Analysing the Effect of Flexibility in Project IRR: The Case of a Silver Mine Project

By Dr. Luis A. Martínez Tipe, PhD Director General & Principal Researcher, CAIDTech Originally published: June 14, 2016

THE IRR - DEFINITION The Internal Rate of Return (IRR) is a very popular measure of investment performance and consequently project appraisal, and it has much to commend it. It is normally explained using its mathematical definition, i.e., the IRR is the discount rate that causes the net present value to equal zero. In particular it takes into account the time value of money.

Basically, the IRR tells the investor the rate of interest she will receive by putting her money into a project. It describes by how much the cash inflows exceed the cash outflows on an annualised percentage basis. Consequently, understanding what IRR is at an intuitive level will go a long way towards improving an investor’s ability to analyse potential investments.

IRR INVESTMENT DECISION RULE The rule for internal rate of return decisions is:

• If opportunity cost of capital (discount rate) > internal rate of return on a project then the investor is better served by not going ahead with the project;

• If opportunity cost of capital (discount rate) ≤ internal rate of return on a project then go ahead with the project;
  

THE SILVER MINE PROJECT EVALUATION IN THE FACE OF SILVER PRICE UNCERTAINTY As shown in a previous article titled "Valuing a Silver Mine Project with Options to Close and Defer Investment" (https://www.linkedin.com/pulse/valuing-silver-mine-project-face-price-uncertainty-dr-luis-martinez?trk=prof-post) a Silver mine project was evaluated under silver price uncertainty and considering the options to close mine operations in bad economic conditions, and the option to delay initial investment for one year.  

The results show that the best strategy to follow was to delay project investment for one year and invest if silver prices goes up to USD21.1/Oz, otherwise not to invest – note that current silver price was set up to USD16/Oz (see Figure 1).

Figure 1. Silver project strategies. Note the Base case strategy (Trad. NPV) generates a value of US$ 8.49 million, while the strategy to delay and invest (Expanded NPV) generates US$ 16.26 million.

ONE MORE QUESTION FROM MANAGEMENT What is the effect of flexibility (i.e., option to close mine operations in adverse economic situations and the option to delay mining investment for one year) in project internal rate of return?

ANALYSIS To answer the management question the analysis calculates the IRR for both the traditional Base case NPV analysis and the Expanded NPV analysis with flexibility (See Figure 3).

From the figure we can conclude the following: 1. The IRR for the traditional NPV (with a value of USD 8.5 million) analysis is 15% (black coloured line), which is greater than the initial investment cost of capital of 10%. Then following the decision rule this result indicates to invest. 2. The IRR for the Expanded NPV analysis (let's call it the Expanded IRR) with flexibility (with a value of USD 16.3 million) is 30% (Blue coloured line), which is significantly greater than the initial capital cost of 10%, and almost double the traditional IRR. Then following the IRR decision rule the strategy is to invest but following the strategy of delaying one year and investing if prices goes up. 

Figure 3. Internal rate of return analysis for both traditional NPV and Expanded NPV with flexibility. Note the Expanded NPV never gets negative because is either invest or not invest. COMMENTS AND RECOMMENDATIONS

Real options analysis, is an advanced process that complements traditional NPV allowing it to deal with uncertainty in a practical fashion. Basically, it uses uncertainty (i.e., risk and potential) to generate value by allocating strategies in place over time to minimise risk and maximise potential. This statement is confirmed by the results shown in Figure 3, which indicates that the inclusion of flexibility in the evaluation process not only adds value to the project by unlocking hidden value, but also makes it less risky providing the confidence to the investor to make the decision to go ahead since the Expanded IRR is significantly greater than the traditional IRR. Note that as explained in the initial paper, “Valuing a Silver Mine Project with Options to Close and Defer Investment” the real options process was done using a drift zero silver price model and the cost of capital of 10% for all discounting processes, which facilitated the calculation of the Expanded IRR, however it is important to understand that the real option process implies other complexities which for the sake of simplicity were not included in this paper. Editor's note: This article was written in 2016. Since then, CAIDTech has developed and applied the probabilistic frameworks described here across multiple mine projects in Latin America and Australia, integrating geological variability, operational dynamics and economic uncertainty into a single quantitative model. Learn more at [caidtechnology.com]