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Weekly UpdatesINTRODUCTION
Mining companies and their financiers are exposed to a variety of risks. One of the main risks, completion risk, relates to whether a project is constructed on budget and on time. Uncertainty in the initial capital cost estimate is an important contributor to completion risk. In this article, we undertake a statistical analysis of mining project capital cost estimation.
Engineering capital cost estimation is subject to error and bias (Ostwald 1992). Error is the tendency for actual costs to deviate from the estimated cost. Bias is the tendency for that error to have a mean that is statistically different from zero. This article is principally concerned with bias, though we will also make reference to capital cost error.
There have been a number of detailed statistical studies of capital cost estimation bias in large construction projects. Studies directed by Edward Merrow have found that severe underestimation of capital costs is the norm for advanced chemical process facilities, major public works projects, and energy projects (Merrow, Chapel, and Worthing 1979; Merrow, Phillips, and Myers 1981; Merrow 1988). Smaller projects tend to have less severe cost underestimation, while a sample of 47 megaprojects undertaken between the mid-1960s and 1985 came in an average of 88% over budget (Merrow 1988). Detailed statistical analysis of these cost overruns shows that internal cost growth, and not external unforeseen factors such as scope changes or unplanned inflation, is the major determinant of the overruns. The average overrun for the seven minerals extraction projects in this group was 99%. Merrow in tact singles out the minerals extraction projects for having particularly poor capital cost estimates. Hufschmidt and Gerin (1970) examined cost overruns for a series of large government public works projects and again found that cost overruns were common. In this case, overruns were a result of cost inflation rather than other factors. In fact, once a cost escalation index was applied to the projects, the projects on average came in under budget. Pohl and Mihaljek (1992) examined 1,015 World Bank projects and found that of the 22% average cost overrun, all of it was due to unexpectedly high cost inflation in the 1970s. Cost overruns are also the norm in transportation infrastructure projects (Pickrell 1992; Flyvbjerg, Holm, and Buhl 2002), and in these cases unanticipated cost inflation was again the main factor.
Mining industry studies of mining project capital cost estimates have for the most part been less sophisticated in their analysis of the data. Castle (1985) compares the capital cost estimate in a project's feasibility study with the actual cost incurred for 17 international ferrous metal, non-ferrous metal, uranium, and coal mining projects initiated between 1965 and 1980. (1) Of these, 12 experienced capital cost overruns, 10 by more than 15%. The average overrun was 35%. Bennett (1997) finds that for 16 projects completed between 1990 and 1995 as-built capital costs exceeded the feasibility study cost estimate by an average of 27%. Thomas (2001) finds an average cost overrun of 17% on 21 projects. Thomas escalates the real dollar feasibility cost estimate to the construction date, taking into account cost inflation. Without this he estimates that the computed overruns would be 5 to 10 percentage points higher, in line with the previous studies. Gypton (2002) looks at 60 projects initiated in the Western Hemisphere since 1980, some of which were probably included in the previous studies, and finds the average cost overrun to be 22%. In more than half of the cases, as-built capital costs exceeded the feasibility study estimate by at least 20%, and only one quarter of the projects had cost underruns. As a result of this persistent bias, mining feasibility study capital costs are sometimes listed as being accurate to within -5%, +15%, anticipating overruns at the outset (Vancas 2003).
Yearly cost inflation may explain overruns of 5-10% in the later mining studies (Thomas 2001 ), and more in the Castle study, which evaluated some projects in the high-inflation 1970s. Yet even after taking cost inflation into account, there appears to remain a downward bias in the initial feasibility study capital cost estimate.
Completion risk is recognized by both mining companies and financiers. In fact, through completion guarantees, additional equity subscriptions, or standby facilities, financial institutions have measures in place to mitigate this risk (Bennett 1997). Yet the nature of and reasons for bias in capital cost estimates in the mining industry are not well understood. Why does it exist? And why has it persisted over time? Have engineers not learned to adjust their estimates? The objective of this article is to examine the statistical properties of capital cost estimates in mining projects. The article addresses the following questions:
* Why are bias and error present in a capital cost estimate'?
* Which factors influence the bias and error in a capital cost estimate'?
* Why has bias persisted for over 40 years? Why have project engineers not learned to adjust their estimates?
* Should we eliminate error from the capital cost estimate?
* How should we account for bias and error in project valuation?
To answer these questions we have collected a dataset consisting of 46 mining and smelting/mill projects completed between 1995 and 2001. The number of smelting/mill projects is a relatively small proportion of the data set. All projects required external financing. Twenty of the projects were financed by N.M. Rothschild & Sons (Denver) and 26 by the Royal Bank of Scotland. The projects cover a wide range of commodities (gold, copper, lead, zinc, aluminum, nickel, platinum group metals, steel, cobalt) and project types (open pit mines, underground mines, mills, and smelters), with feasibility-stage capital cost estimates, inclusive of contingency, ranging from $7 million to $1,803 million. The capital cost estimates are in real, cumulative undiscounted U.S. dollars, taken from bankable feasibility studies. Actual capital costs are as-built costs as of full production according to the lender's completion test. In order to allow for a meaningful comparison of projects with different capital cost levels, we normalize the as-built capital cost by the feasibility study capital cost estimate to form a capital cost ratio (CCR)--a value above 1.00 indicates an overrun, and a value below 1.00 indicates an underrun (Ostwald 1992).
[FIGURE 1 OMITTED]
BIAS IN THE CAPITAL COST ESTIMATE
One would expect that on average a capital cost estimate is unbiased. However, an analysis of a combination of our database of 46 projects and Castle's set of 17 projects shows that this is not the case. Figure 1 and Table 1 illustrate that the average capital cost overrun is 25% (average capital cost ratio = 1.25), with a standard deviation of 30% (0.30) around that mean. (2) Of the 63 projects, 44 had cost overruns, 7 had cost under runs, and 12 (7 in our data, 5 in Castle's data) were built exactly to budget. These 12 projects most likely came in under budget and were then "spent up" to budget. Fitting the data to a density function in the commercial Monte Carlo software @RISK shows that the capital cost ratios behave as a Pareto (shape = 3.74, origin = +0.93) or inverse Gaussian (mean = 0.36, shape = 0.37, shift = +0.89) distribution. A shifted lognormal distribution with a mean of 0.35, a standard deviation of 0.42, and a shift parameter of +0.91 also cannot be statistically rejected as fitting the data and, because of its familiarity, is the one we have chosen to represent these capital cost ratios. This fitted lognormal distribution is superimposed on the histogram of capital cost ratios in Figure 1. Notable in Figure 1 is a cluster of 3 "outlier" projects whose capital cost ratios were between 2.00 and 2.14.
Figure 1 and Table I indicate a downward bias in the feasibility study capital cost estimate and a positive skew in capital cost outcomes. Such skewness in outcomes has been noted in other types of projects (Flyvbjerg, Holm, and Buhl 2002; Hufschmidt and Gerin 1970: Ostwald 1992). Deviations from the estimated capital cost can arise for a number of reasons, as detailed in many of the references cited earlier. Since the capital cost ratio does not take into account yearly cost inflation, we first examine how inflation potentially affects the measured capital cost bias. The feasibility study cost estimates are in real U.S. dollars and so will naturally underestimate the actual as-built costs. With a typical two-year time lapse between the feasibility study and the start of actual construction, and another year or two before completion, inflation causes part or all of the observed bias. For the majority of the projects in our data set, information about the time lapse between feasibility study and midpoint of construction was not available. We are therefore not able to account accurately for the degree of overrun resulting from cost inflation. To estimate the component of the capital cost ratio due to cost inflation, let Y be the as-built capital cost in nominal dollars and let X be the feasibility study capital cost estimate in real dollars. The capital cost ratio is defined as Y/X. If we deflate Y to a real dollar value assuming two years between the capital cost estimate and the start of construction and another two years of constant capital cost spending during construction, the inflation adjustment factor is (1 - [e.sup.-2r]/2r)[e.sup.-2r], where r is the annual rate of inflation. The actual U.S. dollar mining equipment capital cost inflation rate over the past two decades was 3%/year. (http://www.westernmine.com/westernmine/metcost.htm). Using this as the inflation rate, the real or inflation-adjusted capital cost overrun is 0.914Y/X. The inflation-adjusted average capital cost ratio is then 1.25 x 0.914 = 1.14.
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