Financial Decisions Under Uncertainty for Mining, Oil and Gas Projects - A Capital

Markets Approach.

Dr. Colin Beardsleywww.austraclear.net

Some comments on this Webinar

This Webinar presents an exposure draft of sections of a short E-book on project finance that I’m justcompleting. The main emphasis of this book is to take the part of a possible investor in a project. Suchinvestor may be a corporation in which the company’s weighted average cost of capital (WACC) iscalculated. Or the investor may be an institution that may be interested in a tax effective structure.

I’m grateful to Palisade Corporation for putting on this Webinar. I have the highest regard for thecompany’s software and have used it at a number of business schools throughout the world where I haveheld courses.

All projects are idiosyncratic and require bespoke modelling solutions. I would like to hear from you onwhat you think about the draft in this Webinar. I can be contacted at colin.beardsley@gmail.com –Alternately, please send in questions while we’re live. See http://www.austraclear.net/project-finance/for a number of references on project finance in the public domain. When finished, the E-book plusExcel models will be downloadable at $A25.

Regards,

Dr. Colin Beardsley

Agenda

• What is Project Financing?

• The focus and theme of this presentation.

• The Capital Asset Pricing Model (CAPM).

• Weighted Average Cost of Capital (WACC) and the Security Market Line (SML).

• Basic Project Finance model using Excel.

• Analysing key project drivers using Palisade’s TopRank

• Analysing key inputs using Palisade’s Distribution Fitting Tool.

• Simulated Project Finance modelling using @RISK with correlations.

• Geometric Brownian Motion (GBM) Model of Coal Prices.

• Putting it all together 1: Simulation Project Finance Model with GBM.

• Putting it all together 2: Simulation Project Finance Model with Path Dependency.

• Integrating an Off-Take agreement into the cash flows plus a few words on lenders.

• References

What is Project Financing?

• Project financing is nothing new. Techniques date back to at least 1299 A.D.when the English Crown financed the exploration and the development of theDevon silver mines by repaying the Florentine merchant bank, Frescobaldi,with output from the mines.

• Another form of project finance was used to fund sailing ship voyages untilthe 17th century when investors would provide financing for tradingexpeditions on a voyage-by voyage basis. On return, the cargo and ships wouldbe liquidated and the proceeds of the voyage split among investors.

• Finnerty notes : “Project financing may be defined as the raising of funds on alimited recourse or nonrecourse basis to finance an economically separablecapital investment project in which the providers of the funds look primarilyto the cash flow from the project as the source of funds to service their loansand provide the return of and a return on their equity invested in the project.”

What is Project Financing?

Projects come in many shapes and sizes from tollways and tunnels to themeparks, from building Olympic stadiums to pipelines.

Mining, oil and gas projects share several common characteristics:

• They are long term

• Considerable infrastructure investment is involved

• Cash flows are “quarantined”

• Entities involved are either listed companies or proxies are available to analyserisk/return features

• Projects involve scale economies

• Resources involved have finite lives

The focus and theme of this presentation.

The central theme involves making financial decisions under uncertainty for mining, oil, and gas. I have tried to develop asimple generic modelling approach which is applicable to such projects utilising a relatively inexpensive data-driven capitalmarkets approach. The reasons for this approach are simple:

1. A plethora of data sources are readily available through the internet on commodity prices and companies involved insuch extractive industries.

2. Academic initiatives such as the Capital Asset Pricing Model (CAPM) and Weighted Average Cost of Capital (WACC)lend themselves to quantitative analysis. Such finance theory is readily manageable with the hard practice of projectevaluation.

3. Using advanced techniques such as Palisade’s @RISK Monte Carlo simulation program, risk analysis thrives on highfrequency long series data.

4. The mathematics of finance theory are made tractable using such simulation software.

5. It is possible to integrate option pricing theory such as (1) the Black-Scholes model and (2) Geometric Brownian Motion(GBM) pertaining to asset prices into dynamic simulation. In addition, I have also included path dependency.

6. I have eschewed subjective expert opinion as experience has taught me that such opinion can be horribly wrong inforecasting revenues. It may be that having analysed the available data that some model parameters could be “tweaked” byexperts if they can justify the changes.

7. It is to be hoped that geologists, engineers, architects, quantity surveyors and the like can get the cost of a project withintolerable bounds but ……

Main Emphasis

• The main emphasis of this presentation is to take the part of a possible investor in aproject. The investor may be a corporation in which the company’s weighted averagecost of capital (WACC) is calculated. Or the investor may be an institution that maybe interested in a tax effective structure. The focus of this presentation is narrow.The central theme involves making financial decisions under uncertainty for mining,oil, and gas projects utilising a relatively inexpensive data-driven capital marketsapproach. I have chosen a small Australian coal mining company – Whitehaven Coal– as a test case investing in a hypothetical coal mining project.

• I have assumed, on your part, that you are familiar with a number of Excel basicssuch as relative and absolute cell references; Net Present Value (NPV and XNPV);and Internal Rate of Return (IRR and XIRR); as well as IF statements.

• I have also assumed a working knowledge of regression plus understanding measuresof central tendency (mean, median and mode) and dispersion (standard deviation).There are numerous books available and internet references to satisfy an astute readerwishing to further understanding of spread-sheet modelling as well as basic statistics.

• All projects are idiosyncratic and require bespoke modelling solutions. I hope themethodologies discussed here will assist in building your own models.

The Capital Asset Pricing Model (CAPM).

"Entities must not be multiplied beyond necessity" William of Ockham (c. 1287–1347), an English Franciscan friar, scholastic philosopher and theologian – commonly known as “Ockham’s Razor”.

“Everything should be made as simple as possible, but not simpler”. Albert Einstein Born: March 14, 1879 Died: April 18, 1955.

The modern acronym is K.I.S.S. (Keep It Simple Stupid). The CAPM is a simple concept and derives thefirm’s cost of capital from its covariance with the market return. The classic formula for the firm’s costof equity is:

𝑟𝐸 = 𝑟𝑓+ 𝛽[𝐸(𝑟𝑀) − 𝑟𝑓] where

𝑟𝑓 = 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡

𝐸(𝑟𝑀) = the expected return on the market portfolio

𝛽 = a firm specific risk measure =𝐶𝑜𝑣(𝑟𝑠𝑡𝑜𝑐𝑘,𝑟𝑀)

𝑉𝑎𝑟(𝑟𝑀)

Risk Free Rate and Equity Risk Premium.

• Risk Free Rates are readily available from central banks . Some searching isneeded. The results for the historical equity risk premium in Australia are inthe Excel spreadsheet Australian market risk premium which I’ll open.

• Monthly returns for the two-year Australian Treasury Bond have beendownloaded for the past 20 years.

• These data are combined with the past 20 years of returns of the AustralianAll Ordinaries Index downloaded from Yahoo.

• This index does not include dividends which would add approximately 4% p.a.to returns . The current risk free rate for Australian Government 10 yearBonds is 2.20% per annum.

Beta

• The final metric to be calculated is the regression coefficient (β) forWhitehaven Coal returns on the market returns, the Australian All OrdsIndex, which is the proxy for the stock market.

• The results of the regression for the same time period as the market riskpremium was calculated is in the Excel file Whitehaven Coal againstASX which I’ll open.

• The file contains a considerable amount of information. Note that theprices both of Whitehaven Coal and of the ASX have been transformedinto returns using the formula =LN (Pt+1/Pt) which is copied down forall relevant months.

• The natural log transformation produces the instantaneous rate ofchange between two variables and is used extensively in finance theory.

Downloading data - Stock Exchanges; YahooApart from central banks for interest and exchange rates, there are two main sources of stock market data in the host country - the relevant stock exchange and YAHOO which is marketed in Australia under YAHOO! 7 Finance. A particularly useful downloader Excel application has been invented by Samir Khan that downloads multiple stock data from Yahoo (See http://investexcel.net/multiple-stock-quote-downloader-for-excel/) . The spreadsheet which is available at no cost looks like this with the Whitehaven Coal and ASX data. Note that individual stocks may need an identification suffix which is .AX in the case for Australian stocks and a circumflex (^) for indices.

Weighted Average Cost of Capital (WACC) and the Security Market Line (SML)

Having assembled the data from market sources for the classic CAPM equation:

𝑟𝐸 = 𝑟𝑓+ 𝛽[𝐸(𝑟𝑀) − 𝑟𝑓]

We can calculate Whitehaven Coal’s weighted average cost of capital (WACC). But before doing the calculations, it is useful to interpret the CAPM graphically. Whitehaven Coal’s position on the Security Market Line will be north east of the point M with a vertical intersection from the X-axis at a Beta of 1.384.

Scatterplot of Whitehaven against All Ords

Using the Security Market Line (SML) to calculate Whitehaven Coal’s Cost of Equity

From the classic CAPM model, Whitehaven Coal’s Cost of Equity is 11.71% p.a. from the Excel File Whitehaven Coal Cost of Equity Classic CAPM.

The classic CAPM above does not allow for corporate tax. Denoting the marginal corporate rate of tax by TC, the formula can be rewritten as :

𝑟𝐸 = 𝑟𝑓 ∗ (1 − 𝑇𝐶)+ 𝛽[𝐸(𝑟𝑀) − 𝑟𝑓 ∗ (1 − 𝑇𝐶)]

Assuming a marginal corporate tax rate of 27.5%, I’ll open the Excel file Whitehaven Coal Cost of Equity Tax Adjusted CAPM. This transformation increases Whitehaven Coal’s Cost of Equity to 12.29% p.a.

Finally, we are ready to calculate Whitehaven Coal’s WACC. For this step, we need data from the company’s latest annual report . The following information is needed.

Calculating Whitehaven Coal’s WACC

• Issued capital = 3,144,944 shares

• Current share price (November 10, 2016) = $A3.19

• Market value of equity = $A10,032,370

• Debt = $A960,566

• Market Value of Firm = $A10,992,937

• Debt ratio = 960,566/10,992,937 = 8.7%

• Assumed cost of debt = 6% p.a.

• Marginal tax rate = 27.5%

• Equity Ratio = 91.3%

• Cost of Equity Tax-adjusted CAPM = 12.29%

• Whitehaven Coal’s after tax WACC is therefore:

• WACC = {0.06 x (1 – 0.275) x 0.087} + {0.1229 x 0.913} = 11.6% p.a.

Some comments on simplicity

• Because financial models for project financings are often fairly large and complex, it is important that they are carefully designed and logically structured.

• As new and often more detailed information for a project will often become available during the feasibility study period, models should be designed in a manner to facilitate updates and modifications. It is not unusual for a financial model that starts out relatively small and simple to grow in both size and complexity over time.

• The heart of a financial model is the cash flow waterfall, which differs from the traditional Statement of Cash Flows reported by corporations. A cash flow waterfall computes and presents the project cash flows from top-to-bottom in terms of their seniority.

• Revenue appears at the top, followed by operating and capital expenses, taxes, debt service, and lastly distributions to share- holders. The net change in cash for each period is also reported

Cash Flow Waterfall

Basic Project Finance model using Excel

We look now at how to set up a basic project finance model in Excel using the datafrom the capital markets. This analysis is aimed at providing a “first cut” view of theproject focussing on the main variables affecting the decision to invest

All projects are different. Boards of equity participants and bankers need to becomfortable with the way the “big picture” is analysed and presented.

I’ll open the Excel spreadsheet Basic Project Finance Model which I’ve split intotwo separate sheets – Summary and Model.

The actual model consists of the various cash and tax flows of the project which arenotated. The term stops at eight (8) years to fit in the screen. The formulas are all self-explanatory. The model can be expanded time-wise horizontally or by adding rowsvertically

Setting up the spreadsheetFrom the notes in Column A of the model, a few comments:

1. Recognise how quickly the inflation index compounds in only eight (8) years from 1.00 to 1.27. Overa 20 year period the inflation index would have compounded to (1.03)^20 = 1.81.

2. The debt balance calculates interest at the beginning of the next cash flow period. While this is notentirely correct, it does avoid circular references and makes very little difference to the overall resultson IRR and NPV.

3. Depreciation is a pre-tax provision and will reduce taxable income to participants.

4. Revenues are calculated after depreciation, interest and taxes

5. Cash flow adds back depreciation.

6. Equity cash flow takes in the amount put up by participants (the rest is debt) and picks up dividendspaid to equity holders.

7. Free cash flow is the total up front cost of the project and earnings therefrom.

8. Cash for debt servicing adds back interest

Making the spreadsheet easy to auditIn the summary sheet, note that Input are in the top left hand corner. Outputs are opposite inputs to enable the reader to scope the project quickly

without going through all the detail. A “what-if ” table analysing the impact of the main variables on the most important output, the Equity IRR, is

set out.

Inputs

All input cells are named. Naming cells facilitates auditing what can be a large spreadsheet as the important inputs will appear as (e.g.) Revenues and

are also absolute references. To do this easily, highlight the two Columns where the left hand one defines the name and the right had one is the input

number. Go to Formulas, Define Names, Create from Selection which brings up the follow-ing box. Tick left Column and then OK.

Outputs to the spreadsheet

Management and directors will focus on the project and equity participants’ IRR and NPV and, possibly,debt cover ratios as shown below. It may also be useful to describe the inputs to the results A word ofcaution in that the Excel NPV function does not contain the expenditure in Year 0 and when calculatingit is necessary to include this cell separately

e.g. = Cell $A$1 + NPV(Discount rate, range $A$2:$A$20).

We can also use Excel’s 2 way data table and Solver to provide outputs.

Analysing key project drivers using Palisade’s TopRank

We have used Excel’s “What if ?” analysis to calculate the effect of twoinputs on a given output. Palisade’s TopRank program greatly enhances thestandard What-If and data table capabilities of Excel.

TopRank uses an automated What-If analysis to determine which of yourmodel inputs affect your “bottom line” results the most. TopRank typicallyvaries the value of each input, one input at a time, to see the effect of thatinput.

However, TopRank can also run a Multi-Way analysis, where it tries allpossible combinations of values for a set of inputs and shows you theresults for each combination.

Tornado Graph of Inputs to Equity IRR

Spider Graph of Inputs to Equity IRR

Analysing key inputs using Palisade’s Distribution Fitting Tool

“If you torture the data long enough, it will confess.” Ronald Coase, Economist, Born:December 29, 1910; Died: September 2, 2013

A particularly useful tool for analysing past data is the Distribution Fitting app on the@RISK ribbon. I’ll open the Excel file Distribution fitting Australian coal monthlyand click on the icon - third from the right in the Model group.

The best fit for the coal price past data is a triangular distribution with a mini-mum of$69.815, mean of $81.860, and a maximum of $103.569. A note of caution – the redtriangle above represents a probability density function (PDF) which is slightly skewed tothe right. The area under this PDF is 100%; 90% of the values for the input data arebetween $75.27 and $96.54 while 89.7% of the fitted distribution lies between these values.

This type of analysis differs from the usual worst case/most probable/best case instandard spreadsheet formats which assigns equal probabilities to each of the cases. Thetriangular distribution is popular in that it is intuitively easy to understand but as can beseen from the figure above the fit is approximate with lumpy data (the blue bars). However,explaining what has happened to a Board of Directors using the triangular distributiontogether with the graph of prices in the Excel file will provide a useful “feel” for themarket.

Fit comparison for monthly coal prices 2012 to 2016

Fitting distributions to data – 10 year monthly coal returns 2006-2016

Correlations

• When identifying the uncertain values in your Excel worksheet, you have to decide whetheryour input variables are uncorrelated or correlated.

• If you decide that a set of variables is correlated, you can use special @RISK functions tomodel their dependent behaviour. It is extremely important to correctly recognizecorrelations between variables; otherwise, your model might generate nonsensical results.

• A classic example is if you ignored the relationship between Amount of Rainfall and CropYield, @RISK might simultaneously choose a low value for Rainfall and a high value for theCrop Yield, something that would almost never occur.

• I’ve correlated inflation and interest rates in the spreadsheet examples to come. Note that@RISK requires rank order correlation (Spearman’s rho).

• There may well be price/volume/overhead correlations in projects which need to berecognised.

Rank Order Correlation

Probability Distributions used in Project Finance(1) The Triangular Distribution

• This distribution can be either symmetric or skewed (usually to the right). Both typesare shown in the screen shots below. RiskTriang(minimum, most likely, maximum)specifies a triangular distribution defined by a minimum, a most likely value, and amaximum.

• It can be skewed in either direction, depending on the position of most likely relativeto minimum and maximum. This distribution is perhaps the most readilyunderstandable distribution for basic risk models. Its possible drawback for realapplications is that it allows no possible values outside the min-max range.

• In Monte Carlo simulation, this type of distribution takes the place of the usualworst case, most probable, best case guestimates which accord equal probability toeach event.

• In the case of construction costs, the right skew would indicate an increasedprobability that the project costing may be unreliable and the architects, engineers,and builders could get it completely wrong. Regrettably, this situation is not unusual.

Probability Distributions used in Project Finance(1) The Triangular Distribution

The Triangular Distribution can be symmetric (left) or skewed (right).

Probability Distributions used in Project Finance(2) The Normal Distribution.

RiskNormal (mean, standard deviation) specifies a normal distribution withparameters mean and standard deviation. This is the traditional “bell shaped”curve. The use of the normal distribution can often be justified by amathematical result called the Central Limit Theorem. This states essentially thatthe sum of many random quantities is approximately normally distributed,regardless of the distributions of the quantities in the sum. Therefore, thenormal distribution can be used to represent the uncertainty of a model’s inputwhenever the input is the result of many random processes acting together in anadditive manner. Examples could include the total number of goals scored in asoccer season or the amount of oil in the world (assuming that there are manyreservoirs of approximately equal size, each with an uncertain amount of oil).Two potential draw-backs of the normal distribution for real applications are

(1) it is symmetric, not skewed, and (2) it allows negative values. However, if themean is positive and is at least 3 or 4 times larger than the standard deviation,the probability of a negative value is negligible

Probability Distributions used in Project Finance(2) The Normal Distribution.

Probably the distribution which is most used in statistics, the normal distribution is also used extensively in finance as simulating a random process. IQ scores are commonly plotted as distributed normally with a mean of 100 and standard deviation of 15.

Cumulative distribution functionAnother way of looking at a distribution is by using a cumulative distribution function which is shownbelow. We can see that some 68% of IQ scores are between ± one standard deviation of the mean with16% less/more than one standard deviation. This percentage reduces dramatically with 2.3% less/moreand two standard deviations.

Probability Distributions used in Project Finance(3) The Discrete Distribution.

• The final distribution is discrete. RiskDiscrete({X1,X2,...,Xn},{p1,p2,...,pn}) specifies a general discrete distribution with n possible outcomes. Each possible out-come has a value X and a probability weight p that specifies the outcome's likelihood of occurrence.

• The probability weights can sum to any value, but internally, @RISK normalizes them so that they sum to 1. This distribution is very flexible and can be used for any discrete set of possibilities. The distribution can be entered into a spreadsheet as follows:

Values Probability

3.0% 25.0%

4.0% 50.0%

5.0% 25.0%

Probability Distributions used in Project Finance(3) The Discrete Distribution.

The discrete distribution looks like this:

Geometric Brownian Motion (GBM) Model of Coal Prices

• This is a difficult concept. As a bit of history, in around 1827, the Scottish scientist Robert Brown observed the

random behavior of pollen particles suspended in water. This phenomenon came to be known as Brownian

Motion.

• About 80 years passed before Albert Einstein, surprisingly unaware of the work of Brown, developed the

mathematical properties of Brownian motion. This is not to suggest that no work was being done in the interim,

but scientists did not always know what other work was being done, especially in those days. It is not surprising

that it was Einstein who received most of the credit.

• Brownian motion as a basis for modelling assets on which options trade was evidently discovered by a French

doctoral student, Louis Bachelier, in 1900. Bachelier's dissertation at the Sorbonne under the direction of the

famed mathematician Henri Poincaré was at that time considered to be uninteresting and only achieved a grade of

mention honorable instead of mention très honourable which was the requirement for a professorship in France at the

time

• Bachelier’s thesis was discovered more than 50 years later by an American economist, James Boness, who had it translated and reprinted. Although Bachelier solved the option pricing problem only for a very limited case, he pointed others in the right direction.

Geometric Brownian Motion (GBM) Model of Coal Prices

• The Geometric Brownian Motion (henceforth “GBM”) model of asset pricesstates that future returns on an asset are normally distributed and the standarddeviation of this distribution can be estimated from historical data. The morefamiliar name of this standard deviation is volatility.

• The name Geometric Brownian motion has its origins in a physical descriptionof the motion of a heavy particle suspended in a medium of light particles.The light particles move around rapidly, and as a matter of course, randomlycrash into the heavy particle. Each collision slightly displaces the heavyparticle; the direction and magnitude of this displacement is random andindependent from all the other collisions, but the nature of this randomnessdoes not change from collision to collision

• In the language of probability theory each collision is an independent,identically distributed random event). The geometric Brownian model takesthis situation, and using some mathematics, derives the displacement of theparticle over a longer period of time must be normally distributed with meanand standard deviation depending only on the amount of time that has passed.

Geometric Brownian Motion (GBM) Model of Coal Prices

• Prices, the heavy particle, are jarred around by trades, the lighter particles. Each trade moves the prices inproportion to their size. i.e. If an asset’s expected return is 10 per cent per annum then the asset at $50 hasan expected change of $5 while the same asset at a price of $25 has an expected change of $2.50.

• The GBM model describes the probability distribution of the future price of an asset.

• The return on an asset price between now and some very short time later (Δt) is normally distributed. Themean of the distribution is μ times the amount of time (μΔt), and the standard deviation is σ times thesquare root of time (σ Δt).

• An intuitive explanation for the square root above is that the variance of an asset over a short time is σ2Δt.The standard deviation is the square root of the variance. Hence the standard deviation over a short time isσ 𝛥𝑡.

• The mean described above is often called the “drift”. This is the deterministic part of the GBM. Thestandard deviation is the random or stochastic element. The returns are random variables that are normallydistributed with expected value zero. Thus, the probability of a particular range of returns is given by thearea under a normal curve with the peak at zero.

Geometric Brownian Motion (GBM) Model of Coal Prices

• With the expected value of the stochastic component being zero means that the deviation from the

mean μ is just as likely to be positive as it is to be negative. This requires an adjustment to the drift to

compensate that if a positive return of 15% doesn’t quite balance out an equiprobable negative return

of 15%. Mathematically this can be shown to be (1 + 0.15)*(1 – 0.15) = 1 – 0.152 = 0.9775.

• If a positive return of x is followed by a negative return of x this depresses returns by x2. This is a

consequence of (1 + x)*(1 – x) = 1 – x2. If the expected amount by which returns are depressed when

there is a positive return followed by an equal negative return is x2 then the average amount the

stochastic component depresses returns is x2/2 or σ 2/2. Hence, the drift term can be represented as (μ

– 0.5 σ 2). This stochastic process is known in option pricing theory as Itô’s lemma.

• Combining the drift and random elements of GBM through time is perfect for Monte Carlo

simulation. We can use the following equation to simulate future asset prices.

Geometric Brownian Motion (GBM) Model of Coal Prices

• I’ll open the Excel file Geometric Brownian Motion Model and walk

you through the inputs and outputs plus Simulation Project Finance

Model – Normal Distribution IRR Version and Simulation Project

Finance Model - Normal Distribution NPV Version

• First, the year 8 distribution of price for coal look like this:

Year 8 Distribution of Coal Price

Lognormal Distribution

• The shape is known as a lognormal distribution. The minimum is $16.37; the maximum $607.02; the mean is $114.77 with a 90% confidence interval of ±$0.876. We can be 90% confident the price lies between $50 and $215.

• The logarithmic distribution has two (2) very desirable properties as far as asset pricing is concerned. First, it cannot be negative just as asset prices cannot go below zero. Second the right-hand tail can stretch a long way – similar to asset prices as well.

• In option pricing the buyer of a call option buys the present value of the mean ofthe probability distribution on the right of the strike price (i.e. the mean value of theprobability distribution to the right of the arrow).

• Similarly, the purchaser of a put option buys the present value of the mean to the leftof the strike price. Note the distribution is asymmetric.

• We can check the results of, say, a call option using Monte Carlo simulation against the standard Black-Scholes model with Excel files Black-Scholes Call Option and Pricing a Call option with Monte Carlo Simulation.

Black-Scholes Option Pricing Model

Monte Carlo Simulation Pricing a Call Option

Simulation Project Finance Model – Normal Distribution Equity IRR Version - Output

Simulation Project Finance Model – Normal Distribution Equity NPV Version - Output

Project Finance Model with Path Dependency

Next, we’ll look at a path dependent model. I’ll open the Excel file Graph of Path

Dependency using the triangular distribution and Simulation Project Finance

Model – Path Dependent – IRR Version and Simulation Project Finance Model

– Path Dependent – NPV Version. We analysed already coal prices which showed

that prices conformed to a triangular distribution with the following parameters:

=RiskTriang (minimum,most likely,maximum) in Year 0

Minimum Value 69.82$

Most Likely Value 81.86$

Maximum Value 103.57$

Simulation Project Finance Model – Path Dependent – Equity IRR Output

Integrating an offtake contract into the cash flows

• It is common practice for lenders to require an offtake contract to underwrite some portion of theproject revenues. The effect on IRR and NPV can be analysed easily by stripping into the spreadsheetthe amount underwritten as the product of tons per coal and the underwritten amount plus adjustingthe anticipated amount of coal left at the projected market prices.

• I’ll open the Excel file Simulation Project Finance Model – Path Dependent IRR Version with Offtake Agreement. In the bottom right hand corner, I’ve assumed that lenders will require an offtake agreement of 50,000 tons at $70 per ton (=$3,500,000) for the full 8 years.

• The offtake of 50,000 tons reduces the likely number of tons of coal per annum by 50,000 tons to a minimum of 30,000, most likely of 40,000, and maximum of 50,000.

• The cash flows in the model window reflect the underwritten offtake by stripping in an additional row

Impact on Equity IRR of offtake agreement

Simulation Project Finance Model – Path Dependent – Equity NPV Output

Doing Multiple Simulations

• It is possible to do multiple simulations us the following @RISK function with the syntax =RiskSimtable({val1,val2,...,valn}) specifying a list of values that will be used sequentially in individual simulations executed during a run of simulations.

• I’ll open the Excel file Simulation Project Finance Model – NPV Version with debt simtable.

• The debt financing percent is a negotiated variable with lenders, not a random variable. However, it would be very useful to analyse what the impact of various percentages on, say, the Equity NPV. (Changes in the proportion of debt financing will not impact on the Project NPV).

• In the cell to the left of the Debt Finance Percent I’ve entered the formula as follows: = RiskSimtable({0.5,0.6,0.7}). Note the double brackets. The number of simulations is set to 3 to correspond with the number of arguments in the formula.

Results from multiple simulations

The program will show the graphical output for the three simulations. Close the graph window and hit Summary in the Results ribbon which produces the following report. Note the mean NPV increases with the increase in debt percent.

A few words on banks and other lendersProperly structured, project finance can offer quality business for banks and other lenders because suchfunding minimizes the twin risks of adverse selection and moral hazard and can also earn handsomefees. Following is a simplified schematic of a project loan structure.

Adverse Selection• Screening potential borrowers for their credit quality before making a loan encounters

the problem of adverse selection. Borrowers may be honest or dishonest; their projectsmay be viable or not; but there is one commodity the borrower possesses that the lenderdoes not: the borrower has more information. George Akerlof focused on ex anteasymmetric information costs in a classic article dealing with 'lemons' in the used carmarket.

• Akerlof argued that the seller of a used car knows whether or not the car is a lemon (i.e.bad mechanical history). Buyers are not stupid and will only pay a price that reflects theestimated average frequency of lemons in the used car market. Such a price is high forlemons but low for better quality vehicles offered on the market. Hence the sellers ofbetter cars withdraw them from sale and the average frequency of lemons increases.

• As customers learn this they make greater allowance for an increase in the lemonpopulation and reduce the prices they are willing to pay. This procedure may continueuntil there is no market although institutional arrangements like guarantees, or thecertification of cars by dealers who exploit a reputation for good cars, may keep the usedcar market alive.

• Similarly, with asymmetric information, a lender cannot distinguish between a goodcredit risk or a bad credit risk and will charge an interest rate reflecting the averagequality of good and bad borrowers. High quality borrowers will not borrow and mayutilise other markets (via securitisation) thus worsening the mix.

Adverse Selection (Cont.) & Moral Hazard• In assessing project loans, banks and other lenders minimise risk by developing their own

models and also by using expert opinion on the project. Banks and other lenders receiveexpert advice as part of their due diligence procedure in analysing project loans. In addition,banks and other lenders have also developed sophisticated spreadsheet packages whichenable sensitivity analysis utilising different scenarios as discussed earlier in this book.

• In addition, lenders will insist on security over the assets and undertaking of the singlepurpose project company. Another way out is also provided by the credit of the purchaservia the inevitable off-take agreement.

• Monitoring a loan after the loan is granted to ensure the borrower is not acting contrary tothe lender's interests brings into play the concept of moral hazard. Moral hazard arisesgenerally from the inconsistent incentives arising from a contract specifying a fixed valuepayment between the debtor and the creditor.

• A little reflection on the nature of a project loan will show that, properly structured, moralhazard risk is negligible. Lenders will insist on monitored drawdowns of progress payments.Thus, the project will be constructed following due diligence procedures laid down betweenborrower and lender. The lender reserves the right to withhold advances which are notspecifically approved for use in the project. Clearly there are scale economies in monitoringlarge projects. Also lenders will have timely access to information on the progress or anyvicissitudes that may be encountered on the way.

Some final comments on volatility

• There is an understandable view that volatility may connote downsiderisk. In a capital markets context, volatility also connotes opportunity forgain.

• Of the two stochastic models above, the GBM model produces riskierout-comes with more probability of gains and losses. The pathdependent model is clearly more conservative.

• Mining, oil and gas industries are risky. Although the models developedare idealised, both the Equity IRRs and NPVs and the Project IRRs andNPVs are overwhelmingly positive, and so Whitehaven Coal should bepart of the project.

• It would be appropriate to conduct both types of analysis on a realproject to compare and contrast outcomes.

References – Recommended reading in boldAustralia, Reserve Bank of. Capital Market Yields Monthly: Government Bonds. Retrieved from http://www.rba.gov.au/statistics/tables/#interest-rates

Baird, B. F. (1989). Managerial Decisions Under Uncertainty - An introduction to the analysis of decision making. Wiley series in engineering and technology management.

Benninga, S. (2014). Financial Modeling (4th ed.). MIT Press.

Benninga, S., & Sarig, O. (2002). Risk, returns, and values in the presence of differential taxation. Journal of BANKING & FINANCE, 1123-1138.

Brealey, R., Myers, S., & Allen, F. (2008). Principles of Corporate Finance (9th ed.). McGraw-Hill Irwin.

Chance, C. (1991). Project Finance. IFR Publishing Ltd.

Chance, D. M. (1998). Essays in Derivatives. Frank J. Fabozzi Associates.

Chriss, N. A. (1997). Black-Scholes and Beyond - Option Pricing Models. Irwin.

Comer, B. (1996). Project Finance Teaching Note.

Finnerty, J. D. (2013). Project Financing: Asset-Based Financial Engineering (3rd ed.). Wiley.

Grey, S. (1995). Practical Risk Assessment for Project Management. John Wiley & Sons Ltd.

Gumbel, E. (1944). Ranges and midranges. Annals of Mathematical Statistics, 15, 414-422.

ReferencesHarvard Business School. (1999). An Overview of the Project Finance Market.

Hertz, D., & Howard, T. (1984). Practical Risk Analysis. John Wiley & Sons.

Hertz, D., & Thomas, H. (1983). Risk Analysis and its applications. John Wiley & Sons.

Hoffman, S. (1998). The Law and Business of International Project Finance. Kluwer Law International.

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Hull, J. C. (2006). Options, Futures, and Other Derivatives. (6th, Ed.) Prentice Hall.

Johnson, N., Kotz, S., & Balakrishnan, N. (1995). Continuous Univariate Distributions (2nd ed.). Wiley Series in Probability and Mathematical Statistics.

Kensinger, J., & Martin, J. (1988). Project Finance: Raising Money the Old-Fashioned Way. Journal of Applied Corporate Finance, 1.3.

Luenberger, D. (1997). Investment Science (1st ed.). Oxford University Press.

Megill, R. (1977). An Introduction to Risk Analysis. Petroleum Publishing Co.

Morgan, M. G., & Henrion, M. (1998). Uncertainty - A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge University Press.

Murtha, J. (2000). Decisions Involving Uncertainty - An @RISK Tutorial for the Petroleum Industry. Palisade Corporation.

ReferencesNersesian, R. (2011). @RISK Bank Credit and Financial Analysis (2nd ed.). Palisade Corporation.

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Raftery, J. (1994). Risk Analysis in Project Management. E & FN Spon.

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Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 119-138.

Vose, D. (2000). Risk Analysis - A Quantitative Guide (2nd ed.). Wiley.

Winston, W. (1999). Decision Making Under Uncertainty with RISKOptimizer (2nd ed.). Palisade Corporation.

Winston, W. (2001). Simulation Modeling using @RISK. Duxbury.

Winston, W. (2008). Financial Models Using Simulation and Optimization II (2nd ed.). Palisade Corporation.

Winston, W. L. (2004). Microsoft Excel - Data Analysis and Business Modeling. Microsoft Press.

Winston, W., & Reilly, T. (2015). Financial Models Using Simulation and Optimization (4 ed., Vol. 1). Palisade Corporation.

About the Author

• Dr. Colin Beardsley has more than 40 years’ experience in international capitalmarkets. He was a member of the Australian Stock Exchange Limited (ASX) whileSenior Partner Corporate Finance and Fixed Income with a leading Sydneystockbroker.

• After leaving the capital markets, Colin completed a PhD in finance and wasappointed Adjunct Professor at a leading business school in the UK. He ran coursesin Corporate Finance, Credit Analysis, Portfolio Management, Option Pricing andTrading in Australia, the United Kingdom, South Africa, Hong Kong, Singapore,France, the Netherlands and Estonia.

• In the early 1980s, Dr. Beardsley was the founder and first chairman of AustraclearLimited which provides a wide range of depository, registration, cash transfer andsettlement services for debt instrument securities in financial markets in Australia andthe Asia-Pacific region. Austraclear now settles more than A$80 billion oftransactions per day through a real-time link to the Reserve Bank of Australia’s RealTime Gross Settlement (RTGS) system.