# Project Evaluation Methods

NOT A FINAL PRODUCT. DON’T JUDGE

## Contents

Current Industry Methods

All mining is performed for profit. Since there are many possible ways to mine a deposit and many deposits to chose from, one must be able to select the best deposit and the most efficient mining techniques, for the deposit that are available. For investors, this problem is compounded by the numerous mining companies to choose from. A measure must be used that can be applied to all projects of varying scope and design so that they may be compared. Given the variability in the type, length and cost of mining projects, different measures may favor different projects; therefore the measure to use is not always clear. Table 1 displays the results of a survey in 2002 of the Chief Financial Officers of Fortune 1000 companies, outlining the use of different methods to measure value.

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There is a good consensus formed on methods such as Net Present Value (NPV)link and Internal Rate of Return (IRR)link with other tools being used regularly. On top of the basic methods there are supplemental tools shown in table 2.

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Due to the numerous methods available with varying degrees of use, the prospect of valuing different options in a project is not always a simple one. Some of the tools in the survey will be discussed along with the significance of their results.

Net Present Value (NPV)

NPV is the most common method for evaluating a project with 85.1% of respondents’ using it always or often. An overview of the method can be found here. link to project page

The main variable in the NPV equation that must be determined by the group doing the analysis is the cost of capital or interest rate, in the provided explanation. The cost of capital can be considered in two ways; the hurdle rate for the company considering the project which must be passed for to consider it, or what the company pays for the capital it invests, calculated using the weighted average cost of capital or WACC. link

Hurdle Rate

While the hurdle rate may be the calculated WACC for a company, it is essentially a way to describe the value when it deviates from the calculated cost of capital. One example is large companies valuing long mine life projects. Often large mines can have an operating life of 50+ years and due to the effects of discounting at your cost of capital any cash flow beyond year 30 will not have a large effect on the NPV. For example, revenue of $50 million discounted at 12% for year 31 only contributes $1.5 million to the NPV. This causes a bias of long mine life projects being undervalued. Larger companies want large project to both significantly increase their cash flow and provide long term growth. To properly value these projects they may use a hurdle rate of 4%. In the example this would increase the discount value from $1.5 million to $15 million in year 31, an increase of one order of magnitude. This trend of large companies using lower cost of capitals is also displayed in WACC calculations, as the equity in large companies tends to be more “patient” capital however not to this degree.

When choosing a cost of capital for a project, approximate it by comparing the size and location of the site to a company that would most likely buy it; therefore properly valuing for your target audience.

Weighted Average Cost of Capital (WACC)

The weighted average cost of capital simply takes the weighted average cost of both debt and equity capital. The cost of debt is the rate the company pays the bank. The cost of equity capital is found using stock charts with the capital asset pricing modellink or by polling large owners. WACC uses the following equation:

*WACC=(ke×We)+(kd [1-t]×Wd)*

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Where: ke is the cost of equity capital, We is the percentage of equity in the capital structure, kd is the cost of debt, t is the marginal tax rate and Wd is the percentage of debt in the capital structure.

The marginal tax rate is needed because interest paid on debt for a business is deductable for tax purposes, so the true cost of debt is the fraction paid after using the deduction.

Capital Asset Pricing Model (CAPM)

Calculating the cost of equity capital can be difficult; the most commonly used method is the capital asset pricing model. The model uses the riskless interest rate and the market premium, and alters them using systematic risk as a modifier described by a stocks beta. This creates the following linear equation for cost of equity capital:

*E(Ri)=Rf+B(RPm)*

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Where: Rf is the riskless interest rate, B is the beta of the stock and RPm is the risk premium for the market as a whole.

The riskless interest rate is typically the rate on a 30-day, 5-year or 20-year US Treasury bond.ref>Pratt, S. (1998). Cost of Capital: Estimations and Applications. New York, New York: John Wiley & Sons, Inc. </ref> The Beta can be found for many stocks in financial papers or by using Google Finance link. The market premium is found using historical data comparing the gain in the stock market over the riskless interest rates for the period in question. Given the forward looking nature of NPV, an assumption is made that the markets will hold the observed trend.

The difference in betas between large and small cap companies helps to reconcile how small cap companies are riskier and investors expect higher returns while large cap companies are safer and investors expect lower returns.

Internal Rate of Return (IRR)

Internal rate of return is the second most common tool used and is one of the easiest to calculate. The IRR uses the same equation as NPV, except the cost of capital is solved for the sum of the cash flows equal to zero. So the IRR is the cost of capital that would give you an NPV of zero.

Excel has an IRR function that requires all after tax cash flows to be in one row sequentially. Another way in excel to find the IRR is to have all the cost of capitals linked to one cell, and then use goal seek to have the sum of the row of cash flows equal to zero by varying the cost of capital.

IRR Comparison

Calculating IRR is easy but the effort comes in the evaluation of the IRR versus other IRR’s. If it is larger than a company’s hurdle rate or WACC, it is a good indicator. However, if the project has any unusual risk it may need a higher IRR. A 12% IRR for a project in Timmins Ontario with well defined typical geology and close infrastructure and labour markets is far more attractive than a 12% IRR on a project in a remote part of China in a previously un-explored area. The risks differ greatly and where risk is high it must be justified by a higher IRR. This is also consequential in comparing different options within same project. Using double benching may increase the IRR but it has to be sufficient to offset the incurred risk of slope stability.

The problem with both these examples is that they are qualitative not quantitative and there is no hard and fast rules for converting qualitative risk into IRR. Often, in order to accurately quantify risk, a monte carlo simulation will be utilized. Common qualitative concerns outside of project technology decisions that should be considered include but are not limited to:

- metal prices/economy - Inconsistency in the sale price of your product and the cost of your consumables
- political/social - Chance of labour disputes, trouble permitting and in extreme cases chance of government extortion or land seizure
- location – Infrastructure for power and water access, transportation costs and geological certainty for previously unexplored areas with unknown structure

Each of these in the extreme cases can warrant several points of increase in the calculated IRR in order to make the project on par with other similar projects without these risks.

Real Options

In an attempt to better quantify the impacts of risk, real options have increased in popularity. In the 2002 survey only 1.6% of CFO’s used it always or often but in more recent Harvard Business Review articles they claim an increase in the methods popularity.^{[5]} Real options are usually used in two basic forms.

One way is to put a value on a choice or option; having a flexible plan is more valuable than a rigid plan that can’t change in response to, for example, commodity price fluctuations. For a simple phased project the second phase will be built if it will be profitable or canceled if not. The fundamental idea is that the second phase does not cost you anything if not built and gives the opportunity for upside. So the choice is worth the variability of the upside multiplied by the time till the decision.

Secondly, real options are used to more accurately predict revenue. Instead of using pre determined prices, the options of the commodity that trades are used in a formula to predict the prices and account for fluctuation.

Payback Period

The third and fourth most used methods are payback and discounted payback periods, reportedly used 52.6% and 37.6%, respectively by CFO’s always or often. As two of the older and simpler techniques, they are still very popular.

Payback period is the amount of time it takes to recuperate the capital expenditures for a project from cash flow. Discounted payback is the same except discounted cash flows are used to calculate the payback period. Often investors or managers prefer a payback of three years or less, however mines typically have longer payback periods. A three year payback is more feasible for proposed mine upgrades. For example, a new piece of equipment should pay for itself in no longer than three years by increasing productivity or saving maintenance costs. If this is not the case the proposal may not look favorable as a rough rule of thumb.^{[6]}

Notes

- ↑ Ryan, P. A. & Ryan, G. P. (2002). Capital Budgeting Practices of the Fortune 1000: How Have Things Changed? Journal of Business and Management , Volume 8, Number 4, Winter.
- ↑ Ryan, P. A. & Ryan, G. P. (2002). Capital Budgeting Practices of the Fortune 1000: How Have Things Changed? Journal of Business and Management , Volume 8, Number 4, Winter.
- ↑ Pratt, S. (1998). Cost of Capital: Estimations and Applications. New York, New York: John Wiley & Sons, Inc.
- ↑ Pratt, S. (1998). Cost of Capital: Estimations and Applications. New York, New York: John Wiley & Sons, Inc.
- ↑ Copeland, T. & Tufano, P. (2004). A Real-World Way to Manage Real Options. The Harvard Busniess Review, March 2004 P. 1-12
- ↑ Anthes, G. ROI Guide: Payback Period. Sun Wind Power Systems: Files. www.sunwindpowerinc.com/files/files/ROI_Guide.doc. Accessed: March 5, 2010

References

Anthes, G. ROI Guide: Payback Period. Sun Wind Power Systems: Files. www.sunwindpowerinc.com/files/files/ROI_Guide.doc. Accessed: March 5, 2010

Armitage, S. (2005). The cost of capital : intermediate theory. Cambridge, New York : Cambridge University Press.

Chew Jr., D. H. (1999). The new corporate finance : where theory meets practice . Boston, MA : Irwin/McGraw-Hill.

Copeland, T. & Tufano, P. (2004). A Real-World Way to Manage Real Options. The Harvard Busniess Review, March 2004 P. 1-12

Pratt, S. (1998). Cost of Capital: Estimations and Applications. New York, New York: John Wiley & Sons, Inc.

Ryan, P. A. & Ryan, G. P. (2002). Capital Budgeting Practices of the Fortune 1000: How Have Things Changed? Journal of Business and Management , Volume 8, Number 4, Winter.