Luiz Eduardo Teixeira Brandão

Using Binomial Decision Trees to Solve Real-Option Valuation Problems

Traditional decision analysis methods can provide an intuitive approach to valuing projects with managerial flexibility or real options. The discrete-time approach to real-option valuation has typically been implemented in the finance literature using a binomial lattice framework. Instead, we use a binomial decision tree with risk-neutral probabilities to approximate the uncertainty associated with the changes in the value of a project over time. Both methods are based on the same principles, but we use dynamic programming to solve the binomial decision tree, thereby providing a computationally intensive but simpler and more intuitive solution. This approach also provides greater flexibility in the modeling of problems, including the ability to include multiple underlying uncertainties and concurrent options with complex payoff characteristics.

The option value of government guarantees in infrastructure projects

The participation of private capital in public infrastructure investment projects has been sought by many governments who perceive this as a way to overcome budgetary constraints and foster economic growth. For some types of projects, this investment may require government participation in the form of project guarantees in order to reduce the risk to the private investor, and as a consequence, the government assumes a contingent liability which may have significant future budgetary impacts. We present a minimum traffic guarantee (MTG) real options model that differs from most of the literature in the field by using market data to determine stochastic project parameters. This model can be used to assess the value of these guarantees, allows the government to analyse the cost–benefit of each level of support, and proposes an alternative to limit the exposure of the government while still maintaining the benefits to the private investor. We apply this model to the projected 1000 mile long BR‐163 toll road that will link the Brazilian Midwest to the Amazon River. We conclude that the use of public–private partnerships (PPP) with guarantees and caps on total government outlays can be modelled effectively using option pricing methods and can be a solution to attract private investment to high risk public infrastructure projects.

Valuing the switching flexibility of the ethanol-gas flex fuel car

Renewable energy sources are becoming more important as the world’s supply of fossil fuels decrease and also due to environmental concerns. Since 2003, when the ethanol-gasoline flex fuel car became commercially available in Brazil, the growth of this market has been significant, to the point where currently more than 50% of the fuel consumption of cars in Brazil is from renewable biofuels (ethanol). This has been made possible due to the success of the flex fuel car, which can run on ethanol, gasoline, or any mix of these in the same fuel tank, and which is sold at a premium over the non-flex models.Flex fuel cars, on the other hand, provide the owner with the flexibility to choose fuels at each refueling stop. Given the uncertainty on future prices of ethanol and gas, this option adds value to the owner since he can always opt for the cheaper fuel whenever he fills up his car. We use the Real Options method to analyze the value of the flex fuel option assuming both a Geometric Brownian Motion and Mean Reverting diffusion processes for the prices of gasoline and ethanol and compare the results arising from both methods. We conclude that the flex option value is significant using either method and twice as high as flex premium charged by the car manufacturers, which helps explain the success that this type of automobiles have gained in Brazil since 2003. Our results also indicate that consumers should be willing to purchase flex fuel cars even if manufacturers increase the flex premium.

Volatility estimation for stochastic project value models

One of the key parameters in modeling capital budgeting decisions for investments with embedded options is the project volatility. Most often, however, there is no market or historical data available to provide an accurate estimate for this parameter. A common approach to estimating the project volatility in such instances is to use a Monte Carlo simulation where one or more sources of uncertainty are consolidated into a single stochastic process for the project cash flows, from which the volatility parameter can be determined. Nonetheless, the simulation estimation method originally suggested for this purpose systematically overstates the project volatility, which can result in incorrect option values and non-optimal investment decisions. Examples that illustrate this issue numerically have appeared in several recent papers, along with revised estimation methods that address this problem. In this article, we extend that work by showing analytically the source of the overestimation bias and the adjustment necessary to remove it. We then generalize this development for the cases of levered cash flows and non-constant volatility. In each case, we use an example problem to show how a revised estimation methodology can be applied.

Government Supports in Public-Private Partnership Contracts: Metro Line 4 of the Sao Paulo Subway System

In November 2005, the state government of Sao Paulo, Brazil, announced the intention to bid a 30-year contract to build, operate, and explore passenger services for the Metro Line 4 of the Sao Paulo Metropolitan Subway System. Given the high risk of the project, to attract private investors the bid documents stipulated that the government would offer risk-mitigation mechanisms such as subsidy payments and a minimum demand guarantee (MDG). Because an MDG has option-like characteristics, the real-options approach is used to analyze the effect of these incentives on the value and the risk of the Metro Line 4 concession project, and their cost and risk to the government. The results indicate that the incentives proposed are effective in reducing the risk, and increase the net value of the project by 36% at a cost to the government of 5% of the total value of the project. Additionally, it is shown that for a given cost, the most effective risk-reduction mechanisms are the ones that include a higher portion of minimum demand guarantees relative to the subsidy payment. The approach developed can assist transportation authorities in designing optimal incentive mechanisms.

Risco privado em infra-estrutura pública: uma análise quantitativa de risco como ferramenta de modelagem de contratos

Public private partnerships (PPP) are contractual arrangements in which the government assumes future obligations by providing project guarantees. They are considered a way of increasing government efficiency through a more efficient allocation of risks and incentives. On the other hand, the assessment and determination the optimal level of these guarantees is usually subjective, exposing the government to potentially high future liabilities. This article proposes a quantitative model for the evaluation of government guarantees in PPP projects under the real options approach, and applies this model to a toll highway concession with a minimum revenue guarantee. It studies the impact of different guarantee levels on the value and the risk of the project, as well as the expected level of future cash payments to be made by the government in each case. It concludes that it is possible for the government to determine the optimal level of guarantees as a function of the desired level of risk reduction, and that the design and modeling of PPP contracts can benefit from the use of quantitative modeling tools such as the one presented here.

Avaliação econômica de projetos de transporte: melhores práticas e recomendações para o Brasil

This article presents the results of an extensive documental research and literature review of worldwide procedures for economic project appraisal, and identifies best practices and state-of-the-art techniques in this area, as well as the criteria adopted in Brazil for this purpose. In the light of international benchmarks, it makes recommendations for improvements in the use of these methods in Brazil regarding the appraisal of safety measures, time savings benefits and social development that result from transportation-related infrastructure projects.

The value of switching inputs in a biodiesel production plant

There has been a growing concern in recent years about the quality of the environment and dependence on fossil fuels to supply the worlds energy needs, which has created an interest in the development of renewable and less polluting energy sources. One of these alternatives is the biodiesel fuel, which has many advantages over the fossil based diesel, or petro diesel. In this paper we use the real options approach to determine the value of the managerial flexibility embedded in a biodiesel plant that has the option to switch inputs among two different grain commodities. Our results indicate that the option to choose inputs has significant value if we assume that future prices follow stochastic processes such as Geometric Brownian Motion and Mean Reversion Models, and can be sufficient to recommend the use of input commodities that would not be optimal under traditional valuation methods. We also show that the choice of model and parameters has a significant impact on the valuation of this class of projects.

Flexibility and uncertainty in agribusiness projects: investing in a cogeneration plant

La generacion de energia de la biomasa se ha convertido en una fuente creciente de interes en vista de la creciente preocupacion sobre el posible agotamiento de los combustibles fosiles en todo el mundo. En este articulo nos fijamos en una planta productora de azucar y etanol en Brasil, que tiene tan bien una posibilidad de expansion como una opcion de agregar una unidad de cogeneracion que le permita la venta de energia excedente generada por la quema del bagazo de cana de azucar, mientras que la segunda opcion es dependiente de la primera. Fueron modelados los precios del azucar, etanol y electricidad, como procesos de reversion a la media geometrica y fue aplicado el enfoque de opciones reales para cuantificar esta flexibilidad en la gestion, ya que estas dos opciones tienen diferentes activos subyacentes. La opcion de expandir la produccion es una funcion del valor esperado de los precios de futuros de azucar y etanol, mientras que la opcion de invertir en una planta de cogeneracion dependera del precio futuro de la electricidad. Ambas decisiones se modelan como opciones americanas compuestas sobre sus activos subyacentes. El modelo se resuelve utilizando un arbol binomial recombinante para reversion sin censura a la media propuesta por Bastian-Pinto, Brandao y Hahn (2010) utilizando el software DPLTM. Los resultados indican que la flexibilidad de escoger el momento optimo para invertir en las dos opciones de expansion genera un valor significativo: la inversion en la unidad de cogeneracion anade un valor igual a la expansion de la produccion de azucar y etanol, y representan a 44% del VAN proyectado tradicional de

Incentivos governamentais em PPP: uma análise por opções reais

195,900,000. Se concluye que, dado que solo la mitad de las plantas de cana de azucar en Brasil tienen unidades de cogeneracion instaladas, y tambien dada la demanda cada vez mayor de fuentes limpias y renovables de energia, esto puede indicar que existe un potencial importante para inversiones y desarrollo de unidades de cogeneracion de bioelectricidad, asi como de adaptacion de las plantas mas viejas, y que los incentivos que el gobierno ha dado son una contribucion efectiva en este desarrollo.A geracao de energia a partir da biomassa tem se tornado uma fonte crescente de interesse em funcao das crescentes preocupacoes com a possivel exaustao das reservas de combustiveis fosseis mundiais. Neste artigo, analisamos uma planta de producao de acucar e etanol no Brasil, a qual possui tanto uma opcao de expansao quanto uma de agregar uma unidade de cogeracao, a qual permitiria a venda de energia excedente, gerada a partir da queima do bagaco da cana-de-acucar, e a segunda opcao e condicionada pela implementacao da primeira. Modelamos os precos de acucar, etanol e energia eletrica como processos de reversao a media geometrica e aplicamos a abordagem de opcoes reais para quantificar essas flexibilidades gerenciais, considerando que essas duas opcoes possuem diferentes ativos subjacentes. A opcao de expansao de producao e funcao do valor esperado dos precos futuros de acucar e etanol, enquanto a opcao de investir numa planta de cogeracao ira depender dos precos futuros de energia eletrica. Ambas as decisoes sao modeladas como opcoes americanas compostas sobre seus respectivos ativos subjacentes. O modelo e resolvido utilizando uma arvore binomial recombinante nao censurada para reversao a media proposta por Bastian-Pinto, Brandao e Hahn (2010) usando o software DPLTM. Os resultados indicam que a flexibilidade de escolha do momento otimo de investir em ambas as opcoes de expansao gera um valor significativo: o investimento na unidade de cogeracao agrega um valor equivalente ao valor da expansao de producao de acucar e etanol, e representam ate 44% do VPL tradicional de R