Investments in Mining Projects: A Prototype Software

Abstract

The objective of this project is to develop a prototype software for valuation of investments in mining projects. The software is intended to be able to deal with a variety of situations. They include the use of different valuation methods (both traditional - net present value, internal rate of return, and real options-based - mainly an option value), as well as different types of decisional situations (deferral, abandonment or expansion options). In order to be user friendly and easily accessible, the software uses Visual Basic as a front end. [PUBLICATION ABSTRACT]

Headnote

Abstract

The objective of this project is to develop a prototype software for valuation of investments in mining projects. The software is intended to be able to deal with a variety of situations. They include the use of different valuation methods (both traditional - net present value, internal rate of return, and real options-based - mainly an option value), as well as different types of decisional situations (deferral, abandonment or expansion options). In order to be user friendly and easily accessible, the software uses Visual Basic as a front end.

Keywords: Project valuation, real options, mining projects, software for investments

1. Introduction

A wide range of methods and techniques is available to valuate an investment. Along the life cycle of a mining project, appropriateness of use of a given method might depend on the specifics of the decisional situation involved. People involved in the investment decision making process for such a kind of project - either analysts or investors, might then face the hassle of choosing not only a valuation method but also a software. To make matters worse, most of the available commercial software is either: (1) linked to a single specific valuation method or type of methods, (2) not easily accessible (in terms of cost, technical complexity, availability - as might be the case of some less developed countries), and (3) not appropriate for a straightforward application for mining investment projects.

On the other hand, people involved in the decision making process in the above type of projects usually has a somehow structured knowledge of the behavior of the variables that might affect the project profitability.

This paper presents a prototype software which for a given decisional situation:

1. Allows the user to select alternative valuation methods - either conventional [8, 9, 10] or ROA-based [1, 5, 6, 7], and the profitability measure(s), and

2. Assumes some sort of basic knowledge by the analyst on the behavior over time and the nature - either deterministic or probabilistic, of a set of uncertainty sources (such as the commodity market price, the size of the deposit, the rate and cost of its depletion) which are used as inputs to model the net cash flows over the economic life of the project.

Furthermore, aimed at being user friendly and easily accessible, the software uses Visual Basic as a front end.

2. Investment projects in mining

Life cycle of a mining project involves four different stages [2]: (1) Exploration, (2) Investment and development, (3) Exploitation, and (4) Conclusion. For valuation purposes, the objective of an investment analysis study is directly linked to the current project stage. Sources of uncertainty are related to a variety of both external (to the project) as well as internal variables. They include [3]: Economical variables (such as the commodity market price), and Geological-technical (such as the size of the deposit, the rate and cost of the deposit depletion). Decisions made along the project life might affect the project profitability as well. In this regard, issues such as the rate of exploitation (both in terms of its magnitude as well as of the timing of rate changes) should be explicitly considered. Table 1 displays relevant issues to consider for the investment analysis in mining projects.

1. DECISIONAL CONTEXT:

* Alternative(s) to consider (Abandonment, deferral, expansion, contraction options?).

* Investment worth approach/measures to use (Recovery period, Net present value, IRR, option value?).

2. VARIABLES AND PARAMETERS IDENTIFICATION AND ANALYSIS:

* Variables and parameters affecting cash flows.

* Uncertainty sources relevant for profitability (economical, geological-technical).

* Classification of variables according to uncertainty assumptions (reasonably certain -exploitation cost, operation rate, and uncertain - commodity market price, deposit size, ?).

* Specifics on relevant parameters (discount rate, initial investment, depreciation, tax rate, ?).

Based on the previous issues, the net cash flow, NCFt, for a given time period, t, can be expressed (generalized form) [4] as:

NCF^sub t^ = {[(P^sub t^ - C^sub t^)E^sub t^ - G^sub t^ - D^sub t^] - Md^sub t^} (1 - T) + D^sub t^ ± ΔW^sub t^ (1)

Where P^sub t^: commodity price, C^sub t^: ore extraction cost, Et: exploitation rate, G^sub t^: overhead expenses, D^sub t^: depreciation, Md^sub t^: debt payments, T: tax rate, and ΔW^sub t^: working capital change. It is not uncommon that the investor/analyst has some knowledge on the behavior of some of the variables in equation (1). For example, when dealing with the commodity price (P^sub t^), some reasonable assumptions on its behavior over time can be done. This results in the possibility of defining pattern profiles over time for such a type of variables. Incorporating this kind of knowledge into the subsequent analysis is of an utmost value. Figure 1 shows the different stages for investment analysis.

As an example, consider the following simple case: According to recent price prospects, they are expected to move higher than today's price (on a linearly increasing trend) for the following 10 years. A mine owner considers this as an opportunity to invest in new equipment for a deposit currently under-exploited. He is then to determine the most appropriate time, k*, to make such an investment. The described decisional situation relates to the valuation of a deferral option [1, 5]. Figure 2 shows a flow diagram to determine k*.

Once the situational decision involved has been identified, cash flows are to be estimated over the desired planning horizon. This might require incorporation of the assumed knowledge on the time behavior of the variables and parameters involved. For the aforementioned example, such a knowledge might relate to the linear trend the metal price is expected to be following (note that this might involve modeling of surrounding uncertainty - which can be done by means of randomness modeling).

3. Software characteristics

Dealing with situations common for mining investment projects (such as the one described in the previous section) can result in a rather cumbersome task when using most of the commercially available software, particularly for a small or medium scale firm. The available software might: (1) require extensive modeling abilities for the decision maker/analyst (this is the case of general-purpose software, such as those based on spreadsheets), (2) require highly specialized technical knowledge on financial methods and techniques, or (3) not be appropriate for handling the specific characteristics of the situation under analysis.

A prototype software with the following attributes is presented below [4]: It is written in Spanish (it is to be used in Mexico), user friendly (with regards to information inputs and outputs), does not require programming/modeling efforts, incorporates knowledge available from the investor/analyst on variables and parameters, economically accessible, runs on a personal computer, and allows the user to select either one or several at a time valuation methods (traditional - deterministic, tradition - probabilistic, and real options-based).

Figures 3 and 4 show an example of the input screens of the prototype software. As it can bee seen, they allow the user to incorporate uncertainty for some variables. For example, Figure 3 shows the inputs for a normally distributed market price of a mineral and Figure 4 shows the input of some project parameters.

Figures 5 and 6 show an example of the output screens of the prototype software. Figure 5 indicates the output of a NPV analysis that includes the probability distribution of the NPV (it displays the histogram for the simulated NPVS and the basic statistics for a given project). Figure 6 shows a binomial decision tree of a project in which an abandonment option was considered to model the decisional situation (on the binomial tree it is shown in red color the different states of nature over the planning horizon in which it is appropriate to abandon the project).

Acknowledgments

This software was developed to get the B.Sc. degree in Industrial Engineering for Jorge Hinojosa under the advise of Alejandro Teran. Thanks are due to the Department of Industrial Engineering, ITAM for the support awarded during the project

References

References

[1] Copeland, T., and V. Antikarov, 2001, Real Options. A Practicioner's Guide, Texere, New York.

[2] Cortazar, G., E.S. Schwartz and J. Casassus, 2001, "Optimal Exploration investments under price and geological-technical uncertainty: A real Options model", R&D Management, February, 181-182.

[3] Dias, M.A.G, 2004, Real Options Tutorial, http://www.puc-rio.br/marco.ind/tutorial.html.

[4] Hinojosa, J., 2004, Real Options: A Software Prototype, B.Sc. Thesis, ITAM, Mexico, (in Spanish).

[5] Luenberger, D.G., 1998, Investment Science, Oxford University Press, Oxford.

[6] Merton, R., 1973, "Theory of Rational Option Pricing", Bell Journal of Economics and Management Science, V. 4, Spring 1973, pp. 141-183.

[7] Miller, L.T. and C.S. Park, 2002, "Decision Making Under Uncertainty - Real Options to the Rescue?", The Engineering Economist, V. 47, N. 2, pp. 105-150.

[8] Park, C., S., and G. P. Sharp-Bette, 1990, Advanced Engineering Economics, Wiley, New York.

[9] Ross, S.A., R.W. Westerfield, and J.E. Jaffe, 2005. Corporate Finance, 7/e, McGraw-Hill, New York.

[10] White, J., et. al., 1998, Principles of Engineering Economic Analysis, 4/e, Wiley, New York.