Explicit valuation of investment projects and real options under commodity price uncertainty

The valuation of investment projects and decisions depending on the price of a specific commodity is an important branch of financial economics. Many models for valuing investment projects and real options assume that the commodity price follows a geometric Brownian motion and that the cash flow rate varies linearly with the commodity price. This article presents explicit formulas for project values as functions of commodity price and time for three distinct types of cash flow rates and formulas for project values as functions of commodity price and reserve. It also includes formulas for options to expand or contract an investment project. The derived explicit formulas enable significantly faster and more accurate valuation of projects and options than previously used numerical methods. Additionally, they provide new theoretical insights by demonstrating how project value is influenced by model parameters and identifying conditions under which the resulting value is close to the traditional net present value.