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24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 2018

Question 24 of 29: Refined IRR via Adjacent 5% Table 6 Brackets

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 6.3: Refined IRR via Adjacent 5% Table 6 Brackets (5 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 6A cash flows: Investment −80M (now); Y1–Y4 = 50, 30, 20, 10M; Y5 = 7M + 5M terminal = 12M. Alternative 6B: Investment −80M; Y1–Y5 = 28M/yr level; Y5 also carries a 10M terminal value (38M total in Y5). Table 6's individual and cumulative PV factors at each 5% step.

Approach. Compute NPV at successive 5% steps for each alternative using Table 6's factors (6A year-by-year; 6B via the 4-year cumulative factor plus the year-5 factor on 38M), locate the adjacent pair of rates where NPV changes sign, then interpolate within that narrow 5-point window.

  1. Screening NPV at 20% and 25% for 6A (individual-year Table 6 factors): $$NPV_{6A}(20\%)=-80+50(0.8333)+30(0.6944)+20(0.5787)+10(0.4823)+12(0.4019)=+\boxed{3.72\text{M}}$$ $$NPV_{6A}(25\%)=-80+50(0.8000)+30(0.6400)+20(0.5120)+10(0.4096)+12(0.3277)=-\boxed{2.53\text{M}}$$ NPV changes sign between 20% and 25% — this is the bracket.
  2. Screening NPV at 20% and 25% for 6B (cumulative 4-yr factor + year-5 factor on 38M): $$NPV_{6B}(20\%)=-80+28(2.589)+38(0.4019)=+\boxed{7.76\text{M}}$$ $$NPV_{6B}(25\%)=-80+28(2.362)+38(0.3277)=-\boxed{1.41\text{M}}$$ NPV also changes sign between 20% and 25% for 6B.
  3. Interpolate 6A within its 20–25% bracket: $$IRR_{6A}=20+\frac{3.72}{3.72-(-2.53)}\times5=20+\frac{3.72}{6.25}\times5=20+2.98=\boxed{22.97\%}$$
  4. Interpolate 6B within its 20–25% bracket: $$IRR_{6B}=20+\frac{7.76}{7.76-(-1.41)}\times5=20+\frac{7.76}{9.17}\times5=20+4.23=\boxed{24.23\%}$$
  5. Compare with the crude 6.2 estimate. The narrow-bracket IRRs (22.97% for 6A, 24.23% for 6B) are markedly lower than the crude 5%/50% linear estimates (29.9%/32.9%), confirming the exam's own warning that the wide-interval straight line overstates IRR due to curvature — the narrow-bracket figures are the reliable ones.
AlternativeBracket usedRefined IRR
6A20%–25%22.97%
6B20%–25%24.23% (higher)

Both alternatives comfortably clear the company's 15% minimum acceptable rate. Comparing the two, Alternative 6B has the higher (better) IRR — its level USD 28M/yr cash flow stream, though less front-loaded than 6A's, compounds to a larger total present value at these discount rates because of its larger terminal value and more even distribution; 6B is therefore preferred on the IRR criterion.

Check: an exact numerical root-find (Newton/bisection on the true compound-interest formula, bypassing Table 6's rounding) gives IRR6A = 22.89% and IRR6B = 24.16%, confirming the Table-6 linear-interpolation results above to within about 0.1 percentage point.