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South Africa?s now a member of this body, tailored on the World Bank, and headquartered in Abidjan-Cote d'Ivoire. As a funding agency for capital projects within 59 member countries of the ADB it is to be expected that there are guidelines to the requirements for funding application and for project management and control.

Jan 1, 1996

By T van Zyl

Some standards are being used by the corrosion industry on a daily basis. This talk will cover how a standard comes into existence, the different types of standards and the voluntary/ compulsory nature of different standards. The maintenance of standards is discussed This talk also looks at how standards should be referenced, what reference to the mark scheme can be made and which national and international standards might be of value in the corrosion industry.

Jan 1, 2006

By B. F. Giyani, A. Salama

Tanzania is a country with a variety of mineral deposits, including metallic minerals, gemstones, mineral fuels, industrial minerals, and critical minerals. This study provides an overview of mining legal framework, mineral occurrence and production, challenges in the mining sector, and government initiatives. The aim is to demonstrate the development of the mining sector in Tanzania and explore the potential for further mining investment in the country. The mineral production data showed generally increasing trends over the years, for example, gold production increased from 42 tonnes in 2018/2019 to around 50 tonnes in 2023/2024. Despite the growth, the mining sector encounters several challenges, including a lack of detailed geological information on mineral deposits, inadequate infrastructures in some remote mining sites, the existence of informal artisanal miners, and mineral smuggling. The Tanzanian government has introduced several initiatives to address these challenges, including carrying out the highresolution airborne geophysical survey to increase geological information in some areas, the formalisation of artisanal and small-scale mining, establishing mineral markets to combat mineral smuggling, and encouraging mineral value addition within the country.

Oct 24, 2025

By C. Musingwini, A. S. Nhleko, P. M. Muke

Open-pit mine planning includes the determination of a long-term open-pit mine production scheduling (OMPS) plan. The OMPS plan is generally a three-dimensional (3D) block extraction sequence that seeks to maximise the net present value (NPV) of future cash flows, while complying with technical and operational constraints. The OMPS problem is computationally complex because it involves the analysis of large datasets, while simultaneously incorporating both multiple hard and soft constraints. The OMPS problem has been solved using deterministic or exact approaches, heuristic, and metaheuristic models. When compared to heuristic and metaheuristic models, deterministic approaches tend to take much longer to solve the OMPS problem when the number of constraints increases. Therefore, this paper presents a metaheuristic model which utilises a genetic algorithm (GA) framework to solve the OMPS problem. The GA-based model was applied to the Newman1 and Zuck Small mining instances, which are publicly available from the online MineLib database. The NPVs for the OMPS plan generated using the GA-based model for the two case studies were compared to the best-known published MineLib solutions obtained using the TopoSort heuristic model at the time of this study. For the Newman1 instance the equivalent annual NPVs were approximately US$6.6 million for the GA-based solution and US$5.1 million for the TopoSort solution. For the Zuck Small mining instance, the equivalent annual NPVs were approximately US$99.8 million for the GA-based solution and US$102.5 mil for the TopoSort solution. These results show that the GA-based model produced comparable solutions to some of the best-known solutions, thus, indicating strong potential application of GA-based models to solve OMPS problems.

Sep 1, 2021

By Jack Levin

Dr Laurence AlIison Bushel, a former President of the Chemical, Metallurgical and Mining Society of South Africa, now The South African Institute of Mining and Metallurgy, was born in Queenstown on 20th June, 1910, and died in Johannesburg on 4th November, 1991. There were three distinct periods in the career of Laurie Bushel, each enlivened by some special interests or achievements.

Jan 1, 1991

By H. Ramazi, A. Amini

"This article is devoted to the introduction of a new technique of electrical resistivity data processing called residual resistivity (RR). We define RR as measured resistivity minus background resistivity. To determine the background resistivity, the data acquired from electrical resistivity measurements along a given survey line is evaluated, and then an equation is fitted to the data corresponding to a chosen measurement station as a function of current electrode spacing (or array length). The RR technique was applied to several synthetic models to compare the conventional resistivity inversion of each model with its RR-based inversion. A case study was carried out in a karstic area in Zarrinabad, Lorestan Province, western Iran, to detect the location and geometry of probable cavities by conventional resistivity inversion and RR-based inversion. The results showed that the anomalous zones are better highlighted in the RR-based inversion images in comparison with the conventional inversion images. In some cases, anomalies detected by the RR-based images were hidden in the conventional method. IntroductionThe geoelectrical resistivity method has been widely used since the early 20th century, and plays an important role in several fields such as groundwater and subsurface mineral exploration, geotechnical and environmental investigations, and archeological studies (Bayrak and Senel, 2012; Candansayar and Basokur, 2001; Fehdi et al., 2011; Hee et al., 2010; Osella et al., 2003; Wilkinson et al., 2010). The goal of geoelectrical resistivity surveys is to determine the distribution of subsurface resistivity by measuring the current-potential difference on the ground surface (Aizebeokhai et al., 2010). In the electrical resistivity method, an electrical current is injected into the ground by two electrodes, called current electrodes (AB), and the potential difference is measured between another pair of electrodes, the potential electrodes (MN). Several methods of interpretation are available for application to electrical resistivity data, the simplest being the graphical interpretation of the apparent electrical resistivity pseudo-sections along each survey line. A second method, electrical resistivity inversion, has been developed to create relatively accurate two- and threedimensional computational resistivity models of subsurface sections (Loke and Barker, 1996; Niwas and Mehrotra, 1997; Nordiana et al., 2014; Oldenburg and Li, 1994; Papadopoulos et al., 2009; Yilmaz and Narman, 2014). In the inversion method, models of subsurface objectives are mathematically inverted to reach optimal solutions subject to prescribed objective functions, constrains, and convergence criteria. A common problem when using the electrical resistivity inversion method is that the inversion model of an electrical resistivity profile may be non-unique because different inhomogeneities in the investigation media can result in the same electrical response (Smith and Vozzof, 1984)."

Jan 1, 2016

By V. Maseko, C. Musingwini

"When considered collectively, Mineral Resources and Mineral Reserves are arguably a key asset for any mining company. Mineral Reserves are the economically mineable portions of Mineral Resources. They therefore provide a good indication of the economic prospects in the short to medium term and associated non-financial impairments for mining companies, hence a focus on Mineral Reserves. An assessment of modifying factors for converting Mineral Resources to Mineral Reserves revealed that Mineral Reserves were most sensitive to long-term commodity prices, hence the focus on long-term commodity prices. The justification for selecting gold and platinum mines is that they collectively make a significant contribution to South Africa’s earnings from mining.The introduction of the South African Code for the Reporting of Exploration Results, Mineral Resources and Mineral Reserves (SAMREC Code) in 2000 informed the basis for analysing long-term commodity price assumptions for major South African gold and platinum mining companies between 2000 and 2016. The analysis revealed that the least number of non-financial impairments occurred when long-term commodity prices were within ±5% of spot prices. This finding suggests that this range is the ideal range for long-term commodity price assumptions to improve confidence in Mineral Reserve declarations and minimize impairments. Introduction The South African Code for the Reporting of Exploration Results, Mineral Resources and Mineral Reserves (SAMREC Code) defines a Mineral Resource as ‘a concentration or occurrence of solid material of economic interest in or on the Earth’s crust in such form, grade or quality and quantity that there are reasonable prospects for eventual economic extraction’ (SAMREC, 2016, p. 18). Mineral Resources are categorized according to increasing levels of geoscientific confidence or knowledge, from Inferred to Indicated and lastly, Measured categories. The SAMREC Code defines a Mineral Reserve as ‘the economically mineable part of a Measured and/or Indicated Mineral Resource’ (SAMREC, 2016, p. 25). In some of the other reporting codes such as the Australasian Code for Reporting of Exploration Results, Mineral Resources and Ore Reserves (the JORC Code), a Mineral Reserve is synonymous with an Ore Reserve. The conversion of Mineral Resources to Mineral Reserves involves applying modifying factors, which are non-resource considerations. The modifying factors used in the Mineral Reserve estimation process include mining, metallurgical, processing, infrastructure, economic, marketing, legal, environmental, social, and governmental factors. Each of these modifying factors consists of several components which require due consideration in the estimation of Mineral Reserves. Table I shows some of the components typically considered for each of the modifying factors."

Mar 1, 2019

By M. Saghaeian, R. Hejazi, L. Hosseini, M. V. Sheikhzadeh

Blaine number has long been used to evaluate the pelletising ability of iron concentrate in the industry. Much information and practical data are available about the effect of Blaine number on pelletising efficiency of different concentrate types. But not many researchers have focused on the effect of Blaine increasing method on pelletising behaviour of coarse concentrates. In this paper the effect of two different grinding methods (i.e. HPGR and Ball Mill) on physicochemical properties of coarse magnetic concentrate green and fired pellets were investigated. Microstructural studies by Field Emission Scanning Electron Microscope (FESEM) showed that the concentrate for which the Blaine number had been increased through HPGR grinding, has flake-like morphology. In contrast, increasing the Blaine number through ball mill grinding results in more granular particles. Two samples were prepared using HPGR and ball mill. The Blaine number of the HPGR product and ball mill product were 900 cm2.gr-1 and 1200 cm2.gr-1 respectively. The results revealed that pellet properties of this HPGR product are comparable to that of the ball mill product; this is due to the fact that the flake-like morphology leads to enhanced pelletising performance of coarse magnetite concentrates. Keywords: Iron pelletising, Blaine number, HPGR, ball mill, coarse particles

Jan 1, 2020

By H. S. Sichel

"The valuation of diamond ferous deposits depends on (i) the density distribution, (ii) the size distribution of stones and (iii) the selling price structure prevailing at a particular time.In the density distribution the stochastic variable is defined as the Dumber of individual stones found per sample unit irrespective of the stone size. The density distribution is discrete and allows for barren sample units.As diamonds often occur in clusters, a Poisson mixture distribution is derived which is entirely new, as existing discrete distributions cannot represent the stone number frequencies found in nature.For the sizes of diamonds, which are measured by weight, a new compound logarithmic normal distribution is developed.Combination of (i), (H) and (iii) leads to a meaningful appraisal of diamond ferous ground expressed in monetary value per production unit of mining.Finally, confidence limits are calculated which allow for inference from sampling to recovery."

Jan 1, 2014

By D. Almond

Low-grade, complex mineral deposits have resulted in the need for complicated large-throughput processing plants delivering increased productivity, reliability, and utilization, together with reducing operational costs. Complex mineralogy has resulted in complicated process flow sheets designed to recover minerals as efficiently as possible. In addition, the remote location of many minerals-processing plants, continuously rising energy costs, and fierce competition pose significant challenges to the modern mine, compounded by a global scarcity of qualified and experienced operational personnel. Over the last decade the Internet and automation technologies have undergone major advancements. Automation technologies, solutions, and concepts that existed, but were considered risky or unreliable prior to the year 2000, have now gained acceptance and matured. Furthermore, new technologies and different collaboration schemes have appeared, offering innovative solutions to the mining industry to address many of the challenges described. These advancements in reliable remote systems that access technology through the Internet provide significant opportunity to support mining operations, enhance process performance, provide engineering services, and proactively anticipate and execute maintenance services. This paper references a global survey of automation trends in the mining industry and the potential for an intelligent collaborative environment using automation technologies to exploit opportunities in operating the plant of the future, increasing effectiveness, and reducing operational costs. A variety of possibilities are described, including asset management solutions, remote access capabilities, performance monitoring solutions, advanced process control technologies, and the formation of an intelligent collaborative environment. A real example where this technology is used to support the operation and maintenance at a cement plant in Egypt is given to underpin the concepts described in this paper.

Jan 1, 2012

By M. Onifade, O. S. Otuogbai, A. F. Mulaba-Bafubiandi, O. D. Eniowo, H. Grobler

Artisanal and small-scale miners in Nigeria struggle to attract formal financing to upgrade their operations to a more sustainable form of small-scale mining operation. Literature shows that for an investment to attract formal sources of financing; the business must be considered creditworthy by potential lenders. This means that the credit risks associated with the investment must be bearable for the potential lender. This study looks at how artisanal and small-scale miners can attract formal funding, which will help them take the leap from artisanal state to a form of sustainable small-scale mining operation. This study evaluates the creditworthiness of artisanal and small-scale mining operators using key credit risk parameters identified in the literature and through primary investigation. A quantitative study is conducted on a sample of 100 artisanal and small-scale miner establishments in Nigeria to evaluate the effect of these identified credit risk parameters on creditworthiness. It is shown in this study that being a member of a mining cooperative society, which is a form of social collateral, best improves the chances of access to formal financing for miners within the sample group. This underpins the role of social collateral, in both the formal and informal economy, and its influence in improving the creditworthiness of a typical artisanal and small-scale miner.

Jul 23, 2025

By S. Lohmeier, D. Gallhofer, B. G. Lottermoser, T. Schirmer

At a time of resource consumption, it is important to study the chemical composition of mining and metallurgical wastes to prevent the dissipative loss of metals and metalloids from the mining value chain. In particular, the recovery of critical elements from wastes is an option to increase the resources of such materials that are economically significant and have an overall supply risk. In this paper we report on the chemical composition, in particular the critical element content, of granulated slag originating from historical smelting activities in the Tsumeb area, Namibia. Laboratory-based inductively coupled plasma–mass spectrometry (ICP-MS) and X-ray fluorescence (XRF) analyses as well as portable X-ray fluorescence (pXRF) demonstrate that the slags are on average enriched in base metals (Cu 0.7 wt%, Pb 2.7 wt%, Zn 4.7 wt%), trace metals and metalloids (Cd approx. 50 mg/kg, Mo approx. 910 mg/kg) as well as critical elements (As approx. 6300 mg/kg, Bi approx. 3 mg/kg, Co approx. 200 mg/kg, Ga approx. 100 mg/kg, In approx. 9 mg/kg, Sb approx. 470 mg/kg). While metals and metalloids such as As, Mo and Pb can be determined reliably using pXRF instruments, the technique has inherent limitations in evaluating the contents of certain critical elements (Ga, Sb). However, there are positive correlations between the As, Mo, and Pb contents determined by pXRF and the Ga and Sb contents obtained through ICP-MS and XRF. Thus, quantitative pXRF analysis for As, Mo, and Pb allows calculation of Ga and Sb abundances in the slags. This work demonstrates that pXRF analysers are a valuable tool to screen smelting slags for their chemical composition and to predict the likely contents of critical elements.

Mar 1, 2021

By A. Haque

The shear behaviour of infilled joints produced from ordinary gypsum plaster (gyprock) and bentonite was investigated in the laboratory under Constant Normal Stiffness (CNS) conditions. Shear tests were performed on saw-tooth profiles having Joint Roughness Coefficients (JRC) of 4.75 and 9.25 under an initial normal stress (sno) of 0.30 to 1.10 MPa, and at a normal stiffness (kn) of 8.5 kN/mm. Test data under the same sno and infill thickness to asperity height ratio (t/a) were analysed for two different sets of JRC. The peak shear stress plotted against the t/a ratio under constant sno revealed an increase in peak shear stress with the increase in JRC, up to a t/a ratio of about unity. The effect of roughness on the peak shear stress was observed to be minimal when the t/a ratio exceeded 1.40. A mathematical model for the prediction of peak shear stress due to the increased infill thickness has been developed based on a hyperbolic stress-strain relationship and energy balance principles. The model predictions are in good agreement with the laboratory observations. Le comportement de cisaillement des joints remplis produits à partir de plâtre ordinaire et de bentonite a été étudié dans le laboratoire sous des conditions de rigidité normales constantes. Des essais de cisaillement ont été réalisés sur des profils en dents de scie ayant des coefficients de rugosité des joints (CRJ) variant de 4,75 à 9,25 sous un effort normal initial (sno) de 0,30 à 1,10 MPa, et une rigidité normale (kn) de 8,5 kN/mm. Le résultat des essais conduits sous la même contrainte et épaisseur de remplissage au rapport aspérité/hauteur (t/a) ont été analysés pour deux ensembles différents de CRJ. La variation de l'effort de cisaillement maximal contre le rapport t/a sous une contrainte normale constante a indiqué une augmentation de l'effort de cisaillement maximal avec l'augmentation du CRJ, jusqu'à un rapport de t/a proche de l'unité. L'effet de la rugosité sur l'effort de cisaillement maximal a été minimal quand le rapport t/a a excédé 1,40. Un modèle mathématique pour la prévision de l'effort de cisaillement maximal dû à l'épaisseur accrue du remplissage des joints a été développé sur la base de la variation entre contraintes hyperboliques et déformation et sur des principes de bilan énergétique. Les prévisions du modèle sont en bon accord avec les observations de laboratoire. Das Scherverhalten in mit gewöhnlichem Gips und Bentonit gefüllten Klüften wurde im Labor unter Bedingungen konstanter Normalsteifheit (CNS) untersucht. Scherversuche wurden durchgefürt für Sägezahnprofile mit Werten des Fugenrauhigkeitskoeffizienten (JRC) von 4.75 und 9.25 unter Normalspannungs-werten (sno) von 0.30 bis 1.10 MPa, und bei Normalsteifheit (kn) von 8.5 kN/mm. Testresultate für gleiche Werte von sno und Verhältnis Fülldicke zu Rauhigkeit (t/a) wurden untersucht für zwei verschiedene Werte von JRC. Die Beziehung zwischen maximaler Schubspannung und und t/a Verhältnis unter konstantem sno zeigte einen Anstieg der maximalen Schubspannung mit zunehmendem JRC, bis zu einem t/a Verhältnis von etwa 1.0. Der Einfluss der Rauhigkeit auf den Maximalwert der Schubspannung war minimal solange das t/a Verhältnis den Wert von 1.40 überstieg. Ein mathematisches Modell wurde entwickelt für die Vorhersage der Schubspannung die von zusätzlicher Fülldicke erwartet werden kann, ausgehend von einer hyperbolischen Spannungs-Dehnung Beziehung und dem Energiegleichgewichts-prinzip. Die Modellvorhersagen zeigten gute Uebereinstimmung mit den Laborbeobachtungen.

Jan 1, 2003

By J. Githiria, D. Wachira

The conventional truck and shovel haulage system has become expensive to operate in most mines due to current strict environmental conditions, increase in depth and size of open-pit mines, increase in labour costs, and fuel costs. These factors have motivated the search for alternative material haulage options in open-pit mines. In-pit crushing and conveying (IPCC) system has been regarded as a plausible alternative in material haulage systems. However, usage of IPCC has been limited to a few mines due to limited knowledge of IPCC performance, and other technical factors of the system. This paper investigates, and evaluates the productivity performance of four types of IPCC systems (fixed, semi-fixed, semi-mobile, and fully mobile IPCCs) using mine productivity index (MPi). Using a model developed by MATLAB, the MPi for the four systems is computed using input variables such as availability, utilisation, performance and number of trucks and shovels in a limestone quarry. The mine productivity index for fixed, semi-fixed, semi-mobile, and fully mobile IPCC is obtained as 67.13%, 69.02%, 70.52%, and 71.52% respectively. In conclusion, the fully mobile in-pit crushing and conveying system is the most appropriate IPCC in the quarry, due to its better productivity performance compared to the other three IPCC systems and the truck and shovel system currently in use.

Sep 1, 2021

By Antoine F. Mulaba

Introduction Copper and cobalt oxide mineral deposits formed by the atmospheric weathering of near surface sulphide deposits are commonplace in the Democratic Republic of Congo. The most common route for the extraction of these metals is a hydrometallurgical one in which the base metal oxides are dissolved in sulphuric acid and then concentrated further by solvent extraction. However, as many of these deposits are relatively low grade (i.e. 0.5-1.8%Co and 2-4% Cu) and can also contain large amounts of acid consuming gangue minerals (i.e. dolomitic, micaeous, and/or siliceous), the hydrometallurgical route becomes uneconomic due to the excessive acid leaching costs. Some means of pre-concentration ahead of leaching is then desirable to improve the process economics. Apart from the small scale mining (Pan. Afr. News Agency, 2000) handpicking, although not easy, oxide concentration by flotation has been suggested. For the flotation process, the two most common approaches are controlled potential sulphidisation (CPS) and the fatty acid flotation method. The preferred method is dictated by the nature of the mineral makeup of the gangue. Being secondary deposits, the gangue associated with these ores is often complex and can play a significant role in the overall flotation efficiency. Laboratory flotation experience gained from the testing of a number of different ores of this type has revealed that it is not possible to prescribe a set method for the flotation of various ore types. Each ore needs to be analysed very carefully before and after laboratory flotation on an individual basis in order to arrive at an acceptable flotation technique Laboratory flotation testwork was carried out on three different samples from the DRC in attempts to isolate some of the more important variables affecting the flotation of copper and cobalt oxide minerals from these weathered deposits. This paper describes some early results achieved and experiences gained with these different ores ahead of a more detailed flotation test program which will follow in the near future on receipt of a significant quantity of a more representative sample. Controlled Potential Sulphidisation (CPS) was used in an attempt to achieve acceptable recoveries of both copper and cobalt.

Jan 1, 2005

By P. Malíková, I. Osičková, R. Sousedíková, P. Rys, J. Dvořáček, S. Heviánková

Each mining project goes through the same life-cycle, from prospecting and exploration to closure and post-closure periods. This prompts the question whether the closure of a mine constitutes the end of its life-cycle or whether the decommissioned mine can be employed for some other purpose. Best-practice references indicate that there are many viable options. In our opinion, the production of service water is one such option. Laboratory research was carried out on the water from a flooded underground coal mine in Ostrava- Karviná coal district, Czech Republic, concerning the production of service water from pumped minewater. The research proved the practical feasibility of service or process water production. Given the effect of global climate change with regard to water resources, good prospects for this additional resource can be assumed since the water has to be pumped in any case for safety reasons.

Oct 1, 2022

By C. Musingwini

The South African mining industry continues to be a major source of employment at a time when at least 25 per cent of the working age population is unemployed. At the same time the industry faces a skills shortage in many of the disciplines necessary for its future health. The University of the Witwatersrand, University of Pretoria, University of Johannesburg, and University of South Africa have historically produced mining graduates for the South African industry, with any shortfall being met by the recruitment of overseas graduates. More recently the global shortage of engineers and other mining industry professionals has seen a reversal of this trend and a very significant emigration of well-educated and highly skilled personnel. The traditional career path for mining graduates is in production and mine management. However, there is the parallel and possibly more pressing need for specialized skills in such fields as ventilation, rock engineering, mine planning, mineral resource evaluation, and mineral asset valuation. It is in these essential areas that chronic shortages continue to hamper the development of the industry and may well frustrate its ambitions to be safe, healthy, and profitable into the future. The permeability of skills across sectorial boundaries within the mining industry requires that skills shortages in the platinum sector are not looked at in isolation, but within the context of the entire industry. This paper reviews the efforts being made by the universities at both undergraduate and postgraduate levels to meet the needs of the South African mining industry, in terms of the required numbers and the range of specialized skills.

Jan 1, 2012

By M. Hopf

Numerous developments and improvements have been made to tap-hole designs. On the other hand, there are very specific designs in operation that have endured for many years without any modification. Nobody likes design changes because of risk - the risk of atypical wear, potential hazards, and costly repairs entailing enormous production losses. So the philosophy ‘never touch a running system’ is maintained, because among other things there is no efficient working monitoring technology for tap-holes. In the past few years a couple of new technical solutions have been investigated and developed. Not all theoretical solutions are possible in practice. However, metallurgists are inventive, and the last word regarding efficient working tap-hole monitoring technologies has not yet been spoken.

Jan 1, 2014

By M. Rossouw

The paper sets out the strategic importance of South Africa?s mining and minerals sector to the national economy. It relates how inexorable and accelerating urbanization and industrialization in emerging markets, especially in China and India, will translate into sustained demand for the minerals that South and southern Africa have in abundance. It warns that while countries buying raw materials from South Africa use these inputs as the basis on which to build value-added, employment-creating industries, South Africa is failing to exploit the economic benefits inherent in its mineral wealth, exacerbating its shortage of skills.

Jan 1, 2011

By S-J. Park

When evaluating mining investment opportunities, one should consider the risks associated with mineral exploration and development. These are commonly classified as technical, economic, and political risks, and are accounted for in the investment decision by changing the discount rate. Thus, a company may use different discount rates associated with varying risks in order to compensate for the variability of success. The discount rate has a tremendous effect on the economic evaluation of mineral projects. Even when all other factors used as inputs for calculating the NPV (net present value) are equal, the project under consideration may be accepted or rejected depending upon the discount rate. Determining a realistic discount rate for a given project is therefore the most difficult and important aspect of cash flow analysis. It should be determined with the consideration of proper technical, economic, and political conditions surrounding the specific project undergoing economic evaluation. One key problem for determining the appropriate discount rate is that it typically depends more on subjective perception of the degree of risk or other experience factors than on a systematic approach. Thus, this study aims to identify, analyse, and document the type, role, and impact of risk factors influencing the determination of discount rates, and then to determine discount rate by using the aforementioned factors.

Jan 1, 2011