# Project economics

Note: This article gives a general overview of the main topics involved in project economics. For the expanded articles on certain topics see: Depreciation, Discount rate, Taxation

A critical issue relevant to a mining operation is project economics. It is not restricted to the scope of a mining operation and may be used to determine whether such actions such as replacing equipment or lining a shaft to save on operating costs is viable.

Project economics considers the Net Present Value (NPV) of an operation as a benchmark for determining the value of an asset to the project. In order to calculate the benefit of project economics, the project manager must know the operating cost, the availability, the capital cost, the UCC (Undepreciated Capital Cost), the method of depreciation, the scrap value (or salvage value) and the expected life of each asset involved.

## Introduction

The easiest way to keep track of your project's economics is with a spreadsheet. An example of this record-keeping method can be found here: File:Project Economics.xls. To use this spreadsheet, enter known values into the outlined boxes at the top and the calculations will be performed automatically.

In order to understand how this spreadsheet works, the following sections outline the calculations performed. Using this method, you can adapt the spreadsheet to include other things such as UCC or Avoided Costs, where applicable.

## Cash flow

A calculation of cash flow will determine whether the value of your project is greater than the cost of the resources which have been consumed. A cash flow can be found over any period, but is often calculated every six months, annually or over the life of a project. Since taxes are deducted annually in most countries, cash flows are often calculated annually when determining the NPV of the project.

The project is determined to be commercial, or financially attractive if the Value terms (such as Revenue or Avoided Costs) are found to be greater than the Consumption costs (such as capital costs, operating costs, taxes, etc.) in which case the project is financially viable, or:

${CF_t} = {{Revenue} \mathop - {Costs}}$

### Revenue

Revenue is the income generated by a company through its business activities. Revenues encompass all sources of income for the company. The main source of revenues in mining operations is through the sale of goods. The goods sold by companies are typically ore to a mill or concentrate to a refinery. Revenue can also be generated using alternate methods such as sale of assets, investments and royalties. Assets such as equipment and properties can be strategically sold by a company to generate revenue. Companies can also generate some revenue through stock and bond holdings in financial markets. Royalties are a percentage of revenues from an external party; they are a payment to the company for use of its property, patents or resources.

In mining projects, revenues often cannot be generated early in the mine life. This is because the deposit cannot be reached without first developing access and infrastructure. However, emphasis is placed on generating revenues early in the mine life. This is to ensure that the company is able to handle its liabilities, has cash-at-hand and does not become insolvent.

### Costs

Mining operations can be some of the most expensive projects in the industrial world and thus costs play an extremely important role in making decisions and testing feasibility. Within an operation, the costs can usually be grouped into two categories, Capital Expenditures and Operating Expenditures.

#### Capital expenditures

Capital Expenditures or CAPEX encompass all costs that are incurred through a one-time purchase of sorts. CAPEX usually has a constant price, even if this cost is spread out over the life of the project. In mining operations, any physical or durable already-produced fixed assets fall under CAPEX. These expenditures can be identified the low frequency of cost incursion and frequency of purchase. Most CAPEX are long term assets that are purchased usually once (sometimes a few times throughout project life) and generally incur costs only at the time of purchase. In general, any equipment, property, industrial building or assets with a useful life beyond the taxable year are considered CAPEX. [1]

#### Operating expenditures

Operating Expenditures or OPEX are the counterpart to CAPEX. OPEX encompass all costs that are associated with production or maintaining capital. These expenses therefore can be expected to differ greatly over the life of a project. Unlike CAPEX, OPEX can be identified by the relatively high frequency of purchase and cost incursion. These costs are usually incurred every year, if not multiple times throughout the year and their magnitude can depend on production output and capital use. In general, any fees, wages, depletable goods, maintenance or assets with a short useful life are considered OPEX.[2]

Some examples of CAPEX and OPEX for different aspects of a mining project can be seen in the table below.

 Aspect CAPEX OPEX Shaft Shaft sinking, hoist installation, skips/cages Power, replacement cables Hauling LHDs (or trucks), ore pass Worker wage, machine maintenance (lube, parts, teeth replacement), fuel Blasting Drilling rigs Wages, explosives, fuel, maintenance Processing Grinding mills, flotation cells, hydrocyclones, leach pads, tailings infrastructure Maintenance, chemicals, wages, water

### Depreciation

See main article:Depreciation

Depreciation is a term used to spread the cost of a asset across several years for taxation purposes. This will reduce the annual taxation costs levied against the project until the end of the depreciation schedule. Depreciation is typically calculated straight-line, which means that a fixed percent value is used annually to determine the depreciation claim.

In order to find the value of a depreciation claim using the straight-line method, first determine the scrap value of the asset at the end of the project's life. The value of the asset may reach zero (or become negative), in which case a separate analysis may be conducted to determine whether or not it is worth it to replace the asset.

Straight-line method

$\mbox{Annual Depreciation Expense} = {\mbox{Cost of Fixed Asset} - \mbox{Residual Value} \over \mbox{Useful Life of Asset} (years)}$

It may be easier to determine the original value of the asset, then keep track of the depreciation available. The depreciation available is the original value minus the depreciation claim annually. It is important to note that there is a maximum amount which can be depreciated in many jurisdictions. In Canada, the limit is defined by the Canadian Revenue Agency (CRA). The limit on machinery such as an LHD is 30% per annum using the Classes of Depreciable Property guidelines.[3]

### Discount rate

See main article:Discount rate

Discount rate is used in cash flow analysis to adjust future streams of revenue and account for a variety of economic factors. Some of these factors include the time value of money, the uncertainty of future cash flows, and other factors associated with the specifics of the project being analyzed (i.e. commodity, location, experience of property owner). By choosing an appropriate discount rate, a better idea of the viability, feasibility and profitability of the project can be obtained and more informed investment decisions can be made. The discount rate is one of the main parameters that must be selected in order to calculate the NPV of a project.

### Inflation

Inflation is a general increase in prices and fall in purchasing power of a currency.[4] The rate of inflation can be applied to a net present value equation to determine the present value of a future expenditure or revenue.

#### Causes

Canadian Consumer Price Index Inflation Rate[5]

Many schools of thought exist on the causes of inflation and can be divided into the quality theory of inflation and the quantity theory of inflation. The quality theory includes the expectation of a seller accepting currency to be able to exchange that currency at a later date for goods or services. The quantity theory rests on the equation of money supply, velocity and exchanges.[6]

#### Measures

The inflation rate can be calculated by monitoring the change in price of certain basket of consumer goods and services. This is known as a consumer price index and is used by many central banks. Different price indexes may also be assembled since inflation can vary from industry to industry. The chart to the right illustrates the historical inflation rate as measured by the Canadian consumer price index.

#### Control

It is in the interest of federal governments to keep inflation from fluctuating rapidly. Central banks can implement monetary policy to control the supply of currency and achieve a target inflation rate. The Bank of Canada has targeted 2% inflation per year with a range of 1-3 percent for the last two decades.[7]

## Taxation

See main article:Taxation

With reference to project economics, taxation can have both positive and negative effects on NPV. In order to calculate the taxable income, the operating cost, depreciation claim, UCC and any other taxable costs are subtracted from revenue. The taxable income is then multiplied by the tax rate to find after tax revenue cash-flows. Various rules and regulations, specific to the mining industry, must be adhered to depending on the taxable asset being analyzed. Having a strong understanding of the provincial and federal taxing regulations is a vital component in calculating an accurate NPV and project valuation.

## Net present value

Net present value or NPV, is a determination of the worth of a project to the company at a set period in time. This is accomplished by discounting the cashflow in each year back to the time of interest (usually present time) and summing all of these discounted flows together. The present value of a cashflow essentially exhibits what monetary value it has right now. That is to say that with a properly calculated present value, one would be indifferent to obtaining the dollar value of the PV today, or the undiscounted cashflow later on in the project. The calculation of the present value of each cashflow is done via the following formula:

$PV_i = \frac{CF_t}{(1+i)^{t}}$

NPV is therefore the summation of all these discounted cashflows given by:

$NPV = \mathop \sum_{t = 0}^n \frac{{C{F_t}}}{{{{\left( {1 + i} \right)}^t}}}$

Where CF is the cash flow at year t,i is the discount rate, and n is the total number of periods.

The present value often negative in year 1 due to the accumulation of large capital costs at the beginning of the project. As production increases and revenue is generated via the sale of commodities, present values become positive in later years of the project. NPV is a good indication of whether the capital costs incurred at the beginning of the project are offset by the commodity revenue later on. If a project's NPV is less than zero this means that after taking into account all the economic factors and possible costs/revenues, there will be a net loss. Thus when used at an investment decision criteria, generally any project with a positive present value is accepted while those with a negative present value are rejected.

## Sensitivity Analysis

A spider plot showing the effects of metal price changes on NPV. It can be seen that the NPV is much more sensitive to the Zn price than it is to Ag or Au.

Sensitivity analyses measure the effect of variations in estimated parameters on the investment decision criteria of a project such as IRR, NPV or payback period. In every project there are multiple parameters that are used to quantify the criteria used in investment decisions. Some of these parameters include capital costs, metal price, operating costs, project life, salvage values and reclamation costs. There is uncertainty/variation that comes along with each of the parameters and thus it becomes important to determine the effects of this uncertainty on the overall project value. This is commonly accomplished through sensitivity analyses.

Typically, a sensitivity analysis is done on each individual parameter to determine the potential effects of its variation. The selected parameter is varied within the range associated with its uncertainty and the end result of this (on NPV for example) is noted. By running this analysis on each of the parameters, it can identify which of them have the greatest effect on the project and therefore which parameters require attention first.

The most common method for interpreting the results of a sensitivity analysis is a spider plot. In a spider plot (see plot to the right), relative changes (percentage) in the selected input parameter are plotted against the absolute changes in the decision criteria. The steps to a sensitivity analysis can be summarized into the following list:

1. Select an investment decision criteria as the basis for the sensitivity analysis.
2. Identify the most important project input parameters (capital costs, operating costs, discount rate etc.) relative to the selected decision criteria.
3. Determine the uncertainty associated with each of these inputs. This includes both increases and decreases in the parameter.
4. Using a reasonable step between the boundaries of the uncertainty range, calculate the resultant decision criteria for each step.
5. Plot this absolute change in decision criteria against the relative change in project parameter.
6. Visually analyze to determine which parameters have the greatest effect on the decision criteria and look further into these parameters.

Sensitivity analyses do a great job of answering a lot of the “what if” questions associated with parameter variation. If a parameter is found to have a considerably larger effect on the decision criteria, it might be worth it to invest more time into research to ensure that the estimation is as reliable as possible, thus reducing its effect on the criteria.

## Applications

Applications of project economics are broad and involve any kind of financial optimization problem in the mining industry. The NPV of an existing asset could be compared to a the NPV of purchasing a new one with a lower operating cost to determine whether or not it is worth upgrading to the new asset. This can be applied to the concept of lining a shaft where the NPV of the unlined shaft is compared to the NPV of lining the shaft, where the operating cost of the unlined shaft is higher but lining the shaft entails a steep capital cost per area of the shaft.

## References

1. http://www.investopedia.com/terms/c/capitalexpenditure.asp-http://www.investopedia.com/terms/c/capitalexpenditure.asp
2. http://www.investopedia.com/terms/o/operating_expense.asp-http://www.investopedia.com/terms/o/operating_expense.asp
3. http://www.cra-arc.gc.ca/tx/bsnss/tpcs/slprtnr/rprtng/cptl/dprcbl-eng.html Classes of Depreciable Property
4. Oxford University Press. Inflation: Definition [online]. Available: http://www.oxforddictionaries.com/definition/english/inflation