Evaluating product exchange options in integrated steel mills

There are two basic ways to produce steel on a large scale: using iron ore and coal in blast furnaces or employing ferrous scrap in electric arc furnaces. The first requires a larger initial investment but is more competitive in terms of scale gains. The disadvantage is the need for uninterrupted operation, reducing the flexibility to adjust production. To mitigate this problem, it is common to invest in steel rolling assets, generating the possibility of diversifying production and valuable product exchange options. In this work, employing Monte Carlo simulation, we calculate the value of a product exchange option in a steel mill composed of a blast furnace with a hot roller. The results show that this option can generate a significant increase on the NPV of blast furnace steel making projects, and also reveals the importance of choosing the type of stochastic process for the steel in determining the option’s value.


INTRODUCTION
teel is made up by an alloy of iron and carbon.There are two basic ways of producing it in large scale: the use of raw materials like iron ore and coal, by means of the method known as production in blast furnaces or integrated steel mills; or the use of scrap iron by means of electric steel plants, known as minimills or semi-integrated steel mills.
In the blast furnace production model, coal has the function of both fuel and reducer in the steel manufacturing process.As a fuel, coal allows high temperatures of approximately 1500 degrees Celsius, which are essential for the fusion of the iron ore.Coal also aids in the removal of oxygen from the iron, acting as a reducer, precisely because it allows its association with carbon.Several stages must be carried out until one achieves raw steel in the format of plates or billets.Production in a blast furnace demandsalmost always greater initial investments, but, on the other hand, it is more competitive cost-wise.Another advantage is that, once the structure for the functioning of a blast furnace is defined, the increase in productive capacity through the installation of new furnaces usually occurs at costs proportionally lower to the increase in production.This situation obviously allows for increasing gains in scale.The disadvantage is the need of an almost uninterrupted functioning of the blast furnaces, which decreases the flexibility in the adjustment of the scale of production.
Steel is a commodity with great price volatility.So that one can understand this variation, the price of a ton of hot rolled steel in the American market fluctuated during one interval from, approximately, US$ 250.00 to, approximately, US$ 1.200,00, during the period between January 2000 and September 2009.Not only that, the demand for steel is highly unstable.For this reason, it is possible to classify the steel sector as cyclical, with abrupt variations in the quantities sold between the economic "booms" and the recessions.This variabilityin prices as in the quantities demandedsignificantly affects revenues and, consequently, the economic results of the steel mills.
One widely used strategy in integrated steel mills, with the objective of decreasing the variability in demand and in the steel prices, is the switch of product.There are several different types of steel demanded by different sectors of the economy, and the variations in the prices of these products, although correlated, are not identical along time.To make the most of this flexibility, steel companies typically make investments in rolling assetsthe final step of the steel working process, in which the format of the steel is defined, depending Evaluating product exchange options in integrated steel mills 104 BBR, Braz.Bus.Rev. (Engl.ed., Online) Vitória, v. 10, n. 1, Art. 5, p. 102 -126, jan.-mar. 2013 www.bbronline.com.br on the intended usegenerating the possibility of diversification of production and valuable options of product switch.
The objective of this article is to evaluate the incremental benefit of the options of product switch in the steel industry, more specifically in integrated mills.To this end, a hypothetical case will be used to determine the value of a productive process involving the investment in a blast furnace and a hot rolling mill, simulating, through the Monte Carlo Simulation, that project's value based on these two types of different stochastic processes: Geometric Brownian Motion (GBM) and Regression to the Mean Reversion Movement (MRM).
To facilitate the understanding of the work, it was structured in the following manner: after this (i) introduction, (ii) there will be a review about the real options in project evaluation and, then, (iii) an overview of the steel sector will be presented.Finally, (iv) there will be a case study and (v) general conclusions.

PROJECT ANALYSIS BY THE REAL OPTIONS THEORY
The traditional view of finances on corporate investment is that companies should only invest in projects when the expectation of a return is greater than the minimum hurdle rate of return (opportunity cost of capital).The internal rate of return (IRR) and the net present value (NPV) currently constitute the most widely used criteria in the analysis of investment opportunities.These techniques use expected cash flows from projects and risk adjusted rates.
Among them, the NPV is considered the most robust tool for demonstrating the creation of value for investors, and allowing the prioritization of projects in decisions that involve the choice between multiple investment opportunities.
In situations where there is high uncertainty and significant managerial flexibility, however, it is possible to realize that the traditional evaluation rules are not capable of providing complete answers for the investment decision.It is precisely in this context that it is necessary to seek another type of tool that considers the optimization process of the managerial choices in environments of uncertainty.These tools are the evaluation method of real options.
The real options approach considers the present value of future cash flows generated by real assets (projects), contingent on the exercise of optimizations determined by means of the use of strategic alternatives in the most ample states of nature possible during the life of the real asset.The objective of these optimizationsthe use of strategic optionsis the During the last decades, the evolution of financial models, along with the progress in computer techniques, has increased considerably the use of the real options theory in a wide range of industries with different types of approaches in Brazil and the world.Myers (1977) was the first to use the term real options based on the idea that real assets could be evaluated in an analogous manner to financial options.Tourinho (1979) used the theory in studies applied to natural resource exploration projects.Later, Brennan & Schwartz (1985) developed applications of options of temporary interruption of the operations and abandonment of mining projects.Another relevant contribution was made by Bjerksund & Erken (1990), in which they evaluated temporary interruption options, of abandonment and delay and also the effect of their interactions in the development analysis of an oil field.Along the same lines, Dias & Rocha (1999) developed an investment model under conditions of uncertainty in the exploration and production of oil.
The real options theory also began to be widely applied in the electrical sector.Herbelot (1992) studied strategic options in thermoelectric plants in the USA, with the objective of satisfying the environmental requirements of the Clean Air Act Amendment.Gomes (2002) generated a model of real options to choose the best moment to invest in thermoelectricity in Brazil.Moreira, Rocha and David (2004) evaluated the effects of the renovation of the electric energy sector in the investments in thermoelectricity, based on the real options theory.
The scope of the real options theory also extends into the real estate market.Titman (1985) analyzed the value of delaying real estate investments in urban land in the city of Los Angeles.Quigg (1993) evaluated the prices of land in Seattle (USA) and developed a model on the option to wait to invest.Williams (1991)  alternative of altering the choice of final products.In a similar manner, in cases in which the final products can be produced with the use of different inputs, the management can choose the set of inputs that proves to be the most profitable and pertinent to the scenario that would reveal itself in the future.Among important works developed on product switch options, we can quote those by Bastian-Pinto, Brandão & Hahn (2009).These authors analyzed the product switch option in the Brazilian ethanol industry, more specifically the substitution of the final product between sugar and alcohol, taking also its prices as correlated regression to the mean processes.More recently, Dockendorf & Paxson (2009) analyzed the option of product switch in a fertilizer industry, more specifically the trade of the production output: ammonia and urea.This important managerial flexibilitythe changing of the final productexists in the steel industry and constitutes an important strategy to lessen the great volatility in steel demand and prices.Presently, depending on the intended use, several types of steel can be produced, varying in terms of format, different levels of purity, or also through the intentional adding of chemical elements for the obtainment of desirable characteristics like resistance to corrosion or greater levels of hardness.Among the several uses of steel products, the following can be highlighted: civil construction, automobile and capital goods production, home appliances, packaging and tubes for several uses.This option requires, however, investments in the production plants, more specifically in the rolling units, for the manufacturing of various steel products.No works were found in the literature relating to the valuation of the flexibility of product switch in the steel mill.
It is important to note that the uncertainties present in projects are frequently modeled as a Geometric Brownian Motion (GBM), which assumes a constant growth (drift) rate and a variance that grows linearly in time.Its mathematical formulation can be given by the differential equation: dS = μSdt + σSdz, where μ is the drift of the process and σ it's the volatility parameter.Nonetheless, there may be cases where the uncertainty does not follow a GBM.This is the case when the uncertainty depends on an equilibrium level such as the case of non-financial commodities (Pindyck, 2001, 1999, Brennan & Schwartz, 1985).Specifically in relation to the price of commodities or commodity producing assets, it is a common assumption that these follow a Mean Reverting process -MRM model (Schwartz, 1997, Schwartz & Smith, 2000).In this case, the expected value of the process will revert to a level of balance in the long run, and contrary to the GBM, its variance will be restricted to a limit.
The mathematical formulation of the geometric reversion process know as model 1 by Schwartz (1997) is given by the differential equation: dS =h ( ln(S ) -ln( S )) Sdt + s Sdz , in which η is the velocity of the process regression, S the level of long term balance and σ is the volatility parameter.However, there is no consensus about which stochastic process is more adequate, and as Dixit & Pindyck (1994) suggest, the definition of the process depends as much on statistical as much as theoretical considerations.

OVERVIEW OF THE STEEL SECTOR
Steel is an alloy of iron and carbon that is distinguished from molten iron, basically, for having a lower carbon content and greater malleability (deformation capacity), as a result of the differences in the productive processes used in the manufacturing of the two products.
The beginnings of steel production pre-date the Christian era.There are records that the Egyptians, in 900 B.C., already had knowledge of the techniques for producing steel that were used in the manufacturing of weapons like knifes and swords.However, the wide scale production of steel started only in the 19th century, after the Industrial Revolution, when the technological evolution made possible the construction of larger and more efficient furnaces.
Presently, depending on the intended use, several types of steel can be produced, varying in terms of format, different levels of purity, or also through the intentional adding of chemical elements for the obtainment of desirable characteristics like resistance to corrosion or greater levels of hardness.Such characteristics, added to the abundance of existing raw materials for its production and its relative low cost, confer strong advantages to steel if compared to the competing materials, making this the most important metallic alloy in modern society.
According to research carried out by IBS, currently the consumption of steel accounts for 90% of all metallic alloys used around the world.Among the several uses of steel products, the uses should be highlighted: in civil construction, in automobile and capital goods production, in home appliances, packaging and tubes for several uses.It is estimated that, in Brazil, these segments demand, approximately, 95% of all the steel consumed.
The investments in the steel sector are, however, fraught with uncertainties.The main risk factor in the sector is its cyclical characteristic, which causes great variations in prices and quantities demanded by the market.So that one can understand this variability, the price of a ton of hot rolled steel in the American market fluctuated during one interval from, operational structure in the sector, with a strong participation of fixed costs, causing great volatility in the returns in steel projects, as well as in the stock of companies in this segment.

Productive processes
There are basically two forms of large scale steel production: using as raw materials iron ore and coal in blast furnace mills; or in mini-mills (electric steel plants), using molten scrap iron in electric furnaces.The blast furnace mills are also known as integrated mills, whereas the electric ones are called semi-integrated mills.
In the blast furnaces, coal performs the functions of fuel and reducer in the manufacturing of steel, allowing high temperatures to be reached (above 1000 degrees Celsius), which is essential for the fusion of the ore and helping to remove the oxygen from the iron, allowing its fusion with carbon.In this process, the iron is liquefied, becoming pig iron.After treatments to remove impurities, we arrive at the raw steel, in the shape of plates or billets, which later are transformed into sheets, bars, strips, wires, and in other products, with varied uses.The production process in the blast furnace mills can be summarized in five basic steps: preparation, reduction, refining, casting and rolling.
The great difference in the steel productive processes in the blast and electric furnaces is that, in the second method, there is no reduction phase.For this reason, the mini-mills are also known as semi-integrated mills.The scrap iron is placed directly in the electric furnaces during the refining stage for the production of raw steel that is later rolled and transformed according to the desired use.In the place of scrap, these mills can also use pig iron as a raw material, produced many times in furnaces that operate with charcoal by the so-called "pig iron producers".

Steel Products
The technological evolution that occurred in the steel industry, during the last decades, allows a large versatility in the use of steel nowadays.The current types of steel products are innumerable and vary in terms of composition of the alloys, formats and types of finish.
The sophistication achieved is such that, depending on the level and type of demand, specific and customized products can be developed for clients' needs.For the automotive industry, for example, special steels are produced with high resistance to corrosion, with several different thicknesses adequate to the production of parts and body and with coatings and finishes intentionally prepared for the generation of efficiency in the production of vehicles.
Besides the advantages to the transformation industry, high technology in the steel and iron industry has been generating benefits for end consumers, by providing greater durability and safety to products made of steel.For example, one can quote the high power and ductility of the steel used currently in the production of vehicle chassis.With this type of special material, it is possible to develop in the body of automobiles "intelligent crumple zones" which, in the case of collisions, initially deform more easily to better absorb the impact, later becoming more rigid by means of a transformation in its structure, which provides better protection to the driver and other passengers in the vehicles.Specifically in relation to the composition of the steel alloys, these can vary in terms of purity or by the addition of substances for the obtainment of desirable attributes.The classification of common steel is given to alloys with content lower than 2% of added elements to the iron and carbon.Steels with 2% and 5% of other elements in their composition will be conferred the label of low-alloy, and for those above 5%, high-alloy steel.
Among the unwanted substances that typically are present in the composition of steel, there are sulphur and phosphorus.These elements intervene, negatively, in the physical properties of steel, causing it to have lower resistance and malleability.The addition of magnesium during the refining process, a product that is anti-sulphurating, seeks, among other procedures, to correct this problem, making steel less brittle and more adequate for the machining stage.
Nickel and chrome are examples of substances that are added to steel to obtain desirable properties.With participations in the composition of steel many times higher than 20%, these elements together with iron and carbon create a high-alloy that is known as stainless steel.
This alloy was discovered in England, during the early 20th century, by Harry Brearley, while he researched more resistant metallic alloys for the weapons industry.Among the main characteristics of stainless steel are: its high resistance to corrosion, high temperatures and abrupt variations in temperature; ease of cleaning as a result of its low surface rugosity, conferring it a hygienic appearance; adequate mechanical resistance added to the facility of conformation and also of union with other materials.These qualities are appreciated in the production of several products like: domestic cutlery and utensils, vehicle tailpipes, visual signage plaques, among others.
Additionally to the development of special alloys like stainless steel, another technology has been creating significant improvements in steel products, regarding resistance and corrosion, which is the employment of coatings such as zinc.An evolution in the area of coated steels is a process known as electro-plating, by which means steel is covered in a protective layer of zinc and still suffers a series of thermal treatments that give it greater protection against atmospheric oxidation.The galvanized steel plates present also a good welding quality and better adaptation to painting when compared to plates with pure zinc coating.
As to the format and levels of finishing, there are several possibilities that differ in their adaptation to their intended use.Among the refining and rolling stages, there is the casting phase, in which raw steel (or semi-finished) is produced, which can be manufactured in the shape of plates, blocks or billets.Through the rolling process, the semi-finished steel is reheated again and mechanically pressed, generating flat steels and long steels.
The flat steels are characterized by having a width much greater than its thickness, differentiating it mainly in terms of the thickness of the plates and coils produced.In daily life, there is a great variety of products using flat iron, which can go from the material used in the production of beverage cans to thick plates used in the construction of ships.
The long steels are characterized by having a length that is extremely superior to that of the other dimensions.There are examples of long steel profiles, bars, tubes, bars and machine wire.The use of long steels is diverse, and they can be employed directly in civil construction, or also as a raw material in the production of automobile parts, manufacturing of nails, screws, among others.

CASE STUDY: PRODUCT SWITCH OPTION IN INTEGRATED STEEL MILLS
One important strategic alternative found in the steel mill is the choice of the Technology Change Option, more specifically the Product Change Option.In situations in which the demand or price of the steel products that the company produces changes, the management has the alternative of altering the output of production to mix that can prove to be more profitable.The calculation of the value of this option starts with the simulation of the project cash flow in every possible state of nature and in each period, considering the possibilities of a mix of products and also possible adjustment costs in production.
In this section, using the Monte Carlo Simulation, a Product Switch Option in Integrated Steel Mills will be prices.Initially, a base case will be presented that consists of the valuation of a blast furnace project and a hot rolling mill, both with a production capacity of 2.8 million tons/year of steel, using the discounted cash flow method, with the purpose of determining the static NPV of this project.After that, the above real option will be calculated, using two different types of stochastic processes: GBM and MRM, for the modeling of the prices of the output products.At the end of the section, a comparative analysis will be made of the obtained results, with the purpose of recognizing the potential of the earned value and the possible implications of the adoption of each type of price process tested in the decision making in investment projects in the steel industry.

Base Case
We consider an integrated steel mill project composed of a blast furnace with an annual production capacity of 2.8 million tons of steel, whose investments for the assembly of the plant total an amount of R$ 4,140 million.The capital cost for this type of project is 10.12% a year, in real terms.This is estimated considering the risk free interest rate (r) of 5% in actual terms, the mean beta in the sector of 0.93, obtained from Damodaran (2011), and the market risk premium is estimated based on the difference between the historical average of Ibovespa returns, obtained from BM&FBOVESPA (2011), in actual terms of 10.5% (E(rm)) -referring to the period between 1994 to 2010 -and the fixed income return (r) in Brazil in actual terms.
Based on the CAPM formula, we arrive at the estimated value: At the time of the valuation of the project, the net revenue per ton of steel plate was US$ 500, with the dollar traded at R$ 1.80.The analysis of the historic series of deflated prices for six different types of steel in Brazil obtained from the IBS ( 2009) for the period between January /2000 and April/2009 (Figure 2), shows an average growth rate of 4.67% a year, in actual terms.However, it is considered more appropriate to use a drift of 2.5% in actual terms for the prices of steel products, since structural changes have occurred in the sector after the end of the economic crisis, at the end of 2008 and in 2009.This value of drift used (2.5%) was obtained from a series of steel plates obtained at Bloomberg ( 2009), covering January/1996 to December/2009, with a growth rate (drift) during this period of 2.48% on average, per year.This series was not used for the other parameters, because contemporary series are necessary for the two types of steel (plates and hot coils), in order to determine the specific volatilities and speed of regression to the mean, and the correlation between the returns of the two prices.In all the analysis below, the net revenue S per ton per type of steel will be modeled, considered as the price of this type of steel (in US$/ton).It is supposed that these other production costs and expenditures will be corrected in time only by inflation (0% in actual terms) and even though the blast furnace operates, on average, at 90% of its installed capacity.Therefore, they are considered without growth in the analysis.The initial investment will be depreciated linearly during 20 years and, by simplification, it is considered that the necessary reinvestments for the maintenance of the plant are similar to the depreciation.In this manner, the cash flow in quarterly terms can be calculated by the equation (1): Where: FCXs -Project Cash Flow during the quarter s (in R$ 1,000.00);Considering a capital cost for this type of project of 10% per year, in actual terms, the incremental static NPV of the coiled hot-rolled strips is estimated in R$ 796,830 million.

Product Change Option in Integrated Mills -GBM
The incremental NPV static analysis of the rolling mill undervalues, however, the important product switch alternative, by assuming that during the entire evaluation period the production will be exclusively of coiled hot-rolled strips.It occurs that, during certain periods, as a result of the oscillations in the prices of steel products provoked by momentary variations in supply and demand, the production of steel plates can be an alternative more interesting than the production of coils.The value of the product switch option can then be obtained In which: Assuming that the steel prices follow a GBM, growth drifts were used for the log of S s and * similar to those used in the projection of cash flows of the base case, of: (µσ 2 /2) = 2.5%.As a volatility parameter for the steel plates, σ = 34.32% was used, estimated on logreturns of the price indices of the steel plates of the series presented in Figure 2. As a parameter of volatility for coiled hot-rolled strips, σ = 9.84% was used, also estimated from log-returns of the price indices of uncoated steel plates from the series presented in Figure 2.
Additionally, the two price processes previously mentioned were supposed as correlated, being the parameter ρ = 0.238 estimated from the correlation of log-returns of S s and S * .For the simulations of the correlated processes, the Cholesky decomposition was used, according to which two random variables, both following normal correlated distributions (ZA and ZB), can be simulated together by the equation: Z B = rZ A + (1-r ) Z w , in which ZW is ZA are independent pattern normal distributions.For the modeling of the option, it was also necessary to estimate the risk premiums (πS and πS*), which, subtracted from the drifts (μσ 2 /2), allow the discount of the expanded cash flows using risk free interest rates, r = 5%, in the case in question.The estimation of the risk premium can be made by the method described by Hull (2006, chap. 31) and used in the works of Irwin (2003), Brandão and Saraiva (2007), Blank, Baidya and Dias (2009).The method estimates the premium from the correlation of the returns of the asset and the market returns, of the volatility of the asset returns, of the volatility of the market returns and the market risk premium, as demonstrated in the equation (6): r s p = i,m i p o m (6) Where: p i -process risk premium of asset prices i;  o -process volatility parameter (per year);

Figure 1
Figure1presents a Simplified Production Flow demonstrating the steps described for 2 production models: blast furnace mills (integrated mills) and mini-mills (semi-integrated mills).

Figure 2 -
Figure 2-Index of Deflated Monthly Prices of Steel Products in the Brazilian Market -Jan/2000 to Apr/2009 Source: IBS, prepared by the authors.Among the main production costs is iron ore, whose price on the date of the work is US$ 45 per ton.It is supposed that the quarterly price increases of the ore are equivalent to the estimated drift for the steel prices.The other production costs, except for depreciation (coal, coke, energy, other materials, personnel and maintenance), total US$ 255 per of produced steel and the general expenses (administrative and commercial) reach R$ 200 million in annual terms.It is supposed that these other production costs and expenditures will be

OPT0-
directly by a neutral simulation to the risk of incremental flows obtained by the sale of plates in relation to the sale of strips, and the due discount of these flows by the risk free tax, as demonstrated by equations (3) and (4):n E * [FCXI * ] FCXI * = Max[Cap ´UC ´ (S -S * + OCP * ) ´TC ´ (1 -AI )Ds; 0](4)S s Evaluating product exchange options in integrated steel mills 116 BBR, Braz.Bus.Rev. (Engl.ed., Online) Vitória, v. 10, n. 1, Art. 5, p. 102 -126, jan.-mar.2013 www.bbronline.com.brValue of the Change Option in time 0 (in R$ 1,000.00);E * [×] -Neutral Expectation to Risk in time 0; FCXI * -Incremental Cash Flow of the Sale of Steel Plates in relation to the Sale of Coiled Hot-Rolled Strips during the quarter s (in R$ 1,000.00);Cap -Plant Installed Capacity in tons/year; -Use of the Installed Capacity; Ss -Net Revenue per Ton of Steel Plates during the quarter s (in US$); * s US$); -Net Revenue per Ton of the Coiled Hot-Rolled Strips during the quarter s (in TC -Exchange Rate (R$/US$); US$); OCP * -Incremental Production Costs of the Coiled Hot-Rolled Strips per Ton (in AI -Tax Rate Δs -0.25 To obtain Risk-Neutral Expectation, E * [×] , a Monte Carlo Simulation method was used of the Risk-Neutral GBM of the Net Revenue processes (S) of the Steel Plates and Hot Strips, using @Risk software, through the equation (5): i,m -correlation of the returns of asset i with market; o i -volatility of the returns of asset i; o m -volatility of the market returns; p m -market process risk premium; S m Evaluating product exchange options in integrated steel mills 118 BBR, Braz.Bus.Rev. (Engl.ed., Online) Vitória, v. 10, n. 1, Art. 5, p. 102 -126, jan.-mar.2013 www.bbronline.com.brdescribed above, the risk premiums were estimated in πS = 0.33% and πS* = 0.37%.In possession of the estimated incremental flows, E * [FCXI * ] , s discounted at a risk free rate r = 5% p.a., a value of R$ 760 million was obtained for ProductChange Option, which would increase in 95% the static NPV estimated for the coiled hotrolled strips project, as can be observed in Figure3, referring to the Monte Carlo Simulation.