{6A}\approx5+\frac{29.7}{29.7-(-23.9)}\times45=5+\frac{29.7}{53.6}\times45=5+24.9=\boxed{29.9\%}$$
Alternative 6B (6B's own 5%/50% trial, computed the same way as the worked 6A example, using Table 6's cumulative PV factors for the level USD 28M annuity plus the year-5 terminal value): $$IRR_{6B}\approx5+\frac{49.1}{49.1-(-30.1)}\times45=5+\frac{49.1}{79.2}\times45=5+27.9=\boxed{32.9\%}$$

Alternative	Crude 5%/50% IRR estimate
6A	≈ 29.9%
6B	≈ 32.9%

Check: as the exam itself notes, this straight-line 45-point interpolation systematically OVER-estimates IRR because the true NPV-vs-rate curve is convex, not linear over such a wide span — Question 6.3's adjacent-5%-bracket method below gives the materially more accurate figure.