An analytical theory of project investment: a comparison with real option theory

Purpose – The paper seeks to develop an analytical theory of project investment. Design/methodology/approach – The authors derive a partial differential equation that the variable cost of a project should satisfy, determine a proper initial condition through a thought experiment, and solve the equation. Findings – A formula of variable cost as an analytical function of fixed cost, uncertainty of the environment and the duration of a project is obtained. Practical implications – The analytical formula enables systematic comparison of returns of different investment under different market conditions to be made. This refines the insights from real option theory in many ways. Since all production systems need fixed investment to lower variable costs, by providing an analytical theory about the relation among fixed costs, variable costs and uncertainty, this theory contributes a new foundation to investment theory and other different fields. Originality/value – An analytical theory of project investment about the relation among fixed costs, variable costs, uncertainty of the environment and the duration of a project, which is the core concern in most business decisions, does not exist in the current literature.