# Alternative Valuation Methods of the DCF Model

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The objective of this dissertation is to review and critical evaluation of alternative valuation methods complimentary to the Standard Discount Cash Flow model and the impact on management decisions within the mining industry using the Rio Tinto QMM project as an applied example.

The objective of this dissertation is to explore Sustainable and Responsible Investing (“SRI”) as driver for more responsible and sustainable practices with the potential of impacting positively on broader society and to gain a holistic view of the industry, which includes identifying the main actors and understanding the key issues within the industry. The dissertation further aims to evaluate SRI within the context of the global financial crisis (“Crisis”) to understand the challenges and opportunities facing the industry during this difficult time and in particular whether the Crisis will act as a catalyst for mainstreaming SRI.

## 1.2 Scope

### The dissertation is designed to gain an understanding of

The dissertation is designed to gain an understanding of the SRI industry to be able to evaluate the impact of the global financial crisis (“Crisis”) on SRI, SRI's relevance to the global economy and the potential positive impact SRI can make on the world. To facilitate this understanding, the dissertation will visit the power and the politics of the SRI industry and identify the actors involved in the investing industry that have the potential of promoting or resisting SRI. This dissertation endeavours to evaluate the impact of the Crisis on SRI which will help assess whether SRI will become mainstream.

“Facebook has raised $500m of an anticipated $2bn in new funding from Goldman Sachs and other investors in a deal that values the dominant social network at around $50bn. That valuation implies Facebook is now worth more than Time Warner or Yahoo and almost twice as much as Google at the time of its 2004 initial public offering. It is also almost double the amount indicated by private sales of Facebook stock on secondary markets just five months ago.” (FT.com, 2011)

“Glencore, the world's largest commodities trader, and mining company Xstrata are leading the list of possible buyers for the Colombian coal assets of Drummond, a family-owned US coal mining company. The mining interests – which include a railway and a port – could fetch $6bn-$8bn. An important managerial decision within any business is the optimisation of its asset configuration. This decision cannot be validated or measured without the generation and evaluation of potential alternatives. Asset valuation forms an integral part of the evaluation process.” (FT, 2010)

“Minmetals announced late Wednesday night that it would pay Oz Minerals just under $1.4bn, up from $1.2bn, ahead of the crucial shareholder vote. The higher price offered by the Chinese metals group took into account the improvement in commodity prices and mining asset valuations in the months since Minmetals made its recommended offer earlier this year.” (FT, 2009)

What conditions allow these valuations and what methods are implemented to determine the value of these companies?

According to Aswath Damodaran, Professor of Finance at the Stern School of Business at New York University, there are three general misconceptions in relation to valuations:

Myth 1: A valuation is an objective search for “true” value

Myth 2 : A good valuation provides a precise estimate of value

Myth 3: The more quantitative a model, the better the valuation

In the same paper he follows up with the followings “truths” in relation to valuations:

Truth 1: All valuations are biased. The only questions are how much and in which direction. The direction and magnitude of the bias in your valuation is directly proportional to who pays you and how much you are paid.

Truth 2: There are no precise valuations; the payoff to valuation is greatest when valuation is least precise.

Truth 3: One's understanding of a valuation model is inversely proportional to the number of inputs required for the model – simpler valuation models do much better than complex ones.

## Literature Review

The aim of this literature review will be to consider the key valuation models; discounted cash flows, relative valuations and real option valuations to provide the background to our research thesis as to whether real option valuations can be utilized as a complimentary approach to the standard discounted cash flow model and the impact and benefits this may have on management decisions within the mining industry.

### To assist individuals and companies in the valuation process, there exist a number of valuation methods:

Discounted Cash Flows which will form the basis of our enhanced valuation model

Relative Valuations and their benefits and limitations

Black-Scholes and Merton Models, to ascertain their suitability for use in the mining industry

Real Options and whether its implementation can enhance asset valuations

Monte Carlo Simulation Model as a viable alternative to Real Options

### Schools of Thought

FM34

The pivotal question in relation to asset valuation is what method to implement in order to evaluate investments, taking into consideration high risk, high return investments and the means of communicating this potential value to investors in a concise and understandable manner.

Historically this has been approached using the discounted cash flow or net present value framework. The accuracy of this approach has been questioned on a number of occasions. Studies undertaken by Luehrman, Sporleder, Trigeorgis and Smith have suggested that the discounted cash flow approach is obsolete and concluded that the real option valuation method overcomes many of the limitations associated with the discounted cash flow method (Dixit and Pindyck)

### Timothy Luehrman

Lenos Trigeorgis in his book, Real Options: Management Flexibility and Strategy in Resource

Allocation, considers the theory and practical applications from his research into real options. The initial chapters in the books focus on the increased management flexibility associated with real options

“It is now widely recognised, for example, that traditional discounted-cash flow (DCF) approaches to the appraisal of capital-investment projects, such as the standard net-present-value (NPV) rule, cannot properly capture management's flexibility to adapt and revise later decisions in response to unexpected market developments…….., management may be able to defer, expand, contract, abandon, or otherwise alter a project at various stages of its useful operating life.” (Trigeorgis, 1996)

Trigeorgis (1996) goes on to say: “This managerial flexibility is likened to financial options…….having the right but not the obligation to exercise the option lies at the heart of the option's value.”

### Discounted Cash Flow

NB – C5 and FM5

The discounted cash flow model is widely regarded as the most accurate and efficient method of asset valuation. The various assumptions that are required in the development of the Discounted Cash Flow model introduce significant levels of uncertainty into the valuation. The value of the future benefits delivered by an asset determines its value, whereas the value of an investment is the stream of future cash flows that it will generate for an investor.

The relative valuation methods on the other hand do not focus on the valuation on the intrinsic asset value but rather use models that calculate asset value in relation to the price of similar assets. With relative valuations the most frequently used variables are earning, cash flows, book value and sales.

The discounted cash flow model grew in prominence on the back of the market crash in 1929. Irving Fisher in his book “The Theory of Interest” in 1930 and later John Burr in 1938 in “The Theory of Investment Value” were the first two authors to express the discounted cash flow in current economic language.

Discounted cash flows are impacted to two factors: (a) the time value of money and (b) the risk that the amount of money will not be what is expected. The discounted rate is selected to reflect the risk associated with the underlying asset, the higher the risk the higher the discount rate and this is used to discount all forecast future cash flows to calculate a present value.

In practical terms, most investments or investment projects are valued using the standard discounted cash flow model based on the Weighted Average Cost of Capital (WACC). The Capital Asset Pricing Model (CAPM) is used to estimate WACC. The WACC reflects the return required by investors from the market and will be applied to individual investment projects.

It should however be noted that the WACC determined to reflect the risk associated with a company may not accurately reflect the risk associated with individual nuanced investment projects. The company must then use discretion in determining the appropriate discount rate for individual projects to reflect the risk associated with these unique projects.

According to Brearley, Myers & Allen (2008) when you use a discounted cash flow to value a project, you implicitly assume that your firm will hold the project passively. In other words, you are ignoring the real options attached to the project - options that sophisticated managers can take advantage of. You could say that DCF does not reflect the value of management. Managers who hold real options do not have to be passive; they can make decisions to capitalize on good fortune or to mitigate loss. The opportunity to make such decisions clearly adds value whenever project outcomes are uncertain

The key attribute according to Damodaran (1997) of an effective valuation model will have three variables, the value of cash that will generated, the period in which these cash flows will occur and the uncertainty or risk associated with these cash flows. The assumption supporting the discounted cash flow model is that the value of an asset should be equal to the present value of its future profits or cash flows. Investors see the valuation of their investment as the present value of all cash that could be made available to them in the future.

The discounted cash flow model is used primarily in the following situations:

Start up business or during the early stages of development

In instances were cash flows decline over time (mining companies)

Businesses that have variable capital expenditure exposure

Acquisition and turnaround situations

Where the company has a finite life (mining companies)

A style of the discounted cash flow model has for many years been considered the most appropriate model within the mining industry, however in recent years, driven by ongoing research and the development of new technology, the mining sector has continued to expand. Companies have developed technology that allows them to push the depth boundaries and in some instances explore areas previously seen as to difficult and expensive to develop. Through this mining companies have realised that the discounted cash flow model has restricted management decision making and flexibility and are looking at alternative options to value potential reserves.

The final step in the discounted cash flow model is to add together the cash flows to form the project value of each scenario. These values in relation to individual scenarios are one of the quantitative inputs into the decision making process. To enhance the value and validity of these models, probability distributions for these scenario's are developed.

The limitations of the discounted cash flow model when considered within the corporate finance structure include the limitations of cash flow estimates (quantum, timing & likelihood), impact of residual cash flows, limited information availability and the exclusion of real option decisions. Another limitation is the decision in relation to applied growth and discount rates. The interpretation and assumptions applied to these rates will determine the model outcome and are seen the most subjective or open to manipulation components of the model.

The discounted cash flow model has a number of significant limitations that need to be considered when using the model to enhance the decision making process.

First, due to the nature of the model significant bias is generally included in the evaluation. When considering a substantial project, comprising of a number of smaller projects, the model assumes that the risk associated with all individual projects is equal in magnitude and that the risks occur and are resolved at a constant rate over time.

The impact on long term projects, such as mining, is that the project is excessively discounted into the future and no consideration is included as to the ability of managers to respond to future contingencies. Decision makers can attempt to compensate for this shortfall in the calculation but only if they are aware of it at the time of the model development.

Second, the discounted cash flow model is based on the requirement that a decision is made immediately and does not encourage managers to consider alternatives that can be incorporated in the future.

Third, the decision in relation to the discount rate used is pivotal in the calculation of the discounted cash flow model. In many instances the inability to understand the issues and complications behind this choice is not understood within many organisations.

Finally, the interpretation of risk and the inability to determine the underlying risk is compensated through the organisations decision on the discount rate incorporated and their spread across the sensitivity analysis.

The four implications above highlight the need for an alternative method that reduces bias in relation to risk and the applied discount rates and the increases managerial flexibility and decision making.

## Introduction to Options

### Financial Options

The underlying premise of an option conveys to the holder the right to purchase or sell at a fixed price or strike price an underlying asset on or before an agreed expiry date. The right is not deemed an obligation which therefore transfers to the holder the right to exercise or allow the option to expire. Options are define in two categories – call option which convey the right to buy or put options which convey the right to sell. At the date of expiry, if the value of the asset is less

If at the expiry date, the value of the asset is less than the strike price the option is not exercised and expires with no value. However, if the value of the asset is greater than the strike price the holder of the option will exercise his rights and purchase the underlying asset. The variance between the value of the option and the exercise price is deemed the gross profit on the transaction. The net profit is therefore the gross profit less the initial value paid to acquire the option.

In his 19xx paper, “The Promise & Peril of Real Options”, Aswath Damodaran defines these two basic forms of payoffs in relation to options using highlighted in the diagrams below.

Payoff on Call Option

The diagram below was used by Damodaran to illustrate the cash payoff on an option on expiry.

Damodaran (19xx) explains: “For a call, the net payoff is negative (and equal to the price paid for the call) if the value of the underlying asset is less than the strike price. If the price of the underlying asset exceeds the strike price, the gross payoff is the difference between the value of the underlying asset and the strike price, and the net payoff is the difference between the gross payoff and the price of the call.”

Net Payoff

Strike Price

Price of Underlying Asset

Source: Damodaran (xxxx)

Payoff on Put Option

Damodaran (19xx) goes on to explain the payoff impact on a put option as: “A put has a negative net payoff if the value of the underlying asset exceeds the strike price, and has a gross payoff equal to the difference between the strike price and the value of the underlying asset if the asset value is less than the strike price.”

Net Payoff

Strike Price

Price of Underlying Asset

Source: Damodaran (xxxx)

The central theme of Damodaran's paper “The Promise & Peril of Real Options” published in 19xx is focused on considering the value of options embedded in corporate actions and whether the standard discounted cash flow model excludes these potential contributors to the value of an asset.

Damodaran (19xx) in the paper mentioned above highlighted the following issue: “While it is certainly true that there are options embedded in many actions, we consider the conditions that have to be met for these options to have value. We also develop a series of applied examples, where we attempt to value these options and consider the effect on investment, financing and valuation decisions.”

Need to include a section with our point of view in relation to Damodaran.

## Black Scholes & Merton Models

The initial method of valuing derivatives was published in 1973 by Fischer Black & Myron Scholes, followed later the same year by a second paper published by Robert Merton. These models provided a means of valuation incorporating an ability to deal with financial risk in both theory and practice.

Although specifically developed and applied to options within the financial sector, their models have been expanded to other industries as other economic contracts and decisions are viewed as options, an example being, an investment in a specific mining concession may provide an opportunity or an option to expand outside the specified concession at a later date.

### Black Scholes Model

In 1973 with the publication of their paper “The Pricing of Options and Corporate Liability”, Fisher Black and Myron Scholes developed an option pricing formula that has become the most benchmark method of pricing options. The existence of an option market in Europe and the establishment of the Chicago Board Options Exchange (CBOE) a month before the publication of the Black Scholes paper created not just a market for options but also the need for a rational pricing of options.

The sudden popularity of options and with that the use of the Black Scholes as a method of valuation resulted in the equation being incorporated into a financial calculator developed by Texas Instruments. Within a short period of time in ‘73 and ‘74 the financial world had a market to trade options, the Black Scholes method of valuation and the calculator. An issue that had existed for decades in relation to the rational pricing of options had an answer and Fisher Black and Myron Scholes seemingly became famous overnight successes. Their fame was sealed when Scholes and Robert Merton, reviewed later in this paper, were awarded the 1997 Nobel Prize in Economic Sciences. Fisher Black ineligible for the prize due to his death in 1995 was mentioned as a contributor by the Swedish academy.

The model as published by Black and Scholes is the equation for the valuation of an European call option which is dividend protected, what this effectively means is that there is no possibility of early exercise of the option nor will the payment of dividends affect the value of the option within their model. The determined option value derives both a value for the buyer and seller who will agree a cost to call or strike price and an option exercise date.

The value of the European call option is written as a function of the following inputs:

present price of the underlying asset (S)

strike price of an option (K)

time to expiry of the option (t)

risk free interest rate in relation to the life of the option (rf)

volatility of the underlying asset - expressed as the standard deviation of the annualised compound rate of return of the underlying asset (V)

The equation is shown as:

Value of European Option = SN(d1) – KeÊ³Í N(d2)

where:

d1 = ln(S/K) + (rf + V²/2)t

V √sq root t

d2 = d1 - V √t

and where:

N = normal distribution of the d values which can now be calculated using the NORMDIST function in Excel

Prior to the publication of the equation in 1973 there had been no standard option pricing method, the release of the equation turned the much maligned guessing game into a mathematical equation that helped develop the option market as we know it. The Black Scholes model allowed traders to compare the prevailing option price in the exchange against the theoretical value derived by the Black Scholes model to determine whether an option was over or under valued thereby assisting in the trading decisions.

Although developed in the United States, the Black Scholes model focused on the pricing and hedging of European call and put options as the American market had a only started one month earlier in Chicago. The fundamental difference between the pricing of European and American options is that the European options do not take into consideration the possibility of early exercising. As a result of this American options attract a higher price than their European cousins. The “classic” model as described above does not take into consideration the early exercising of the option.

The Black Scholes model has several underlying assumptions:

the stock pays no dividends,

the option can only be exercised on the expiry date,

the option moves in a manner referred to as “random walk”, that is that the option is free to move both up and down,

there are no commissions charged in the transaction,

interest rates remain constant and

the stock returns are normally distributed, thereby creating a situation where volatility is constant of the life of the option

The Black Scholes model is the most widely used valuation method of options in use, it should however be noted that other methods of valuation do exist which are used when the assumptions as listed above allow for inaccuracies.

http://www.optiontradingpedia.com/free_black_scholes_model.htm - good info on BS

### The Merton Model

In 1970 Robert Merton published a model carrying his name that defined a companies equity in terms of an option on its assets which could then be extrapolated is to assess the credit risk associated with the company. This model introduced the use of continuous time default probabilities to model options on the common stock of a company.

In 1973 he published the Merton Model for pricing European options which was seen as a more generalised pricing formula to the one released earlier in the year by Black and Scholes. It was on the back of this model that he jointly received the Nobel Prize in economics with Myron Scholes in 1997.

The underlying premise of the model is that companies retain a certain amount of debt that will become due for payment at a point in time in the future. If the companies assets are less than the outstanding debt at the time of repayment the company would default on the debt, therefore similar to the European call as published by Black & Scholes, the equity of a company is the European call option on the assets of the company on maturity of the debt with the strike price being an amount equal to the value of the debt.

The model requires three specific inputs:

the equity spot price

the equity volatility

the value of the debt

The Merton Model has been adapted for use outside the financial sector specifically within manufacturing entities enabling them to determine an appropriate level of risk for future transactions. Futures allow companies to hedge against upcoming risk, an example being the future delivery of a certain item at a certain price.

This method is employed within the mining industry, a company may considering a mine based on their ability to sell the metal in advance at a specific price thereby making use of the futures market in that specific metal. The risk in future movements in the price of the metal (underlying asset) is transferred from the mine owner to the buyer of the contract. By design, options allow a hedge against one-sided risks. Effective risk management within a company requires that these financial instruments be correctly priced.

### Monte Carlo Simulation

The Monte Carlo Simulation method allows us (Marseguerra and Zio, 2000) to consider various relevant aspects of systems operation that cannot be easily captured by analytical models (K-out-of-N, redundancies, stand-by nodes, etc.).

As previously discussed risk analysis in some way is part of most decisions we make. In the face of uncertainty and ambiguity, even taking into consideration the fact that we have unprecedented access to information and data we are unable to predict the future. The aim of the Monte Carlo Simulation Model is to allow you to view as many as possible outcomes of your decisions and improve your assessment of the impact of risk beyond a simple sensitivity analysis.

The Monte Carlo method does not exists as a single model but rather as a stochastic technique based on the use of random variables and probabilities to enforce the quantitative analysis and decision making processes to reduce risk. The model is across a number of industries such as finance, manufacturing, engineering, insurance, oil and gas, research and development and the environment. As part of our research we consider its suitability within the mining sector with a key outlook being the ability to examine more complex projects.

The process is a computerised mathematical technique that provides the management team with a range of possible outcomes and the probabilities of their occurrence based on any number of inputs. The model extrapolates outcomes from the highest risk decisions and the possibility of liquidation to the most conservative of decisions and all other possibilities in between in relation to Return on Investment (ROI).

Monte Carlo simulations allow one to substitute a distribution representing the variability in a specific variable instead of making a "single-point" assumption. Instead of a perfect forecast, one can directly simulate real-world variability of process variables. Monte Carlo simulation also allows one to analyze the cumulative effect of the variability in several variables. The end result is a distribution showing the probability that an ROI estimate will result. (Hileman, 2003)

Stanislaw Ulam first considered the model in 1964, later joining forces with John von Neumann to fully develop the application. The technique was first used by scientists working on the atomic bomb named after the city in Monaco renowned for its casinos and the multitude of probabilities associated with gambling.

Monte Carlo operates as a simulation of risk analysis through the development of models with varying possible outcomes by substituting a range of values for any factor that has inherent uncertainty. The model then continuously calculates possible outcomes each time using a set of random variables from the probability functions. The number of recalculations, which can involve thousands or tens of thousands of recalculations, depends on the number of uncertainties and the ranges specified for each one. The model then produces a distribution of possible outcomes. The advantage of using probability distributions allows variables to have different probabilities in relation to different outcomes occurring. As we already know probability distribution provides a more comprehensive approach to describing uncertainty in variables in a risk analysis.

The more common probability distributions are:

### Normal Distribution

Also known as bell curve distribution allows the user to define the mean or expected value and a standard deviation to describe the variation about the mean. All values in the centre around the mean are most likely to occur. The model is symmetric and describes many natural phenomena such as people's heights or birthdays. Examples of variables used to describe normal distributions include inflation rates and gas prices.

### Lognormal distribution

The values are positively skewed, unlike the normal distribution. The model is used to reflect values that do not fall below zero but have unlimited positive potential. Examples of variables described by lognormal distributions include real estate property values, stock prices, and oil reserves.

### Uniform Distribution

Under uniform distribution, all values have an equal chance of occurring; the requirement from a user perspective is to define the minimum and maximum value in each instance. Examples of variables that could be uniformly distributed include manufacturing costs or future sales revenues for a new product.

### Discrete Distribution

In this model, the user is required to define specific values that may occur and the probability of each occurrence. A simple example might be the outcome of a lawsuit - 20% chance of positive verdict, 30% chance of negative verdict, 40% chance of settlement, and 10% chance of mistrial.

Using the Monte Carlo model, the values are randomly sampled from the input probability distributions. Within the process each sample set is known as an iteration with the resulting outcome recorded. The simulation repeats this process over and over again recording all possible outcomes; the final results therefore provide a comprehensive view of what may happen.

The advantages of the Monte Carlo model over the other methods are:

the results shown not only reflect the possible outcome but also the probability of each outcome

the results generated can easily be graphed to visually reflect the probability of occurrence making the model and its results easily understandable by stakeholders

the use of a sensitivity analysis allows the user to determine which inputs have the most significant impact on the bottom line results

using the scenario analysis function, the user can determine which inputs and which values when used together created certain outcomes

the model also allows inputs to be correlated which is the modelling of interdependent relationships between input variables – this highlights the impact of one factor increasing while another factor decreases

The weak point of the Monte Carlo method is the computing time (Marseguerra and Zio, 2000) especially when we deal with the problem of finding suitable maintenance control policies, and the search space for the control variables of the problem to test increases.

### Real Options

FM2 / FM7

Real options are implemented to quantify the value of management flexibility when faced with uncertainty as has been the case in the recent economic environment. They differ from the valuation options we have previously reviewed above in that they are strategic options and they incorporate similar drivers to financial options with the key differentiator being that real option are not traded on the financial markets.

The table below highlights the key differentiators between real and financial options.

Source: PWC (19xx) RO Valuation – best option for identifying real value

Real options allow management increased flexibility in the face of uncertainty in relation to strategic decision. As a concept real options allow management the ability of determining and a means of communicating both the strategic imperatives and values of an investment. The implementation of real option decision making can enhance shareholder value through their correct and timely implementation.

Real options have become accepted as either a replacement method or as an add on to the traditional valuation methods associated with the Net Present Value calculations. The identification, adaptation, managing and exercising of real options has become a significant component of enhancing shareholder value. The real option methods allow corporate decision makers the ability to leverage uncertainty and limit downside risk through having more than one option available when considering strategic decisions over the life of an investment or project.

In the case of the mining industry the decision to extract natural resources from the ground may be delayed should the market price of the resource fall below the extraction costs or vice versa. Strategic decisions such as the above are not incorporated in the standard discount cash flow model where the calculation determines a single present value and are focused on minimising the cost of capital. The effective decision in relation to a real option has the ability to significantly increase the value of investment or project eliminating unfavourable outcomes.

According to Brearley et al (2008) there exist four key real option decisions:

the option to expand if the immediate investment project succeeds

the option to wait (and learn) before investing

the option to shrink or abandon a project

the option to vary the mix of output or the firm's production methods

### Expansion Option

The potential expansion option of a project can be highly valuable to a company. If an investment turns out better than expected the quicker and easier the investment can be expanded can deliver incremental value to the investor.

An example of an expansion option would be a mining company that acquires the right to mine an ore body that is not beneficial to mine today but could become highly profitable in the future if ore prices increase. This is the company acquiring the real option to expand.

### Timing Option

The cornerstone of the discounted cash flow model is that if an analysed project has a positive net present value (NPV), the project should be undertaken. As previously mentioned there is a school of thought considers that in some instances it may be more beneficial to adopt a more considered approach and allow the prevailing market to develop.

If the investment does not deliver as expected and cash flows fall below expectations having the option to reduce your investment can be beneficial.

### Abandonment Option

The third real option, abandonment is the equivalent of a put option.

You exercise that abandonment option if the value recovered from the project's assets is greater than the present value of continuing the project for at least one more period. The binomial method is tailor-made for most abandonment options.

Mix Option

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