An Integrated Valuation and Risk Modelling approach to Dynamic DCF and Real Options

April 20 to 22, 2022
Golden, CO

Course Outline

Day 1 – Morning.       

Introductory comments. A project valuation framework.  Valuation fundamentals.

  • Creating value in the natural resource industries
  • Three elements of a valuation model
  • Project structure – cash flow, design flexibility, stakeholders
  • Project uncertainty – financial, technical, execution
  • Measuring investment quality – NPV (DCF and real options), IRR, MIRR, PI
  • Measuring investment risk – cash flow CoV, event probabilities, expected / conditional losses
  • A technical / financial risk investment framework
    Example: Blackwater Gold Project – a static investment analysis of the New Gold and Artemis design proposals


Day 1 – Afternoon.   

Metal price models.  Simulating metal prices.

  • Characterizing commodity price uncertainty
  • Financial market information vs metal price forecasts
  • Stochastic price models for precious metals and base metals
  • Rebuilding a corporate forecast as a stochastic price model
    Example:  Building a stochastic price model in Excel
  • Converting a stochastic price model into Monte Carlo simulation
  • Simulating metal prices with @Risk
    Example: Building correlated gold and copper simulation models in Excel with @Risk
    Example: Valuing a financing arrangement such as a sliding-scale NSR

Day 2 – Morning.      

Analyzing projects with no flexibility.

  • Modelling cash flows when there is no flexibility
  • Summarizing project production and cash flow information
  • Cash flow profiles
  • Cumulative LOM cash flow streams
  • Unit costs – mill feed, primary metal and equivalents
  • Measuring risk exposure – calculating expected and conditional losses
    Example: Blackwater Gold Project – dynamic investment analysis of the New Gold and Artemis design proposals
  • Corporate income taxes as non-linear cash flows
    Example: Blackwater Project – introducing corporate income tax

Day 2 – Afternoon.   

Binomial techniques.  Introduction to flexibility.

  • Converting a simulation into a binomial tree
  • Approximating a price process with a binomial tree
  • Developing true and risk-adjusted probability price trees
    Example:  Building a binomial price tree in Excel
  • Modelling flexible projects and types of flexibility
  • Cash flow timing for flexible projects
    Example: A simple binomial model valuing a mine with an abandonment option.


Day 3 – Morning.       

Valuing flexible projects and assessing their risk.

  • Impact of flexibility on economic benefit calculations
  • Flexibility and risk exposure
  • Problems with using the Black-Scholes equation to value project flexibility
  • Using the Excel Binomial Real Options / DCF Valuation Add-in
    Example: Blackwater Gold Project – the value and risk impact of early closure on the NewGold and Artemis designs
  • Decisions trees and flexibility maps.
  • Re-interpreting the Artemis Blackwater design as staged development
    Example: Blackwater Gold Project – the value and risk impact of staged development on the       NewGold and Artemis designs

Day 3 – Afternoon.   

Valuing natural resource projects with flexibility.

  • Guest lecture by Professor G Davis: Dynamic cash flow modelling in the mining industry
  • Dynamic cash flow modelling frontiers – technical risk, exploration, risk management
  • Course wrap-up.