IRR vs. NPV Sketch Graph: 24-MMP-A4 Mine Valuation and Mineral Resource Estimation, December 2018, Q25

Question 25 of 29: IRR vs. NPV Sketch Graph

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 6.4: IRR vs. NPV Sketch Graph (1 mark)

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.

NPV vs. trial discount rate for Alternatives 6A and 6B, plotted from Table 6's 5%-step factors. Both curves are convex (concave-up), crossing zero NPV near 23.0% (6A) and 24.2% (6B) — well short of the 29.9%/32.9% a straight line through the 5%/50% points would suggest.

Both NPV-vs-rate curves bend markedly CONCAVE UP (convex) rather than following the straight chord between the 5% and 50% trial points — NPV falls steeply at first as the discount rate rises from 5%, then flattens at higher rates because each additional percentage point of discounting has a proportionally smaller effect on already heavily-discounted cash flows. The true zero-crossing (the IRR) therefore sits well BELOW where the straight 5%/50% chord would cross zero, exactly as flagged in Question 6.2 — the curve, not the chord, is what a narrow-bracket interpolation (Question 6.3) approximates correctly.