24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2016
Question 10 of 29: After-Tax NPV, Present Value Ratio and DCF-ROR
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).
Question 2.4: After-Tax NPV, Present Value Ratio and DCF-ROR (6 marks)
Find. NPV @ 15%; Present Value Ratio (PVR); DCF-ROR (internal rate of return of the ATCF stream).
Approach. Discount each year's ATCF at 15% and sum for NPV; PVR is NPV divided by the present value of the negative (investment) cash flows; DCF-ROR is the discount rate that drives NPV to exactly zero, found by iterating/interpolating on the same discounting formula.
NPV @ 15%. $$NPV = \sum_{t=0}^{5}\frac{ATCF_t}{(1.15)^t} = -8.150-0.357+3.978+2.446+1.704+1.134$$ Individually: PV0=−8.150, PV1=−0.357, PV2=+3.978, PV3=+2.446, PV4=+1.704, PV5=+1.134 ($M). $$\boxed{NPV_{15\%} \approx \$0.75\text{ million}}$$ Because NPV > 0 at the 15% hurdle rate, the project is acceptable to management – though only marginally so.
Present Value Ratio. PVR = NPV ÷ |PV of the negative (investment) cash flows|. The negative-flow years are Year 0 (−8.15) and Year 1 (−0.41), with PV0+PV1 = −8.150−0.357 = −8.507. $$PVR = \frac{0.754}{8.507} = \boxed{0.089\ (\approx 8.9\%)}$$ A PVR of only ≈0.09 means every dollar of discounted investment returns just 9 cents of discounted surplus value above the 15% hurdle – positive, and therefore formally acceptable, but a thin economic margin that would normally prompt management to look for cost/schedule/price upside or additional contingency before sanctioning.
DCF-ROR (IRR). Solve NPV(r)=0 for r by bracketing/iteration on the same ATCF stream (NPV(15%)=+0.754, NPV(20%) is negative, so the root lies between): $$NPV(r) = -8.15 -\frac{0.41}{(1+r)} +\frac{5.26}{(1+r)^2} +\frac{3.72}{(1+r)^3} +\frac{2.98}{(1+r)^4} +\frac{2.28}{(1+r)^5} = 0$$ Bisecting between 15% and 25% converges to $$\boxed{DCF\text{-}ROR \approx 18.4\%}$$ – consistent with the positive NPV found at the 15% hurdle rate (a project's DCF-ROR always exceeds its hurdle rate whenever NPV at that hurdle is positive).
