Choosing Discount Rates - imval.org

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Choosing Discount Rates

Time-Value-of-Money, NPV, Riskin DCF Valuations

IMVAL Perspectives on Mineral ValuationMay 13, 2021

Lawrence Devon Smith

IMVAL Perspectives on Mineral Valuation 2021

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Lawrence Devon Smith2

Lawrence Devon Smith is Principal Consultant at LDSA. He is a mining engineer with over 45 years experience in economic evaluations and project engineering for mining, metallurgical, and industrial projects. He holds a B.A.Sc. from the University of Toronto and an M.Eng. Mining from McGill University. Larry has worked as Director Project Evaluations at Barrick Gold and has held similar positions with BHP-Billiton Base Metals, Rio Algom, SNC-Lavalin, Kilborn, Inco, and Vale. His evaluation experience includes economic evaluations, targeting and ranking studies, scoping studies, optimization studies, pre-feasibility and feasibility studies, risk assessment, and due diligence work for banks and mining companies. Larry has published a number of papers on mineral project evaluation, discount rates, and risk assessment, and is considered an expert in these fields. Larry teaches mineral economics, mineral project evaluation, and “Introduction to Mining”. He is an adjunct professor at the University of Toronto and Schulich School of Business at York University, as well as teaching in-house courses and seminars. He is on the executive of the CIM Mineral Economics Society (MES) and is a past chair of CIM Toronto Branch. He is the recipient of the CIM Robert Elver award for Mineral Economics, a Fellow of CIM, and a CIM Distinguished Lecturer.

[email protected]


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Discount RatesWhy All The Fuss?

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Net Present ValueProject Cash Flow - Impact of Discount Rate

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50,000

150,000

250,000

‐3 ‐2 ‐1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

NPV

NPV ‐ Cash Flow

15.0% 10.0% 5.0% 2.5% 0.0%

In long-life projects, the later years add almost no value on an NPV basis at

high discount rates.

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5Net Present ValueProject Cash Flow - Impact of Discount Rate

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6Net Present ValueProject Cash Flow - Impact of Discount Rate

IRR(Discount rate where NPV=0)

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Risk Adjusted Discount RateRADR

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ithRisk Adjusted Discount Rate (RADR)Typical Ranges (Real)


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0% 2.5% 5% 7.5% 10% 15+%

WACCRange

Typically due toCountry Risk

• Risk Free Investments

• Closure Cost Trust Funds

HighVery Low

Study Range

Operations

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ithRisk Adjusted Discount Rate (RADR)Determining the Discount Rate• The discount rate is one of the most critical valuation decisions.• The determination of the risk adjusted discount rate (RADR) incorporate a

number of components:• Time value of money• Market Risk (within the corporate WACC)• Corporate risk level (within the corporate WACC)• Metal (precious metal, base metal)• Risks associated with the stage of the project• Other risks• Country Risk

• WACC reflects the level of risk for the company. • RADR reflects the level of risk for the project.

• The discount rate must be in real terms for cash flows in real values or in nominal terms for cash flows in nominal values.


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ithRisk Adjusted Discount Rate (RADR)Build-Up• The Risk Adjusted Discount Rate is typically build-up starting with the

corporate Weighted Average Cost of Capital (WACC) and adding increments for the project risk and the country risk.


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Corporate WACC

Project Stage Risks

Other Risks

Country Risk

Project Risks vary with the stage of the project, metal type adjustments, other factors; 0%-5%+)

Country Risk can have a wide range depending on the perceived risk levels in the mining jurisdiction; 0% to 5%+)

The discount rate must be in real terms for cash flows in real values or in nominal terms for cash flows in nominal values.

WACC is typically an After Tax (AT) value. Cash flows should also be after tax.

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ithRisk Adjusted Discount Rate (RADR) WACC - Weighted Average Cost of Capital (ABX 2013)

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Real-NominalWACC must be in real terms for cash flows in real values.WACC must be in nominal terms for cash flows in nominal values.

After TaxWACC is calculated on an after-tax basis.

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LDSmith CIM-MES Industry Surveys: 1996, 1999, 2005

Risk Adjusted Discount Rate (RADR)Adjusting for Project Stages – Industry Practice

Level of Study Gold ∆ Base Metals ∆Scoping 12.4% 6.9% 14.0% 5.5%Pre-Feasibility 11.2% 5.7% 13.0% 4.5%Feasibility 8.8% 3.3% 11.0% 2.5%Operating Mine 5.5% 0.0% 8.5% 0.0%

Values in real

terms

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ithRisk Adjusted Discount Rate (RADR) Case Study: Adjusting for 5% Gold & PEA Risk• Bill Roscoe (CIM Conference May, 2021) examines two aspects of the

RADR issue:• The common use of 5% for gold properties and companies• The actual increment the market adds for PEA-level studies

• LD Smith comments:• PEAs are not a particularly good guide to industry practice for RADR• PEAs attract a significant “Stage” increment for RADR in actual deals


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#Discount

Ratein PEA

Discount Ratefor NPV =Deal Value

Discount Ratefor NPV =

Adj Mkt Cap

PEA incrementover “WACC”

(LDSmith)Transacted Properties (2016-2020)

Average8

5.9% 20% 16% 10%-14%Median 5.0% 18% 16% 11%-13%

Non-Transacted Properties (2016-2020)Average

275.1% - 21% 16%

Median 5.0% - 20% 15%

Qualifying Risk in PEAs for Gold Projects, W.E. Roscoe, CIM convention, MES session, May 2021

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14Risk Adjusted Discount Rate (RADR)Adjusting for “Other” Risks: Metals & Juniors• There are some generic values for WACC (real) for mining companies:

• Gold companies (mid-size to major) are typically in the range of 5%• Base metal & other companies are typically in the range of 7%-8%

• Adjusting for Metals• Adjustments may be needed when a company has a project with a different

metal from its core business:• Base metal project in gold company: add 1%-2% to RADR• Gold project in base metal company: deduct 1%-2% from RADR

• Adjusting for Company Size• The corporate WACC for small, one-project companies (Juniors) will typically

be greater that for larger, producing companies.• A correction in the range of 1%-2% to the generic WACC may be needed.

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15Risk Adjusted Discount Rate (RADR)Adjusting for “Other” Risks: Put in the Cash Flow • Some practitioners try to use the discount rate to address other risks.• These risks are best addressed in the cash flow estimates.

• Types of risks:• Unusual technology• First time a method is being tried• Unusual ore type• Remote location

• These should be addressed in the cash flow estimates as:• Higher capital costs• Extended construction schedule• Delayed start-up (McNulty curves)• Higher operating costs• Lower recovery

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16Risk Adjusted Discount Rate (RADR)Adjusting For Country Risk

(Nevada, Quebec) (Chile, Peru) (DRC)

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ithRisk Adjusted Discount Rate (RADR)Risk Premiums & Increments Above “Risk Free”

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Black = Equity Risk Premium

Red = Country Risk Premium(ERP minus Risk-Free ERP) 2019 Edition - Country

Risk: Determinants, Measures & Implications

A Damodaran

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BHP 2001

Risk Adjusted Discount Rate (RADR)Converting Country Risk Ratings to Discount Rates

Caution! Old data. For illustration only.

Do no use!

BHP recognized that not all the risk is within the country, some of

the risk is international.

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ithRisk Adjusted Discount Rate (RADR)Project Specific Determination• Different practitioners will have different opinions of project stage risk and

country risk. Expect a range of opinions and outcomes.• Analysts typically use 5% (real) for gold operating companies listed in North

America. • WACC reflects the level of risk for the company. • RADR reflects the level of risk for the project.


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RADR Items Project in Nevada

Project inDeveloping

Country+ WACC for gold companies (real) 5.0% 5.0%+ Adjust for stage of project (PEA) 6.0%-8.0% 6.0%-8.0%+ Adjust for country risk 0.0% 3.2%-6.4%= RADR (Min-Max) 11.0%-13.0% 14.2%-19.4% RADR Likely Range (50% country) 11.0%-13.0% 15.8%-16.2%

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Discount RateCautions & Conventions

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ithDiscount Rates In Cost FlowsThe math works in the opposite direction for costs• Consider a comparison of Owner versus Contractor water transport options.• The analysis showed that the contracted trucks had a lower Net Present

Cost at the project’s 5% discount rate and so was the favoured option.• But the engineer indicated that this did not sound right as the contractor

option was deemed to be more risky.• To reflect increased risk the discount rate for the riskier option was increased

to 8% which reduced the Net Present Cost and favoured the contracted trucks even more.

• Problem: With costs, discounting works opposite to what is expected .


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Cost Flows Net Present CostsDiscount Rate 0.0% 5.0% 8.0% 10.0%Owner Trucks 73.8 52.4 44.1 39.8

Contract Trucks 76.8 50.6 40.6 35.4

Discount Rate 0.0% 5.0% 8.0% 10.0%Owner Trucks 73.8 52.4 44.1 39.8

Contract Trucks 76.8 50.6 40.6 35.4

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ithDiscount Rates In Cost FlowsRisk Factoring


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• It is more straightforward to bypass the issue of risk adjusting discount rates for costs as they would feel counterintuitive.

• The suggested approach is:• Calculate the NPV Costs at a risk-free discount rate (WACC or other).• Determine a risk factor for each option.• Multiply the NPV Costs times the risk factor to determine the risk

adjusted NPV Costs.• Select the options with the lowest risk adjusted NPV Cost value.

Option NPV Cost@ 5%

RiskFactor

Risk AdjustedNPV Cost

Owner Trucks 52.4 1.00 52.4Contract Trucks 50.4 1.10 55.4

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Issues, Concerns, Problems Closure Both Costs and Sinking Fund

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NPV

NPV ‐ Cash Flow

15.0% 10.0% 5.0% 2.5% 0.0%

Closure occurs at the end of operations.

Can span decades or centuries.

Closure Costs occur so far out in time that their true value (liability) is

reduced to apparent insignificance and they do not attract the attention

they deserve.

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Issues, Concerns, Problems Closure Both Costs and Sinking Fund

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‐350,000

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250,000

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NPV

NPV ‐ Cash Flow

15.0% 10.0% 5.0% 2.5% 0.0%

Solution: Bring all of the closure costs back to a single NPV value on the last day of operation. Use a 2.5% (real) discount rate as a sinking fund

investment rate.

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ith25Discount Rates & Discounting

Cautions• Real or Nominal?

• Use a real discount rate if the cash flow is real • Use a nominal discount rate if the cash flow is nominal.

• After-Tax• WACC is after-tax; cash flow also needs to be on an after-tax basis.• Discount rates cannot be used to address tax in mining projects.

• Terminal Value NOT FOR MINING• Terminal Value = (Annual Cash Flow) / (Discount Rate)• This calculation is NOT applicable to mining projects• Production varies year by year• Mine lives are generally too short


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ith26Discount Rates & Discounting

Conventions & Practice• Discounting conventions

• Discrete, end-of-year (Typical in mining. Excel default)

• Reference Date: • Use “Shovels in the Ground” date, no matter how far in the future it is.• Always describe the Reference Date from which the NPV is measured.• Do not compress Capital Costs into a “t=0” period; spread them out as

per their schedule. (Finance grads often make the t=0 mistake.)

• Use the same discount rate in all years.• Caution: Some authors have suggested otherwise

• Use the same discount rate for all cash flow items• Caution: Some authors have suggested otherwise.


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The RADR ParadoxRisk Adjusted NPV

Risk in Monte Carlo

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ithDiscount Rates In Risk Adjusted NPVWhat Is The Math Doing To Each Item?• By using larger and larger discount rates:

• All values reduce exponentially• Values further out in time are reduced much more.


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ithDiscount Rates In Risk Adjusted NPVWhat We Really Want The Math To Do• For illustration purposes 5% (real) is used as the reference rate.• By using factors, cost can increase and revenues can reduce.


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Risk Adjusted

NPV

Initial Capital is increased to

reflect expected risk levels.

Revenue is reduced by

expected risk levels.

Operating Costs are

increased for expected risks.

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ithDiscount Rates In Monte CarloRisk Free Discount Rate – Risk Is In The Cash Flow• A risk free discount rate is typically used in Monte Carlo.• Risk is addressed by applying risk distributions and probabilities to the cash

flow variables.• These combine to give an output with a distribution and probabilities.


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Risk Adjusted Cash Flows 5.0%

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ithDiscount Rates In Monte CarloSeveral Variables Interact at the Same Time• Inputs variables have distributions and probabilities.• These combine to give an output with a distribution and probabilities.


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Variable 3

Variable 2

Variable 1

OutputDistribution

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Questions?


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•

Notes

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ithRADR Risk Adjustments by Mining AnalystsExample 1 - RBC Gold• Some observations about the use of discount rates and adjustments to

discount rates in an analyst report:

• Discount rate applied on a risk-weighted basis, generally higher for base metal assets or high technical/political risk.

• Percentage of NAV attributed to mining assets/investments not currently in production

• Some companies have a different “Preferred Discount Rate”


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The Gold Standard: Spot Gold Comparable Tables, RBC Capital Markets 2021-05-03

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ithRADR Risk Adjustments by Mining AnalystsExample 1 - RBC Gold


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The Gold Standard: Spot Gold Comparable Tables, RBC Capital Markets 2021-05-03

% NAV in Development

Discount rate applied on a risk‐weighted basis.

XXX

XXXX

X

XX

XXX

XX

XX

?

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ithRisk Adjusted Discount Rate (RADR) Adjusting for Project Stages – Industry Practice


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LDSmith CIM-MES Industry Surveys: 1996, 1999, 2005

StudyStage

GoldRate

GoldIncrement

Base MetalRate

Base Metal Increment

PEA/Scoping 13.8% 6.0% 13.8% 4.3%PFS 11.5% 3.7% 12.8% 3.3%FS 9.5% 1.7% 11.2% 1.7%Operating 7.8% 0.0% 9.5% 0.0%

StudyStage

GoldRate

GoldIncrement

Base MetalRate

Base Metal Increment

PEA/Scoping 12.4% 6.9% 14.0% 5.5%PFS 11.2% 5.7% 13.0% 4.5%FS 8.8% 3.3% 11.0% 2.5%Operating 5.5% 0.0% 8.5% 0.0%

Ross D. Lawrence, Income Approaches to ValuationVALMIN ’01, Sydney, Australia October 26-27, 2001

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ithRisk Adjusted Discount Rate (RADR)Influencing Factors


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KPMG Mining Reporting Survey 2016

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38Risk Adjusted Discount Rate (RADR)Adjusting for “Other” Risks: 5% WACC for Gold• Many practitioners use 5% for gold projects and gold companies.• This includes mining analysts for financial institutions• The basis for using this figure is:

• It is a reasonable approximation of the WACC (real) for mid-tier and major gold companies.

• It is easier to use one discount rate when comparing values for a portfolio of companies.

• However, the WACC may be several percent higher for:• Small, one-project companies (Juniors)• For companies with all their assets in riskier jurisdictions

• A correction may be needed for the generic 5% discount rate for gold.• This could be in the range of 1%-3%. • Suggest check the corporate WACC (real) if available.

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39Risk Adjusted Discount Rate (RADR)Adjusting for “Other” Risks: Different Metals• WACC is particular to each company.• Two similar companies (metal and size) will not necessarily have the same

WACC.• However, there are some broad similarities that can be observed:

• Gold companies have a WACC (real) in the range of 5%• Base metal companies have a WACC (real) in the range of 7%-8%• Bulk commodity companies have a WACC (real) in the range of 7%-8%

• If a gold company has a base metal project, the market will typically adjust the discount rate upward for that project.• Base metal project in gold company: add 1%-2% to RADR

• If a base metal company has a gold project, the market will typically adjust the discount rate downward for that project.• Gold project in base metal company: deduct 1%-2% from RADR

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ithRisk Adjusted Discount Rate (RADR)Examples


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Item orRisk Adjustment

GoldFS

GoldOperating

Copper in Gold

CompanyFS

Copper in Copper

CompanyFS

Copper in Gold

CompanyFS

WACC 5.0% 5.0% 5.0% 7.0% 5.0%Metal - - 2.0% - 2.0%Stage 3.3% - 2.5% 2.5% 2.5%Country Risk - 2.0% - - 7.5%RADR 8.3% 7.0% 9.5% 9.5% 17.0%

• All values are in real terms• WACC is the expected return for the company• RADR is the Risk Adjusted Discount Rate for the project• Using WACC assumes the project is funded from general corporate funds.• Technology and Remoteness are assumed to be addressed in the cash flow.

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ithRisk Adjusted Discount Rate (RADR)Analyst Application - Increased RADR to Reflect RiskScotiabank Daily Edge• Probe Mines Limited - Don't Wait Until May, Sell Today• Probe has released 34 drill holes totaling 19,000m from its winter drill

program on Borden Lake.

Implications • The drilling ... suggesting that there is little material within the extension that

would be above a reasonable cut-off grade for an underground operation. Infill drilling has the potential to improve the grade of this zone; however, we see limited upside from today's assays.

• We had factored in a 15% increase in tonnage to our resource model for expansion potential to the SE. We have removed that expansion potential and we have also lowered our daily throughput for the underground mine to 1,500 tpd and increased our discount rate by 3%.


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Scotiabank 30Apr2014

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End of Slides

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43Discount Rates And DCF MetricsPurpose and Issues• Discount rates are used to reflect:

• Time value of money• Risks that cannot be readily quantified

• Discount rates are a fundamental part of the calculation of the following major DCF metrics:• Net Present Value (NPV)• Internal Rate of Return (IRR)• Present Value Ratio (PVR)

• Problems With Discount Rates• The main criticism of discount rates and DCF metrics is that they do not

recognize the value of long life projects. • This is particularly noticeable at higher discount rates.

Documents

Choosing Discount Rates - imval.org