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This research determines the optimal investment timing using real options valuation to support decision-making for economic sustainability assessment. This paper illustrates an option pricing model using the Black-Scholes model applied to a case project to understand the model performance. Applicability of the project to the model requires two Monte Carlo simulations to satisfy a Markov process and a Wiener process. The position of project developers is not only the seller of products, but it is also the buyer of raw materials. Real options valuation can be influenced by the volatility of cash outflow, as well as the volatility of cash inflow. This study suggests two-color rainbow options valuation to overcome this issue, which is demonstrated for a steel plant project. The asymmetric results of the case study show that cash outflow (put option) influences the value of the steel plant project more than cash inflow (call option) does of which the discussion of the results is referred to a sensitivity analysis. The real options valuation method proposed in this study contributes to the literature on applying the new model, taking into consideration that investors maximize project profitability for economic sustainable development.

The present research work studies the direct synthesis of hydroxyapatite (Ca10(PO4)6(OH)2), via a heat-assisted precipitation technique based on the reaction between Ca2+, phosphate (PO4)3–, and (OH)− ions under highly alkaline conditions. An assessment carried out on the thermodynamics involved in the formation of hydroxyapatite (HAP) via precipitation reactions highlighted the favorability of using a high pH to perform HAP synthesis in terms of ΔG Reaction and element speciation. On the basis of these results, laboratory experiments performing the synthesis of hydroxyapatite at pH 11 using four different chemical reactions and different ripening times suggested that HAP nanocrystals are formed through the route of amorphous calcium phosphate (ACP) toward hydroxyapatite. Our results pointed out that the product obtained was a nonstoichiometric hydroxyapatite with a calcium to phosphorus molar ratio in the range Ca/P = 1.40 to Ca/P = 1.95, with carbonate ions (CO3)2– being present in the HAP crystals obtained under these experimental settings. In addition, XRD characterization suggested that the reagent used to achieve a high pH exerts an influence on the arrangement of HAP, as the reflection of the (300) plane was more prominent when alkali metal hydroxides were used as the source of (OH)− ions. Lastly, SEM imaging confirmed that carrying out the synthesis under highly alkaline conditions consistently yields agglomerated clusters of primary HAP nanoparticles, irrespective of the ripening time or the particular reaction used.