As Brennan and Schwartz [Brennan M, Schwartz E. Evaluating natural resource investment. Journal of Business 1985;58:135–57] point out in their pioneering work, the valuation of natural resources projects is particularly difficult due to the high degree of uncertainty in output prices of resources. In general, there are two competing procedures to evaluate risky projects in natural resources developments. One is decision analytic, based on traditional discounted cash flow and stochastic dynamic programming [Fleten SE, Maribu KM, Wangensteen I. Optimal investment strategies in decentralized renewable power generation under uncertainty. Energy 2007;32:803–15; Smith J, McCardle K. Valuing oil properties: integrating option pricing and decision analysis approaches. Operations Research 1998;46(2):198–217; Szklo AS, Carneiro JTG, Machado G. Break-even price for upstream activities in Brazil: evaluation of the opportunity cost of oil production delay in a non-mature sedimentary production region. Energy 2008;33:589–600], and the other is contingent claims analysis, based on the no-arbitrage theory of financial markets [Brennan M, Schwartz E. Evaluating natural resource investment. Journal of Business 1985;58:135–57; Emhjellen M, Alaouze CM. A comparison of discounted cash flow and modern asset pricing methods – project selection and policy implications. Energy Policy 2003;31:1213–20; Laughton D. The management of flexibility in the upstream petroleum industry. The Energy Journal 1998;19:83–114; Paddock L, Siegel D, Smith J. Option valuation of claims on real assets: the case of offshore petroleum leases. Quarterly Journal of Economics 1988;103(3):479–508; Schwartz ES. Valuing long-term commodity assets. Journal of Energy Finance and Development 1998;3(2):85–99; Sezgen O, Goldman CA, Krishnarao P. Option value of electricity demand response. Energy 2007;32:108–19]. In this paper, we use the second approach to develop a new model, and the main contributions are providing a tractable and realistic means of incorporating the option value and optimal timing into the investment decision in natural resources and presenting an example that shows option and timing considerations to be important. We demonstrated the validity of the model using both numerical analysis and real data.
