Numerical approximation of a cash-constrained firm value with investment opportunities

We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Moreover, we give regularity properties of the value function as well as a description of the shape of the control regions. Based on these theoretical results, a numerical deterministic approximation of the related HJB variational inequality is provided. We finally show that this numerical approximation converges to the value function. This allows us to describe the investment and dividend optimal policies.Comment: 30 pages, 10 figure

Estimation du coût total associé à la production d’eau potable : cas d’application de la ville de Québec

Une gamme de coûts probables pour l’eau potable distribuée par la ville de Québec, Canada, est déterminée en sommant les coûts annualisés des investissements nécessaires à la reconstruction à l’état neuf des infrastructures d’eau de la ville (conduites d’aqueduc et d’égout, stations de production d’eau potable et stations de traitement des eaux usées) et les coûts annuels d’opération et d’entretien associés à ces infrastructures, puis en divisant le coût total par la production annuelle moyenne d’eau potable sur le territoire de la ville de Québec (106 Mm3/an). La gamme de coûts est obtenue par 50 000 simulations Monte Carlo, en tenant compte des incertitudes sur le coût des divers éléments composant le coût total de l’eau. De cette façon, on calcule un coût total moyen de 2,85 $/m3 et d’écart-type 0,47$/m3. Globalement, 0,70 $/m3 et 2,15$/m3 sont respectivement liés, en moyenne, aux coûts d’exploitation et aux dépenses d’immobilisation. Une analyse de sensibilité des résultats montre que le taux d’intérêt et le coût de construction des conduites sont les paramètres ayant le plus d’impact sur le coût calculé. Ce coût s’avère d’ailleurs beaucoup plus élevé que le prix moyen chargé pour l’eau au Canada et au Québec, qui était respectivement de 1,00 $/m3 et 0,49$/m3 en 1999, mais s’approche du prix moyen chargé en France pour l’eau potable en 2000 (environ 3,33 $/m3 hors taxes), pays où la facture d’eau inclut l’intégralité des dépenses des services d’eau et d’assainissement. La récupération par les municipalités, sous quelle forme que ce soit, de 2,85$ pour chaque m3 d’eau produit permettrait d’assurer un entretien et un renouvellement adéquats des infrastructures d’eau municipales.Canadians are among the greatest water consumers in the world with a mean commercial and domestic consumption of 444 litres per person per day (L/p/d). As a comparison, the mean urban consumption in France is 210/p/d. Since water sources are abundant and apparently cheap in Canada, most people don’t make any effort to reduce their water consumption. However, even though raw water is a free public good, potable water production and distribution as well as wastewater collection and treatment require important operating and investment costs. Major investments will also be required during the coming years in many Canadian municipalities in order to restore water and sewer pipes and to update or, in some cases, build new treatment plants. Potable water delivered by municipalities thus has a cost, and this cost is estimated for Quebec City, Canada, in this paper.The scientific literature only gives a few assessment examples of the real cost of potable water delivered by municipalities. Some authors present general methodologies to estimate the cost of each cubic meter produced, based on the definition of fixed and variable costs (e.g., CABRERA et al., 2003; MCNEIL and TATE, 1991), but application results for these methodologies cannot be found. In 2001, the American Water Works Association (AWWA) compiled revenue and financial data linked to drinking water for 647 American and 24 Canadian municipalities (AMERICAN WATER WORKS ASSOCIATION, 2001). However, this database does not include sanitation costs (wastewater collection and treatment). In November 2002, PricewaterhouseCoopers determined that the total costs for potable water and wastewater in Montreal were $0.54/m3 in 2000 and would reach$0.83/m3 in 2022 (PRICEWATERHOUSECOOPERS, 2002). But this estimate did not include assets that were already paid, and thus underestimated the real cost of potable water. Since many North American municipal water infrastructures are aging and will need to be replaced and/or rehabilitated soon, it is essential to include the cost of all infrastructure (water pipes and sewer networks, drinking water and wastewater treatment plants) when estimating the cost of water.In the province of Quebec, water services are, in most cases, under the responsibility of the municipalities. Depending on the city, the water services are financed directly from the property tax or from a specific pricing method (flat rate or volume-based).The total cost associated with drinking water is the sum of investment, operation, maintenance and repair costs for potable water production and distribution, as well as for wastewater collection and treatment. The first step for the calculation of this cost was to estimate the construction costs of the equipment needed to perform all of these functions. As a case study, we computed the financial resources required to reconstruct Quebec City’s equipment and networks, as they existed in 2002. This reconstruction cost was annualized according to the life expectancy of each piece of equipment. As a second step, the annualized reconstruction cost was added to the annual operation, maintenance and repair costs. The total annual cost was then divided by the mean annual water production in the Quebec City region, to obtain the total potable water volumetric cost. All costs presented in this paper are in 2002 Canadian dollars, using the seasonally adjusted Statistics Canada Consumer Price Index (CPI). To take into account the uncertainty associated with the parameters used to compute the water cost, normal distributions were assigned to these parameters and the total water cost was assessed from 50,000 Monte Carlo simulations. A variance analysis was also performed to determine the impact of each parameter on the computed cost for water.The case study selected to compute the total water cost is the new city of Quebec, as incorporated on January 1st, 2002. The municipalities of Saint-Augustin and l’Ancienne-Lorette were also taken into consideration in the calculation, since these two cities use Quebec City equipment for potable water supply and wastewater treatment. In 2001, the total population of this region was 508,000 inhabitants and the total drinking water production was estimated at 287,882 m3/day (Table 2). The total length of drinking water pipes in this case study is 2,453 km and the sewer total length is 4,133 km (Table 3). In 2002, there were two wastewater treatment plants and three drinking water treatment plants in the region of this case study; the city plans to entirely renovate one of the drinking water treatment plants and to build one new plant next year. The costs and construction years of Quebec’s stations are presented in Table 4. The statistical distributions of all the parameters used to compute the water cost are summarized in Table 1.The 50,000 Monte Carlo simulations led to a mean total cost of $2.85/m3 for water in Quebec City, with a standard deviation of$0.47/m3. This means that the total cost of water has a 95% chance to lie between $1.91/m3 and$3.80/m3 in Quebec. On average, the investment cost represents $2.15/m3 and the maintenance, operation and repair cost is$0.70/m3. The distribution of the total estimated cost is illustrated in Figure 1. Table 5 summarizes the statistical characteristics obtained for the components of the total water cost.The computed cost is much higher than the average price paid by Canadians and Quebecers for their potable water, which was respectively $1.00/m3 and$0.49/m3 in 1999. However, the calculated cost is close to the average price charged for potable water in France in 2000 (about $4.24/m3 including taxes, which means$3.33/m3 without taxes), a country where all costs related to drinking water and wastewater are included in the water bill. Proper maintenance and renewal of municipal water infrastructures would be ensured if cities were to recover $2.85 for each m3 of water produced, in one way or another. Moreover, it should be noted that water meter installation, especially for industrial and commercial users, would become economically beneficial if the exact water cost were to be charged to consumers

Le cadre de travail et l’épuisement professionnel des intervenants sociaux en Gaspésie

Cet article examine l'influence du cadre de travail sur l'épuisement professionnel d'un échantillon de 95 intervenants sociaux en Gaspésie. L'échelle d'environnement de travail (EET) de Moos et Insel et l'inventaire d'épuisement professionnel de Maslach sont utilisés pour mesurer les deux variables. L'absence de clarté dans la définition du cadre et des attentes de travail a une influence sur la fréquence et l'intensité de l'épuisement émotionnel des personnes en moins bonne santé et vivant en couple ; l'intensité de l'épuisement émotionnel est aussi plus forte pour les intervenants sans formation universitaire et sa fréquence est plus élevée lorsqu'ils font leur intervention en contexte d'autorité et dans un milieu où le nombre d'intervenants est plus élevé. Quant à l'absence de clarté, elle influence surtout la fréquence de l'épuisement émotionnel dans les milieux plus petits et en contexte d'autorité

Are emerging deep eutectic solvents (DES) relevant for lipase-catalyzed lipophilizations?

With the recent interest on green chemistry, the scientists have focused on developing new and more efficiient solvents to carry out enzymatic-catalyzed reactions with emphasis on reduced costs, risks and toxicity while improving biodegradability. Among the new available solvents, the multimolecular-based liquids (such as ionic liquids and eutectic solvents) have been the subject of most recent studies. Currently, and mainly due to its environmental and economic features, DES are arousing much interest and curiosity. Regarding the biotransformations with lipases, the so-called “lipophilization” reactions are of major interest. However, they are complex to implement mainly because it is difficult to find a suitable reaction medium. Thus, this review aimed at providing a presentation of these multimolecular- based solvents with general overview of the recent studies dealing with lipase-catalyzed reactions in DES. In addition, emphasis was placed on their strengths and weaknesses, especially with the perspective to be use as efficient and green medium to implement complex and valuable biotransformation such as lipase-catalyzed lipophilizations. (Résumé d'auteur

Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line

This paper examines the dividend and investment policies of a cash constrained firm that has access to costly external funding. We depart from the literature by allowing the firm to issue collateralized debt to increase its investment in productive assets resulting in a performance sensitive interest rate on debt. We formulate this problem as a bi-dimensional singular control problem and use both a viscosity solution approch and a verification tech- nique to get qualitative properties of the value function. We further solve quasi-explicitly the control problem in two special cases

Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line

This paper examines the dividend and investment policies of a cash constrained firm that has access to costly external funding. We depart from the literature by allowing the firm to issue collateralized debt to increase its investment in productive assets resulting in a performance sensitive interest rate on debt. We formulate this problem as a bi-dimensional singular control problem and use both a viscosity solution approch and a verification tech- nique to get qualitative properties of the value function. We further solve quasi-explicitly the control problem in two special cases