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Rational Speculation Model: 3 Step Application to Mineral Plays


Spec Value Appraisal: the Rational Speculation Model applied in 3 steps to mineral plays

The rational speculation model involves a three step procedure that can be applied to any mineral play. What follows is a formal description of the Spec Value Appraisal system. It is intended for sophisticated investors who want to visualize the real world potential of a mineral play, to understand the news flow timeline that dictates an exploration play's progression from imagined potential to quantified actuality, to know in advance what upcoming project news should look like to make or break the outcome scenario, to be able to modify an outcome scenario in response to fresh information, to evaluate how the rest of the market perceives the mineral play's potential, and to apply a profitable speculation strategy that pursues good speculative value and steers clear of poor speculative value. How's that for a mouthful?

Failure risk declines as a play moves through the exploration cycle

The Spec Value Appraiser can be applied to any mineral exploration play involving gold, silver, platinum group metals, base metals, industrial minerals, specialty metals and diamonds. It can also be applied to oil and gas plays, and to some degree to biotech plays. All involve a hypothesis which is tested and modified through a series of steps that culminate in production cash flow. In the case of mineral and energy projects the resource is generally finite and has an absolute value limit. Biotech projects have a limit value in a different sense defined by the population that needs a cure or treatment. The biotech project's cash flow potential is also limited by patent expiry and the stark reality that patent violation can and will destroy an overly lucrative supply monopoly. Until the project is actually in production there prevails an uncertainty that cash flow will ever begin. The market value of the project will hinge on this uncertainty, which is also the probability production will be achieved. As a project approaches production the cash flow parameters become clear and the failure risk declines. The failure risk, also known as the success probability, thus declines because progression through the exploration cycle generates more reliable and extensive information about the project, which in turn forces the outcome scenario and its ultimate project value to be tailored until it conforms with the fundamentals. Imagination and reality become one and the same. The progressive decline in failure risk is the essence of venture capital speculation, which takes as its object not only the probability that the ultimate outcome will be achieved, but also the probability that a project will progress from one stage to the next. This secondary stage shift speculation is the reason project values implied by market pricing of public companies with a stake in the project can fluctuate above and below the valuation channel associated with that project's probability curve.

The market values plays properly well before the engineers go to work

It is important to keep in mind that potential outcome scenarios are constructed from very sketchy information and risky assumptions using a simplistic discounted cash flow valuation model. This type of analysis is best suited for the early stages of the mineral exploration cycle before a prefeasibility study has defined the parameters of a mineral play with the sort of hard numbers with which engineers are comfortable. Back-of-the-napkin style value speculation is appropriate when the uncertainty surrounding a project's potential is still too high for the engineers to touch. By the time it is "safe" for the engineers to tackle valuation of a mineral deposit, the market will already have assigned a value within the ballpark range that the engineers eventually come up with. The biggest speculation gains are thus made during the early stages of the exploration cycle as the market tries to quantify the implications of a discovery play.


Knowing when and why to change your expectations is a speculator's survival key

Stock prices are extremely volatile during the discovery phase because investors can visualize scenarios with a wide range of grade, tonnage, commodity price and cost variables. Almost every scenario generated during the early stages of a mineral play will turn out to be incorrect, which is why there will be wide disagreement among market participants. While most commodities are priced within a long term cyclical range, certain minerals such as gold whose value is not dominated by consumption demand have a far less predictable future price range than base metals such as copper and zinc. While exploration work gradually defines the deposit's physical parameters, which in turn limit the mining scenarios and bring the cost parameters into focus, there is no reduction in the uncertainty of the commodity prices that will prevail during the life of the mine. This unavoidable uncertainty about future commodity price is the mother of disagreement over the ultimate value of mineral projects even as they go into production. Disagreement happens to be a necessary condition for market liquidity. Stocks do not trade when the market is in agreement about the company's outcome scenario and failure risk, the definition of fair speculative value. (Of course, even when such agreement does exist, the equilibrium is undermined by the availability of alternative plays that offer good speculative value which a speculator will seek to capture by selling shares that have only fair speculative value.) As exploration work gradually defines the limits of the play, the scenarios converge toward a consensus that changes only with the arrival of new, unanticipated information. That is the reason the trading pattern of companies with a mineral project headed toward production forms a flat line. Spec value appraisal is not so much important in enabling a speculator to correctly visualize a project's ultimate value as it is in giving the speculator a framework to modify expectations in response to new information and judge whether the investment still represents fair to good speculative value. The promise of changing information in the form of exploration results makes it all work.

The 3 steps in spec value appraisal

1) Outcome Analysis

2) Probability Analysis

3) Risk-Reward Analysis


Outcome analysis requires you to identify the target outcome (what is the junior trying to accomplish?), establish ultimate project values (what would it be worth?), and construct expectation sets for possible outcomes (what would the fundamentals need to look like in order to justify the ultimate project values?). To complete an outcome analysis you must understand the discounted cash flow valuation model, and have access to cost information for the type of production scenario implied by the target outcome. Outcome analysis is an exercise in visualization which requires both imagination and attention to the facts of reality.

Probability analysis requires you to identify a set of milestones leading to the target outcome, and to assign fundamental odds that the target outcome will be achieved from each milestone. To complete a probability analysis you must understand the exploration process for the target outcome, and have access to the probabilities associated with the exploration target. When these probabilities are linked to an ultimate project value so as to generate theoretical project values appropriate for each stage in the exploration cycle, and these theoretical project values are plotted against their corresponding exploration stage, the result is a probability ladder whose upper and lower limits define the valuation channel for a certain ultimate project value. The Implied Project Value Charts contain three such valuation channels for $2 billion, $500 million and $100 million ultimate project values. To make it more obvious that these ultimate project values are hypothetical, the phrase dream target is frequently used in place of ultimate project value.

Risk-reward analysis requires you to compare the project's fundamental odds with the odds assigned by the market so that you can arrive at a Spec Value Rating. It also requires you to make a personal decision about what risk level is acceptable to you, and how much money you can afford to risk at that level. The Implied Value Charts for diamond plays graphically portray how the project value implied by the market relates to the valuation channels.

The Spec Value Appraiser requires considerable work to set up for a project, and requires regular adjustment as the scope of the target outcome and its ultimate project value change. The payoff for this effort is that you will be in a much stronger position to recognize quantum leaps or falls in the success potential of a project. It will also allow you to recognize risk-reward imbalances that signal buy or sell decisions. Most importantly, it forces you to understand what your speculative bet is really all about.

Step One: Outcome Analysis

Before you run a junior through the Spec Value Appraiser you must make sure the company has a project it is exploring for a specific type of target. Exploration can still be at the grassroots stage where the target is purely conceptual, or it can be at a more advanced stage where the target has become a partly outlined deposit. For a junior's theoretical target to be taken seriously, the junior must offer an existing deposit as a model, preferably one in the region. A case must be made why the regional geology is prospective for the deposit type. A secondary case must be made that the junior's land position has the right geology. Once you have established that the junior's target is within the realm of geological possibility, you must address what the best possible outcome will be worth. You can approach this in two ways. You can take a figure such as $1 billion and declare that the junior's target is to define a resource worth $1 billion. In that case you have to work out various deposit configurations whose associated capital and operating costs for a minimum 10 year mine life will equal the ultimate project value in net present value terms. The other way is to define the target in terms of tonnage and grade, and work out the ultimate project value using the discounted cash flow method for a mine with a minimum 10 year life. The former approach works best when the project is still at a grassroots stage, and the latter approach takes over once the conceptual target has turned into an actual target. The outcome analysis gets repeated throughout the exploration cycle, and becomes more detailed with more precise input parameters as each milestone in the exploration cycle is achieved. This can involve shrinking or expanding the target outcome.

Ultimate Project Value = Net Present Value of a Production Ready Project

Using the Hard Value Appraiser in Outcome Analysis

Doing a back-of-the-envelope calculation of what a deposit might be worth if it is put into production at a rate which will deplete the deposit in no less than ten years is straightforward. Figuring out what a deposit needs to look like to be worth a stipulated ultimate project value is more complicated. The reason is that many combinations of grade and tonnage can create the same ultimate project value. However, anybody who remembers their basic algebra and knows how to use a spreadsheet can design a matrix for several distinct possible scenarios. An example of such a matrix, which I call an "Expectation Set of Possible Outcomes", is presented later on. In what follows I will only demonstrate how to produce a value when we have tonnage and grade estimates for a deposit. The Hard Value Appraiser ignores details such as royalties, freight, recovery rates, stripping ratios and concentrate rates. There is no limit as to the complexity you can build into a cash flow model, though the practicality of the model is limited by the reliability of the inputs. During the discovery stage of a mineral play the overall uncertainty is so high that fussing with unknown details does not make a positive contribution to the reliability of the outcome scenario. For the purposes of the Spec Value Appraiser, which is dealing with deposits that are only exploration goals or early stage targets, all we need is a very crude method to give us a ballpark sense of what the deposit might be worth if it were proven up. For hard core mining analysts my Hard Value Appraiser is a joke. For the typical investor who has no idea whether a company's project might be worth $1 million or $1 billion, the Hard Value Appraiser is a quick and dirty way to put the potential outcome into perspective.

The Hard Value Appraiser

A deposit's hard value is the net present value of the future cash flow arising from mining the deposit, extracting the key commodities, and selling them at prevailing market prices. Cash flow is the gross revenue less the operating costs and taxes. The annual cash flows over the life of the mine are discounted to their present value at a rate that reflects the cash flow's risk. The net present value is the present value less the up front capital cost needed to put the deposit into production. If you really want to be fussy, you can discount the NPV again to reflect the number of years it will take before production starts up. I don't do that for the Spec Value Appraiser because the ultimate project value is only a goal toward which the exploration cycle marches. The Spec Value Appraiser is intended to generate theoretical project values for the early stages of the exploration cycle. A more rigorous valuation treatment is required when the project has reached the prefeasibility stage.

Annual Cash Flow Formula

Gross Revenues

Less Operating Costs

equals Operating Profit

Less Taxes

equals After Tax Cash Flow


Here is how you get the items in this formula:

Gross Revenues =Annual production rate (tpy) times grade times commodity price

The tonnage and grade are given, and the commodity price is looked up. The current price may be unrealistic if it is a cyclical high or low. As long as there are no major changes happening in the supply & demand structure of the commodity's market (ie as when new technology renders a commodity obsolete or creates a new demand for it), it may be prudent to use the 10 year cyclical average. The production rate is the tonnage divided by the mine life. I use ten years as a mine life because most deposits are put into production on a scale that ensures a mine life of at least ten years. The bigger the production rate, the greater will be the need to develop infrastructure, and the longer will be the projected mine life for both social and economic reasons. Because the cash flow 11 years or later down the road has a substantially lower present value than that of the first ten years, and because the commodity prices are hopelessly unpredictable that far down the road, I use ten years as the time to deplete a deposit. When calculating the gross revenue you must make sure the tonnage, grade and price variables use common units. For example, don't multiply a g/t gold grade by a $/oz price.

Operating Cost = Annual production times Cost/tonne

The simplest way to get a reasonable figure for the operating cost is to look up the figure for a similar deposit that is in production at a comparable rate. Mining analysts have this sort of data at their disposal, and the reason they get paid big bucks to produce research reports is that they know how to size up a deposit, and match it with appropriate operating costs. The problem with mainstream analysts is that they keep their reference databases secret, and only apply their skills to advanced projects where the deposit is fairly well defined. As rigorous number-crunchers they abhor dealing with fictitious or vaguely defined scenarios. No self-respecting mining analyst would want to be caught dead running a project through something like the Spec Value Appraiser. Some analysts and newsletter writers offer price targets for a project, but they do not offer the parameters and method used to arrive at these targets. For all we know, they might be guessing. In fact, if no effort has been made to contextualize a project with an outcome scenario visualization, price target predicts are just plain arbitrary. As a result there is a huge analytical gap between early stage and advanced projects. The challenge for the average resource stock speculator is to acquire a source of operating cost ranges that allows one to plug ballpark numbers into the Hard Value Appraiser.

Taxes = Operating profit times tax rate

The tax rate will depend on the location of the project. Some countries collect royalties on the gross revenue in addition to a tax on operating profit. The Hard Value Appraiser is only concerned with the effective tax rate on profits. The economics of a mine can be affected by the tax treatment. For reporting earnings companies depreciate the capital cost of the mine on a straight line basis over the projected life of the mine. But for tax purposes different reporting procedures are permissible. There may be a tax holiday where no tax is payable until the capital cost has been recovered. Or the tax rules may require a percentage of declining balance treatment for depreciation. Until we have an advanced project on our hands, it doesn't make sense to worry about the complexities of tax treatment. So we pick a tax rate that is lower than the official tax rate at a level that hopefully would balance out the effect of different depreciation schedules.

Present Value = Annual after tax cash flow times 7.72

Once you have estimated an annual after tax cash flow for a ten year mine life, calculating the present value is simple. What you have is a simple annuity. Just plug the annual cash flow, the number of years, and the discount rate into the present value formula of your spreadsheet or financial calculator. I suggest using 10% if you want a present value that a major would pay to own the project, or 5% if you think the junior who owns the project will survive as a publicly traded company. The reason for the valuation difference is that a deposit bought by a major will disappear into a portfolio of many mines where the deposit's cash flow will only make an incremental difference to the major's financial clout. In contrast, this cash flow within a smaller company will attract a premium from the market on the assumption that a smaller company will be more creative and flexible than a major company in utilizing the cash flow to generate new projects. For the Hard Value Appraiser we don't need to use a financial calculator. For a ten year mine life we can use a cash-flow multiplier that is 7.72 at 5% and 6.14 at 10%.

Net Present Value = Present Value less Capital Cost

The present value figure, however, does not include the up front cost of putting the deposit into production. When we looked up the operating cost for the proposed production rate, we will also have looked for approximate capital costs. Here we are being very superficial because we do not know what special environmental problems the project would face, or what sort of pre-stripping costs or metallurgical complexities a fictitious deposit might have. So we need to make a reasonable guess. The hard value of a project is its net present value, which is the present value less the capital cost of the project. Again, we are only trying to get ballpark figures. As more information becomes available about a project, we can fine-tune both the model and the input parameters. The purpose of outcome analysis is not to see how big we can make the ultimate project value, but to put reasonable limits on it, and provide a framework for refining the calculation of the ultimate project value as more information becomes available.

Expectation Set of Possible Outcomes (example)

 

1 g/t

2 g/t

3 g/t

50,000,000 t

$200 million

$300 million

$500 million

100,000,000 t

$300 million

$500 million

$1 billion

200,000,000 t

$500 million

$1 billion

$2 billion



Above is an example of an Expectation Set for Possible Outcomes of a search for a bulk tonnage gold deposit. The numbers have been arbitrarily chosen to illustrate the concept. Do not use them for anything! The target outcome is a 200 million tonne deposit of 3 g/t gold worth $2 billion. Each possible project value in the matrix would have been derived using the Hard Value Appraiser. An expectation set like this gives a good sense of what a deposit needs to look like to be worth a target value. At the beginning of the discovery cycle the sky isn't quite the limit, but a $2 billion deposit probably is. At the beginning when a specific target isn't in focus yet, the outcome could be anything or nothing. As a target comes into focus and begins to take shape, the speculator will use the Expectation Set to adapt his expected ultimate project value to one that corresponds to the fundamentals being served up by reality. If the deposit falls somewhere between the matrix slots, such as say 75 million tonnes of 1.5 g/t, you can see that the ultimate project value would be somewhere between $300-500 million. Keep in mind that the market will not value a project at the ultimate project value until the exploration cycle has been completed. The market's valuation, or implied project value, at any stage of the discovery cycle will reflect the probability that the project will make it through the rest of the discovery cycle and confirm the ultimate project value. Aberrations do occur, but eventually the implied project value will converge with the theoretical project value. Working out the exploration cycle and the success probabilities is done in Step Two of the Spec Value Appraiser.


Step Two: Probability Analysis

Probability analysis requires us to map out the milestones in the exploration cycle leading to the validation of a commercial deposit, and to assign success probabilities to each level that reflect the chance that the project will go all the way. The milestone sequence is simple enough; mineral deposits go through a fairly standard series of steps from grass roots exploration to a positive feasibility study. However, the probability of achieving the target outcome from each milestone depends on the size of the expected ultimate project value. The bigger the dream, the more improbable will be the achievement of its reality. Speculative exploration ventures are all about chasing after high risk targets. Whatever the odds may initially be at the grassroots stage when a geological target has not yet been identified, each milestone reduces the odds. As the exploration cycle progresses a target comes into focus, acquiring tonnage and grade parameters that gradually match the ultimate project value. As it becomes clear that the deposit no longer has room to grow towards the ultimate project value of the initial expectation set, the original ultimate project value has to be reduced to the reality emerging as a result of the exploration cycle. Sometimes the reality is a sub-economic deposit, in which case the exploration cycle becomes a scratch: there is no payout for the race has been lost. Sometimes the reality is equivalent to a horse that has placed or shown. The payout can still be substantial, just not as big as had been projected in the expectation set. For speculators this realization is of extraordinary importance. Much money is lost because investors fail to realize that reality is falling short of expectations. Most of the time it does. The secret to rational speculation is not about picking those ventures which go all the way to win the race. It is about exploiting the quantum leaps in probability that accompany the achievement of key milestones before the ultimate outcome is known.

Probability Table for $1 billion Ultimate Project Value

Project Status

Theoretical Project Value

Leverage

Odds

Chance

Grassroots: generating targets

$5-10M

100-200

99-199:1:

0.5-1%

Drilling Targets

$10-25M

40-100

39-99:1

1-2.5%

Discovery Delineation

$25-$75M

13-40

12-39:1

2.5-8%

Infill Drilling

$75-150M

7-13

6-12:1

8-14%

Bulk Sampling - Metallurgy

$150-300M

3-7

2-5:1

14-33%

Prefeasibility

$300-400M

2.5-3

1.5-2:1

33-40%

Permitting - Feasibility

$400-500M

2-2.5

1-1.5:1

40-50%

Construction

$500-1,000M

1-2

0-1:1

50-100%

Production

$1,000M

1

0:1

100%



Reading the Probability Table

Here is how you read the above probability table. If the project status is one of owning land on which regional exploration is underway in order to generate drill targets, the chance of coming up with a $1 billion target is 0.5-1%. The payout odds for this high level of risk should be 99-199:1. The leverage of 100-200 is the factor by which the theoretical project value would increase to equal the ultimate project value of $1 billion. What this means is that at the regional exploration stage this project should have an implied value of $5-10 million. In other words, $1 billion divided by the leverage factors of 100 and 200. The next milestone would be the identification of a drill target whose size and surface grade suggest potential for a deposit that would be worth at least $1 billion. Since the critical third dimension and grade continuity are still missing, the odds drop down to a range of 39-99:1. If this milestone still supports a $1 billion ultimate project value, the implied project value should jump into the $10-25 million range. The next stage in the exploration cycle is to drill the target. The milestone sought at this stage consists of several ore grade intersections that suggest an orebody. This justifies a jump into the $25-75 million implied project value range. Which end of the range you choose will depend on how much of the tonnage needed for the ultimate project value can be extrapolated from the discovery holes. The next stage is to delineate the orebody through step-out drilling. The milestone we are seeking here is deposit geometry which supports the size needed for the ultimate project value. This milestone moves the implied project value into the $75-150 million range. Infill drilling is needed to firm up the grade and convert the reserve status from possible to proven and probable. This milestone moves the implied value into the $150-300 million range. At this stage metallurgical studies are needed to establish recoveries and the need for special procedures. If metallurgical work keeps the $1 billion ultimate value alive, the implied project value bumps into the $300-400 million range. A prefeasibility study will work out the best mining scenario and the associated capital and operating costs. If the prefeasibility study is positive and supports a $1 billion ultimate project value, the implied project value moves into the $400-500 million range. While a prefeasibility study is supposed to anticipate permitting obstacles, there are always surprises and delays. Construction can't begin until the development plan is permitted. This milestone moves the implied project value into the $500 million to $1 billion range. The ultimate project value is achieved when construction is finished and production begins. As you can see in the probability table, the success probability at each stage is mathematically linked to the theoretical project value. The appropriate probability range for each exploration stage is partly subjective because there aren't any definitive tables you can look up in a reference manual.

The probability range associated with each exploration stage represents the probability that the project will go all the way to achieve the ultimate project value of the outcome scenario. This series of probability ranges associated with exploration stages is called a "probability curve". When the probability curve is linked to an ultimate project value, a theoretical project value can be generated for each exploration stage. When plotted on a graph of implied project value versus exploration (milestone) stage, the two lines representing the upper and lower limit of the theoretical project value are called the "valuation channel". A project at a certain exploration stage whose implied project value falls within the valuation channel represents fair speculative value, provided that the fundamental evidence generated by exploration leaves intact the ultimate project value that defines this valuation channel. The probability curve can come from success/failure statistics involving legitimate ventures such as the world class diamond project probability curve developed by Kennecott, a subsidiary of Rio Tinto. The third step of the Spec Value Appraiser involves comparing the theoretical project value with the project value implied by the price the market is assigning to the junior's shares.

Step Three: Risk-Reward Analysis

Implied Project Value=Market Price times Fully Diluted Stock divided by the Net Project Interest

Spec Value Rating=Theoretical Project Value divided by Implied Project Value

This calculation assumes that the junior has no assets other than the project in question. Working capital is ignored on the assumption it will be used up in the project's exploration cycle. If a junior owns 100% of a project, its implied value is the market capitalization of the junior. If the junior owns only 50%, then the junior's market cap represents half of the implied project value. We get the implied value by dividing the junior's net interest (0.5) into its market cap. The ratio of the theoretical project value over the implied project value produces the Spec Value Rating.

Spec Value Ratings Table

Over-valued

< 0.8

Fairly valued

0.8 - 1.2

Under-valued

> 1.2



Risk-reward analysis forces you to determine if the reward paid out upon achievement of the expected outcome corresponds with the risk that the expected outcome will actually materialize. If the risk and reward are in balance, a stock's price represents fair speculative value. A Spec Value Rating of 0.8 to 1.2 means the stock is fairly priced. Assuming you are comfortable with the fundamental assessment of the project and the probability of achieving the ultimate project value, the only thing left for you to do is decide: 1) Are you comfortable with the project's current level of risk? and, 2) if so, how much money can you afford to risk at that level of risk? While everything else in the Spec Value Appraiser deals with impersonal facts, these last two questions are personal. How you decide is up to you. The Spec Value Appraiser's purpose is only to package up a speculative opportunity in a rational form.

What if the SVR says the stock is over-valued?

If the Spec Value Rating is less than 0.8, it means the market is much more optimistic about the project's success potential than the fundamentals would justify. When the risk-reward imbalance is severe and the stock looks badly over-valued, a rational speculator will steer clear or sell. Modest imbalances happen frequently because exploration results arrive suddenly and force abrupt adjustments either in the size of the ultimate project value, or in the stage of the exploration cycle. A hot drill hole improves the odds of success sharply, and is reflected in market price gapping. The exploration program typically adds drills to the property as the focus switches from drilling targets to delineating a discovery. This creates confusion as speculators try to figure out where the stock should be trading in light of the new developments. Rational speculators can sell when these over-valued moments appear, or, if they want to buy, wait until prices settle down. If you are holding the position for a first place win, it is worth knowing the stock is currently over-priced, so that if the price does retreat, you don't panic with anxiety that maybe something has gone wrong you don't know about. If an imbalance persists, the stock has become a power play driven by momentum factors that are divorced from the fundamentals. The Spec Value Appraiser is not useful for trading decisions in these cases, though it is an effective tool for monitoring the extent of the over-valued condition. As such it can be effective for short-selling strategies.

What if the SVR says the stock is under-valued?

What speculators are always on the lookout for are risk-reward imbalances that suggest a stock is undervalued. Being undervalued does not mean the market has miscalculated the value of a junior's asset. Remember, a speculative venture does not have any hard assets with a measurable value. Being undervalued means that the market is giving the junior's project much worse success odds than the project fundamentally deserves. Assuming a Spec Value Rating above 1.2 is not due to a mistake in the outcome and probability analyses, it can be attributable to the stock's obscurity, overly bearish general market sentiments, ignorance about the underlying project fundamentals, or controversy about the project and its potential. A high Spec Value Rating is not a signal to back up the truck. On the contrary, it is a warning that something may be wrong which the Spec Value Appraiser would not have identified. Also, the Spec Value Appraiser only deals with a company's flagship project. It does not address other important factors like structure, people and capital, as well as story issues like title and political risk. If the stock still looks undervalued after these factors have been considered, then you have an exceptional speculative buying opportunity.

Extraneous risks such as permitting and geopolitical risk can be factored into the rational speculation model by using a higher discount rate in the net present value calculation used to generate the ultimate project value (dream target). If you use 20% instead of 5% or 10% you will generate a smaller dream target value, which means that a project in a risky location needs to be bigger and/or richer than one in a less risky location to have the same ultimate project value.
 
 

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