24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2016
Question 5 of 29: Project Net Present Value
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, 2016-May. 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 1.1–1.6); candidates then select THREE of the six optional Questions 2–7 (20 marks each) to complete the paper.
Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging estimators, volume–variance relations); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV and cut-off grade methodology, mineable reserves); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, inflation and financing effects on DCF yield, smelter/refining contract terms, net smelter return); SME Mining Engineering Handbook, 3rd ed. (mineral exploration/evaluation stages, ore reserve classification, ore deposit models); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).
Given. Revenue and expenditure by year, Year 0–6 (table above); discount rate r = 10%; end-of-year convention (Year 0 cash flow occurs at valuation date, t = 0, undiscounted).
Find. NPV of the project at r = 10%.
Fig. 1.5 – Net cash flow (Revenue − Expenditure) by year: heavy early-year outlays (development, Years 0–2) followed by positive production-year cash flow (Years 3–6).
Approach. Net each year's cash flow (Revenue − Expenditure), then discount each year's net cash flow back to Year 0 at 10% and sum.
Net cash flow by year. $$CF_t = \text{Revenue}_t - \text{Expenditure}_t$$ giving CF0=−5, CF1=−10, CF2=−20, CF3=+5, CF4=+10, CF5=+20, CF6=+20 ($ millions).
Discount each year at 10%. $$PV_t = \frac{CF_t}{(1.10)^t}$$ PV0=−5.000, PV1=−9.091, PV2=−16.529, PV3=+3.757, PV4=+6.830, PV5=+12.418, PV6=+11.289 ($ millions).
Sum the present values. $$NPV = \sum_{t=0}^{6}\frac{CF_t}{(1.10)^t} = -5.000-9.091-16.529+3.757+6.830+12.418+11.289$$ $$\boxed{NPV \approx \$3.68\text{ million}}$$
Quantity
Value
NPV @ 10%, end-of-year convention
$3.68 million (positive)
Check
The project clears a positive NPV at the 10% discount rate despite three consecutive negative-cash-flow years (0–2) – the Year 5–6 production cash flow ($20M/yr net) is large enough, even discounted 5–6 years, to overcome the front-loaded $35M of net development outlay.
