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24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2017

Question 12 of 18: 4.2: NPV of a 4-Year Cash Flow and Investment Justification

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, 2017-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 five optional Questions 2–6 (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, smelter/refining contract terms, net smelter return, transportation logistics); SME Mining Engineering Handbook, 3rd ed. (cost-estimating relationships, mineral exploration/evaluation stages, ore reserve classification); Evans, An Introduction to Ore Geology and Guilbert & Park, The Geology of Ore Deposits (ore deposit models); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).

Question 4.1–4.2: NPV of a 4-Year Cash Flow and Investment Justification (8 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.

ParameterValue
Annual net cash flow, CF$1,000/yr, years 1–4 (end-of-year)
Discount rate, i5%
Capital invested today, t=0$3,500

Find. (4.1) NPV of the cash-flow stream alone; (4.2) whether the project (net of the $3,500 capital) is justified at 5%.

01234-$3,500 (capital)$1,000$1,000$1,000$1,000Investment cash flow, i=5%period (year)
Fig. 4.1–4.2 – Cash-flow diagram: $3,500 capital outlay at t=0, four end-of-year receipts of $1,000 (years 1–4), discounted at i=5%.

Approach. Discount the four equal end-of-year $1,000 receipts using the uniform-series present-worth (annuity) factor at i=5%, n=4 (4.1); then subtract the $3,500 capital to get the project's net NPV and judge its sign (4.2).

  1. 4.1 – Annuity present-worth factor. $$\left(\frac{P}{A},5\%,4\right)=\frac{1-(1+i)^{-n}}{i}=\frac{1-(1.05)^{-4}}{0.05}=\frac{1-0.82270}{0.05}=3.5460$$
  2. 4.1 – NPV of the cash-flow stream. $$\text{NPV}_{\text{cash flows}} = 1{,}000\times3.5460=\boxed{\$3{,}545.95}$$
  3. 4.2 – Net project NPV. Subtracting the $3,500 capital invested today: $$\text{NPV}_{\text{project}} = 3{,}545.95-3{,}500=\boxed{+\$45.95}$$ Because NPVproject > 0 (marginally so – barely over 1% of the capital outlay), the investment is justified at the 5% interest rate: its 4-year, $1,000/yr cash flow recovers the $3,500 capital and still clears the 5% hurdle, generating a small positive economic surplus. The margin is thin enough that the analyst should flag the result as sensitive – a discount rate only slightly above 5%, or cash flows shaded even a little below $1,000/yr, would flip the sign and make the project uneconomic.
QuantityValue
Annuity factor (P/A, 5%, 4)3.5460
NPV of cash-flow stream (4.1)$3,545.95
Net project NPV (4.2)+$45.95
Investment justified at 5%?Yes (marginally)